# Damage Calculus 101 – Attack, Defense, and Elemental Effects in TTYD

Following my article on evasion badges and misconceptions about how they stack, here’s an in-depth article explaining the Paper Mario: TTYD damage calculation process and all its subtleties.  Normally I’d cover PM64’s equivalent mechanics at least in passing, but Floogal’s GameFAQs guide on Paper Mario stats and attacks is comprehensive and accurate on that matter already, so I’ll not waste words treading already-paved ground.

That said, here’s a list of stuff that will be (mostly) out of the scope of this investigation, unless I flesh out the post after the fact:

• Details about the base attack power for every move with variable damage (any player moves, stackable move badges, etc.)
• Details about various defensive and elemental-effect states of every enemy (e.g. Buzzies having different defenses when flipped than when upright).
• In general, interactions other than simple damage calculation; e.g. flipping shelled enemies, exploding bomb enemies, etc.

For the special point of FP-damage calculation, there’s not much to be said:

• Poison BINGOs erase half the party’s FP rounded up; this cannot be changed in any way.
• Flower Fuzzies deal a 0 HP-damage hit and 3 FP-damage hit simultaneously if the party has at least 1 FP, or a 3 HP-damage hit alone if they have none.  In either case, the FP lost is a constant 3 (or 2 if blocked), and the HP damage is dealt with like any normal HP-reducing attack.
• Point Swaps do not follow damage calculation rules, simply swapping the stats in question (while abiding by the caps of the respective stats, if necessary).

All that out of the way, let’s get into some basic definitions going forward:

### Technical Specifications & Mumbo-Jumbo

• Attacker – The entity responsible for dealing the damage. For stage hazards, the “attacker” is the stage itself.
• Attack – The move, action, stage effect, etc. responsible for dealing the damage.  Has its own base attack power (“ATK”), as well as a number of “properties” determining what parts of the damage calculation process apply.  Of note, each Attack has three properties determining how their ATK can be changed independent of the target’s defenses — “badge-mutability”, “status-mutability”, and “chargeability”.  Most attacks have all of these properties or none; of particular note, Yoshi’s Mini-Egg is not “chargeable”, but does have the other two properties.  Additionally, what are generally thought of as single moves may consist of multiple attacks with different properties; e.g. Tornado Jump / Gulp / Super Hammer’s initial hit (which is susceptible to changing ATK), and successive hit(s) (which are not).
• Element – The class of attack being used, which determines which of the target’s set of defensive parameters (Defenses / Elemental Effects) to use.  The different elemental types are Neutral (“non-elemental” / “null-element”), Fire, Ice, Explosion, and Electric.
• Defender / Target – The entity taking the damage.
• Defense – The base defensive power (“DEF”) used to reduce damage dealt; the defender has a separate Defense value for each Element.
• Elemental Effect – A special effect the defender has for each Element that applies at the end of the damage calculation process.  The elemental effects that can change the output damage are Elemental Weakness, Elemental Immunity, Elemental Healing, and “Iron Cleft Achilles’ Heel” (immunity to all attacks except Gulp); most of the time there is no such special effect for a given attack element and defender.

The properties of any Attack, as well as any entity’s Defense powers and Elemental Effects may change in any number of ways based on their state outside of the damage calculation process; some of the more salient ways will be brought up in the middle of the damage calculation discussion.

Now, let’s get into the meat of things!

### Step 1: Sanity Checks & Elemental Transmutations

A few basic checks happen before any damage calculation occurs:

• If the Attack has the “ignite” property and the Defender has the Burn status, the attack is treated as Fire-elemental for the rest of the process on that particular target, regardless of what its element would have been otherwise.  Unlike the rest of the damage calculation process, I confess I am not aware of any attacks (player or enemy) that work this way, so I’d be curious to know if any readers can help out!
• If the Defender is immune to all attacks (e.g. Doopliss before discovering his name, or Shadow Queen after Phase 1), 0 damage is dealt and calculation stops.
• If the Attacker has any All or Nothing badges equipped, the Attack is “badge-mutable”, and the Attacker missed the Action Command for the attack, 0 damage is dealt and calculation stops.

### Step 2: ATK Calculation

That out of the way, the attack power is calculated first in the following procedure:

• Start with the Attack’s base ATK.  This can be calculated in a number of ways; it can be constant (most enemy attacks and items), influenced by the player’s Action Commands, equipped badges, and/or partner/equipment ranks, etc.  Of note, Hooktail’s attacks being weakened by Attack FX R is factored in at this stage, as is the calculation for Poison Shroom / Poison BINGO’s half-damage-rounded up.
• If Merlee’s ATK curse activated on this entity’s turn and the Attack is “status-mutable”, increase power by 3.  Note that this does not depend on who the Attacker is, but only whether the Attack’s power can be influenced by statuses!  As such, if Mario sets off a Bulky Bob-omb or Bob-Ulk with a Merlee-boosted Fire-elemental attack, their explosions’ power increases by 3 as well!
• If the Attack is “badge-mutable”:
• Add 1 power per the Attacker’s equipped All or Nothing, Power Plus, and P-Up, D-Down badges.
• If the Attacker’s HP is sufficiently low, add 2 power per Power Rush and 5 power per Mega Rush equipped.  The former requires 5 HP or less to activate on player characters and 1 HP on enemies, and the latter activates only at 1 HP.
• If the Defender has the “weak to Ice Power” property (which is separate from elemental Defenses/Effects), add 1 per Ice Power equipped by the Attacker.
• If the Attack is “chargeable”:
• Factor in (and expend) the Attacker’s Charge status.
• If the Attack is “status-mutable”:
• Factor in the Attacker’s Huge and Attack+ status, if applicable.
• If the Attack is “badge-mutable”:
• Subtract 1 power per the Attacker’s equipped P-Down, D-UpHP Drain, and FP Drain badges.
• If the Attack is “status-mutable”:
• Factor in the Attacker’s Tiny and Attack- status, if applicable.

If the final attack power is negative, set it to 0.

### Step 3: DEF Calculation

If the Defender has the “Elemental Healing” effect for the Attack’s element or the Attack is piercing, this whole step is skipped altogether.

• Start with the Defender’s base elemental DEF for the Attack’s element.  This can change based on the enemy’s state; for instance, flipping shelled enemies generally drops all defenses to 0.  Of particular note, Grodus normally has 1 DEF to all elements, but gains an additional 1 DEF to null-elemental attacks per living Grodus X.
• Add 1 defense power per the Defender’s equipped Defend Plus badges.
• If a successful guard command was performed, add 1 defense power per equipped Damage Dodge.
• If the “Defend” command was used this turn, add 1 defense.
• Factor in the Defender’s Defend+ and Defend- (Soft) status.
• Increase defense to 0 if currently negative.
• If Merlee’s DEF curse activated this turn and the Defender is Mario, add 3 defense.
• If Defender is weak to Attack FX R, decrease defense by 1 per hit previously taken with the sound effect.

The final defense power is again brought to 0 if currently negative, and subtracted from the previously-calculated attack power.

The resulting ATK – DEF value is not yet brought up to 0 if negative.

### Step 4: “Non-Pierceable Defense”, etc.

Further alterations to the previously calculated ATK – DEF damage (or just ATK, for defense-piercing / healing attacks).

• Add 1 damage per P-Up, D-Down worn by the Defender.
• If the current damage is greater than 1:
• If the attack has repeated-hit diminishing returns (e.g. Power Bounce), reduce damage by 1 per previous hit, to a minimum of 1.
• If the attack has successive-hit diminishing returns (e.g. Fire Drive), reduce damage by 1 per previous target hit, to a minimum of 1.
• If a successful guard command was performed, subtract 1.
• If the Attack is Fire-elemental, reduce damage by 1 per Defender’s Ice Power badges equipped.
• Subtract 1 per P-Down, D-Up worn by the Defender.
• Multiply damage by the number of Double Pain badges worn by the Defender + 1.
• If the Defender’s HP is sufficiently low (5 or below for player characters, 1 for enemies), divide the damage by the number of Last Stand badges equipped + 1, rounding up to the nearest integer.

At this point, if the absolute damage dealt is negative, it is brought to 0.

### Step 5: Elemental Effects

The aforementioned elemental effect (if any) for the Attack’s element is applied here:

• Elemental Weakness – Final damage is increased by 1.
• Elemental Immunity – Damage is nullified.
• Elemental Healing – Defender’s HP is increased rather than decreased.
• Iron Cleft Weakness – Only Gulp deals damage; otherwise, damage is nullified.

This covers the entire damage calculation process from beginning to end; hopefully this addresses any misconceptions or ambiguities around the matter!

# (Insert Clever Title) – Exploring & Tweaking PM:TTYD’s Systems Imbalance

As the Glitz Pit Discord debuts its “Glitz Pit Ranking Board”, a place for the masses to evaluate Paper Mario and its sequel’s badges, partners, and Star Powers, I want to expound on my opinions on the matter, continuing off my TTYD badge tier list from earlier this year.

Rather than continuing to list my opinions on various cross-sections of the game’s mechanics individually, I thought I’d come up with a somewhat off-the-cuff series of suggestions of how the various mechanical systems in The Thousand Year Door might be tweaked, retaining the current variety of options, but with a more thoughtful application of systems imbalance (see Extra Credits‘ excellent videos on perfect imbalance and marginal mechanics for why some degree of “imbalance” is not only inevitable but desirable), aiming particularly toward challenge runners.  I’ll approach this for the most part by taking a look at some of the least balanced aspects in the original TTYD mechanics, and making minor adjustments to bring options on all sides to (better) viability.  (As a side note, I might intersperse more in-depth analysis at a later date, but I think the reasoning stated now should be sufficient to get an idea of my thoughts on what in the vanilla game is and is not well-balanced.)

With that out of the way, let’s start off with the big one.

### Imbalance Point 1: “Super-multihit” (3+ hit) attacks

Lots of math to follow in this section in particular.

Ask any seasoned Paper Mario veteran what the most broken (non-Special) move in TTYD is, and the vast majority’ll probably say Power Bounce / Multibonk.  Despite the damage dealt dropping by 1 on each subsequent hit, with sufficient base ATK, you’re raising your damage dealt by 1 per hit for each additional ATK point you add — far more than with any other attacks on a single enemy, Jumps and Hammers alike.  Yoshi’s Stampede takes this to an even more ridiculous extreme, raising your damage dealt by 1 per hit per enemy for each additional ATK point.

Let’s look at various formulas that could be used instead, seeing how they compare in damage, expressed in as a difference from a normal Jump-like attack (2*ATK + N) or as a multiple of ATK, for some specific numbers for ATK and hits:

Method 1a: Fixed Damage (e.g. 8, 8, 8, 8, 8…)

 Jump + N @ 3 ATK @ 5 ATK @ 10 ATK 4 hits +6 +10 +20 6 hits +12 +20 +40 8 hits +18 +30 +60 N * ATK @ 3 ATK @ 5 ATK @ 10 ATK 4 hits 4.00 4.00 4.00 6 hits 6.00 6.00 6.00 8 hits 8.00 8.00 8.00

Obviously this scheme scales way too much with high ATK, so it’s no surprise this wasn’t used for most multi-hit attacks (except Mini-Egg, which I’ll address separately later).

Method 1b: Linear Descending (e.g. 8, 7, 6, 5, 4…)

 Jump + N @ 3 ATK @ 5 ATK @ 10 ATK 4 hits +1 +4 +14 6 hits +3 +6 +25 8 hits +5 +8 +32 N * ATK @ 3 ATK @ 5 ATK @ 10 ATK 4 hits 2.33 2.80 3.40 6 hits 3.00 3.20 4.50 8 hits 3.67 3.60 5.20

Definitely an improvement for ATK up to 5 (which is fairly reasonable, as all supermulti-hit attacks have a base ATK no more than 3), but gets way out of hand if you go all-out on attack power.

Method 1c: Geometric Series (50% rounded up, e.g. 8, 4, 2, 1, 1…)

 Jump + N @ 3 ATK @ 5 ATK @ 10 ATK 4 hits +1 +0 +0 6 hits +3 +2 +2 8 hits +5 +4 +4 N * ATK @ 3 ATK @ 5 ATK @ 10 ATK 4 hits 2.33 2.00 2.00 6 hits 3.00 2.40 2.20 8 hits 3.67 2.80 2.40

The ol’ Pro Mode school of nerfing.  In theory, you could use geometric series to bind the total ATK multiplier to whatever you want, but any multiplier other than 50% would be pretty hard for the player to calculate in advance.  Problem is, a geometric series with a factor of 1/2 results in a sum of exactly 2x (barring rounding / the trailing 1-1-1’s), which makes Power Bounce a fairly pointless upgrade over a standard Jump, especially if your ATK has a lot of factors of 2.

Method 1d: Half, Quarter-Repeating Damage (e.g. 9, 5, 3, 3, 3…)

 Jump + N @ 3 ATK @ 5 ATK @ 10 ATK 4 hits +1 +2 +1 6 hits +3 +6 +7 8 hits +5 +10 +13 N * ATK @ 3 ATK @ 5 ATK @ 10 ATK 4 hits 2.33 2.40 2.10 6 hits 3.00 3.20 2.70 8 hits 3.67 4.00 3.30

Similar to the way SMRPG’s Super Jump works, I believe.  The second hit does half the initial hit’s damage, and subsequent hits do a quarter of the initial hit’s damage, both rounded up.  In theory, this should bound the damage dealt in eight hits to around 3x the base ATK, but having to choose a rounding direction (which I chose up, to not have to make an edge case for low ATK) means that some ATK values have slightly higher multipliers.  Pretty solid overall, but let’s look at one more alternative:

Method 1e: Linear Descending x2 (e.g. 8, 6, 4, 2, 1…)

 Jump + N @ 3 ATK @ 5 ATK @ 10 ATK 4 hits +0 +0 +8 6 hits +2 +2 +11 8 hits +4 +4 +13 N * ATK @ 3 ATK @ 5 ATK @ 10 ATK 4 hits 2.00 2.00 2.80 6 hits 2.67 2.40 3.10 8 hits 3.33 2.80 3.30

Surprisingly (to me, at least), this scheme actually ends up being pretty good, probably the best overall.  You have to get into double digit ATK before you start easily hitting substantially more than 3x your ATK, and it never goes below 2x your ATK for four or more hits (and is equal to 2x at 2-5 ATK).  Either this or the previous scheme would probably be my choice to better balance these sorts of attacks.

### Imbalance Point 2: Jump vs. Hammer attacks

Definitely a subject on which many opinions are held, but I don’t think the situation is that unsalvageable.  In theory, Jump and Hammer are balanced such that a casual player uses Jumps for specific defense-less or aerial enemies, and Hammer for everything else due to its less strict timing and blunt damage.  However, when considering the full palette of options the player has, the ease at which extra ATK power can pave over the slight difference in base power, and the hazards that might be faced, it’s not really a surprise that Jumping is supreme for a variety of uses (particularly in single-target situations), and can be made viable in nearly any situation.

Rather than trying to address the situation by removing or otherwise neuter Jump’s multiple hits leading to multiply-increased damage w/increased ATK, I’d approach balancing them for expert use by letting raw single-target damage remain Jump’s niche by-and-large, while bolstering Hammer’s debilitating status effects, elemental power, and spread damage affinity.

The main problem to be addressed, at any rate, is not the attack power differential, but the supreme targeting advantage Jump has over Hammer.  As a tangent, let me first stress that Ice Power and Spike Shield are not the source of the problem.  Ice Power only affects one family of enemies offensively, Embers, that Hammer could only slowly tackle one at a time, while partner moves like Power Shell or Special Moves are far more effective at tearing through them.  Likewise, Spike Shield only affects a handful of enemies fought after its appearance post-Chapter 4; of those, Koopatrols, Moon Clefts, Frost Piranhas, Dark Bristles, and Spunias are still effectively dealt with by Quake Hammer or Fire Drive, and Spiky Parabuzzies would have taken forever to take down with Hammer Throw (compared to Lip Lock or specials), leaving only Poison Pokeys and possibly Piranha Plants specifically switching to be weaker to Jump than to Hammer.

Rather, the real problem with Hammer’s targeting is that you’re stuck with attacking enemies in order, rather than picking and choosing to dish out exact damage to them, or just taking out troublesome enemies in the back; furthermore, its would-be-decent status moves (particularly Head Rattle) are rendered useless by only targeting the front.

Therefore, I propose reworking the Hammer Throw into a new passive-effect badge, Hammer Bro, which makes all single-target Hammer attacks able to target any enemy.  Furthermore, the multi-target attacks would hit all enemies regardless of position (with Fire Drive having the appearance of Blazehammer from the recent Paper Mario games, and Quake Hammer the appearance of Earth Tremor).

With that major change, let’s look at balancing the individual Jump and Hammer moves to align with their new function:

• Power Jump / Smash – Don’t really need to change.  Decent enough as starter / basic power-increasing badges.
• Multibounce – Increasing the FP (and maybe BP) cost couldn’t hurt, otherwise it’s fine.
• Power Bounce – Granted the nerf to PB mechanics above, pretty much fine; maybe increase the FP cost to 4.
• Sleep, Shrink, Soft Stomp – Pretty much fine; Jump having one debilitating status isn’t unreasonable, and the others play well with its new niche.
• Tornado Jump – Rather than doing fixed damage to all aerial enemies after hitting, change it to have a (perhaps slightly reduced) chance of inflicting Dizzy to all enemies with no damage after the initial hit.  Gives it a niche without stealing Hammer’s thunder. Speaking of…
• Zaphammer (new) – Replacing the Hammer Throw slot, this would be a single-target hammer attack that inflicts Paralysis for 3 turns (see the section below on status effects) for 3 FP; stacking badges adds 2 to the turn count.
• Vital Smash (new) – An upgrade to Piercing Blow, since Quake Hammer and Power Smash cover a lot of the same ground as the vanilla one. This move would be a single-target hammer attack that pierces defense, but can have its attack increased by up to 3, leeching the extra damage from Mario’s HP.  The FP cost could be 4 or 5, and additional badges would increase the extra damage (and HP lost) by 2.
• Ice Smash, Head Rattle – Increase the former’s turn count to 3; otherwise, they’re fine, and made a good deal more useful with the potential ability to choose a target.
• Quake Hammer – Fine as it is; if the damage were better or the FP cost lower it’d easily be too powerful when stacked (for reference, see any of PM64’s Quake badges), and as it stands it’s already a go-to option for a number of enemies.
• Fire Drive – Fine as it is, but could be interesting if stacking it increased the base damage and the burn damage by 1, rather than just the base damage by 2.

One final thing; on the general note of FP cost for stacked move badges, I think the current method of linear FP increase for status moves, exponential for the rest is decently balanced; it’s unfortunate that it makes most unusable after using two (maybe three) badges, but the most obvious alternative of stacking linearly would lead to an FP vs. boss HP arms race for cheaply stackable badges like Power Jump.  (It’s possible that something like Super Paper Mario‘s score progression — 1x, 2x, 4x, 6x, 9x… might be slightly more balanced, but that would be more complex and ultimately not change much in practical use.)

What absolutely should be added in any case is a way to select moves at any power up to the maximum for the number of badges stacked; for example, if wearing three Power Smash badges, one should be able to choose between a +2 ATK / 2 FP, +4 ATK / 4 FP, or +6 ATK / 8 FP, like one already can for Double and Triple Dip.  Would make stacking two move badges a lot more palatable in the general case to a lot of players, I imagine.

These two changes address the majority of ‘unfair’ imbalances in TTYD’s systems, but why not go on and take a look at possible ways to tweak other aspects of the battle system.

### Differentiating Status Effects

One of the lesser-appreciated improvements from Paper Mario to TTYD‘s battle system was how much more varied the status effects became.  The Sleep, Freeze, and Stop statuses, all functionally identical in PM64, are at least somewhat distinct in TTYD.  That being said, there’s definitely room for more distinctions; here are my ideas with how to tweak some statuses to improve their viability or make them a bit more unique.  First off, some common statuses that I wouldn’t change at all, for reference:

• Dizzy – 50% miss rate on attacks.
• Confuse – 50% chance of performing a random action (or doing nothing).
• Sleep – Unable to move or defend, 50% chance of waking up when hit.
• Stop – Unable to move or defend.

As for statuses I’d like to see fleshed out a bit more:

• Allergic – Unable to gain new statuses; fine as is, but needs to be used more!
• Fast – Take 2 moves every turn; ditto.
• Freeze – Unable to move or defend; status ends if hit by fire attacks and does 1 damage upon ending.  This status could stand both to be less debilitating / get more use and to be more distinguished from Sleep and Stop, so I’d additionally like to see it halve damage dealt, similar to Super Smash Bros.
• Burn / Poison – Currently identical, deals 1 damage at the end of each turn.  The functionality’s already there for Poison to deal more than one damage every turn, and it’d be cool to see both do that, particularly in later chapters.
• Paralyze – Would like to see the Slow status reworked as this, making the user skip their offensive and defensive actions on odd turns (similar to “Even Turn” runs).  Could be interesting to try to strategize around Para-locking a single enemy, too.
• Cursed – A variation on / replacement for Counter/Payback; rather than applying only to damaging contact moves, this would deal half the total damage dealt back to the attacker after the attack completes, whether or not it was a direct attack.

Finally, there’s an inherent imbalance between ATK-related and DEF-related statuses; for the former, Huge/Tiny, ATK-Up(/Down, which is unused), and Charge all modify ATK power separately, whereas DEF only has DEF-Up/Down.  This could easily be left as is, but some possible changes that might make the stats more in line would be:

• Remove “Huge” status (at least on the player’s side, where the imbalance is biggest), replacing its effects with ATK-Up.
• Remove DEF-Down status, and add a new pair of statuses that operate separately from DEF-Up (“Hard”/”Soft”).  To make things more interesting, these could modify the damage dealt directly, affecting piercing attacks as well (perhaps with an exception made for Special Attacks), and essentially allowing “negative” DEF.
• Introduce “Hard”/”Soft”, and still make use of ATK-Down and DEF-Down.

### Partner Changes

Having experimented around with a number of various partner strategies over the course of the Glitz Pit Community Challenges, I can really appreciate how well the main partners in TTYD were balanced.  By and large, the main problems lie in the brokenness of super-multihit moves, and the latter two partners having a fairly uninteresting move apiece in exchange for relying on overall higher stats.

Before we get to them, though, let’s address the elephant in the room: I really don’t think Ms. Mowz is all that bad, at least for the role she plays in game — an optional partner whose only real purpose is badge farming.  In my opinion, comparing her combat viability to the other partners is somewhat missing the point.  Nonetheless, she could stand the most work in terms of living up to her potential as a purely “marginal mechanic”-based character.

First of all, let’s go really out on a limb and give her the unique distinction of not having upgrades.  Instead, she has a fixed 20 HP, and four moves from the get-go; they’ll be mostly instruments to fit her ‘rogue’ archetype and personality, somewhat like Duster’s “thief tools” in MOTHER 3.

• Love Slap (Base) – 5 damage piercing attack; not too horrible for a base move if you don’t feel like switching and/or all you need is a front-targeting attack.
• Kiss Thief (2 FP) – Steals an item/badge an enemy is holding, or any badge from their random drop table (with increased chances compared to the vanilla game), not just their held item table.  Ideally you should be able to get any badge you want in well under an hour of farming.
• Quick Exit (3 FP) – A move that guarantees a run away from a standard battle, provided you complete a reasonable Action Command.
• Infatuate (4 FP) – Causes the Confuse status to all enemies; outright stealing this one from Vivian, since I’ve got another idea in its place, and it fits Mowz about as well.

With her out of the way, let’s go over the other partners, which have comparably few changes:

Goombella: Pretty much no changes, perhaps upping Multibonk and Rally Wink’s FP cost slightly.

Koops: Probably the most well-rounded and best-balanced partner in the vanilla game; great spread damage moves, and he can tank individual hits well but has low HP and a severe weakness if you get greedy. No changes really necessary.

Flurrie: Definitely underappreciated by me beforehand, but actually fairly well-balanced.  Only definite change would be making Gale Force’s action command slightly easier to fill, and making it enemies defeated with it yield 0 Star Points, akin to Fright Masks and all similar moves in PM64.

Yoshi: Even with the super-multihit attacks better balanced, Mini-Egg is still a fairly overpowered move, potentially dealing heavy damage and having a ludicrously high chance to inflict Shrink status on a single target.  It should either only hit each enemy once, or do no damage regardless of ATK and target at random.

Vivian: To fit her magic abilities, her Ultra-Rank move could be replaced with a move that inflicts the new “Cursed” status on Mario.

Bobbery: Fairly clearly the weakest of the six main partners in the vanilla game, except at a casual level.  To fit his background as a character, I think it’d be interesting to play up the “strategic” aspect of his moveset and his bulk; here’s a sample of how I could envision that working:

• Bomb (Base) – Same as vanilla; 4/5/6 damage to front.
• Bomb Squad (4 FP) – Increased FP cost, bombs still a fixed 3 damage, but the blast range increases with Super Rank, and a fourth bomb is added for Ultra Rank.
• Bob-ombast (Super, 9 FP) – Does 7/8 damage to all enemies on the field.
• Big Bang / Detonate (Ultra) – “Big Bang” (6 FP) spawns a bomb that does up to 10 damage (unaffected by ATK; can be controlled by an Action Command similar to Sushie’s Squirt) to all characters on the field when set off.  After use, “Detonate” (0 FP) becomes available in its place, and must be used to set off the bomb (damaging him, and Mario if he’s vulnerable, in the process).

A random assortment of balance-y things not mentioned elsewhere.  I’ll leave out badges like Pity Flower that have obvious but uninteresting means of improvement, but here are some of the more particular ideas:

• Get rid of fog, or make ‘blocking’ it remove its imposed miss rate on the player’s attacks.  All other stage effects can be worked around much more easily, and add a bit of unpredictability.  That being said, badges that increase/decrease Star Power gained while making the stage effects more/less likely to activate might be interesting.
• Rather than having an “Ice Power” badge to increase ATK and DEF against fire and protect against Burn, it would be cool to have an “Element Shield” badge (and partner variant) to reduce elemental damage taken by 1, and nullify element-based statuses (Burn, Freeze, and Paralysis).  Alternatively, an EarthBound-style “Ice Power” / “Fire Power” / “Earth Power” trio to counter ice, fire, and electricity respectively could be cool (and would make sense for enemies of their respective type to hold), but in practice Mario and his partners don’t use enough non-fire elemental attacks to make separate badges per element balanced in TTYD.  In a future game with similar mechanics, perhaps?
• Similarly, wrapping up immunity to touching spikes, fire, elemental charge, and whatnot in a single “Hazmat Shield” badge (and partner variant) would be a more succinct way of enabling Jump or other contact attacks to freely target anything, akin to the new “Hammer Bro” badge for Hammer.
• The Charge badge, despite not being all that broken considering other ways ATK can be raised (especially if one of the super-multihit changes were to be implemented), should really cost 2 FP, to minimize its “first-order optimality“.
• Lastly, and perhaps most controversial, I hate how polarizing Quick Change is as an option in TTYD.  A cost of 7 BP is far too much to be generally useful in enemy battles; as tempting as that one quick switch would be, you’re missing out on any number of options with that BP cost if you use it — Heart + Flower Finder, Power Plus + FP Drain, nearly enough for two Flower Savers (P), the difference between Jumpman and Power Plus + Fire Drive to keep your options open, et cetera.  Conversely, it’s undeniably one of the most broken tactics in the game if your aim is to abuse Peril and/or ATK-buffed partners without having to have them face any oncoming enemy attacks.  To bridge the gap between these two polar opposite scenarios, I’d love to see the badge altered to be a comparably reasonable 3-4 BP, but have it cost a few FP to perform a quick switch.  This would make it far easier to slot into any badge setup, while simultaneously making it far more interesting to make sure every switch is optimal / necessary.

This sums up my thoughts on how I’d approach tweaking the TTYD combat systems’ balance to expand the range of a veteran player’s options; perhaps I might try to implement a subset of them into a balance mod of the game in the (let’s say very-distant) future.  In the meantime, hopefully this is a starting inspiration for others to think critically about the balance in the Paper Mario (and other) games, or maybe even to implement in the many PM fan engines in development.

# Placing Pins and Tiering Trinkets: A TTYD Badge Tier List

Truly 2017 was a banner year for Paper Mario challenge runs, with the Glitz Pit Discord server surging in popularity and several players popping into the scene.  Discussion of strategies, loadouts, and mechanics of the Paper Mario series has abounded, but the badges, arguably the series’ combat’s defining trait, have always been a particular focal point.  Some badges are loved by all, some ridiculed by all but a few dedicated apologists, and many fall everywhere in-between.

Since stacking badges is what this blog was built on, I’d like to do something a little different here, and exposit my current thoughts on the matter at length, giving my personal ranking of every badge in Paper Mario: TTYD and some justification as to their placements.

To start, I won’t be considering these badges (the “FX-Esque Tier”) in my tier list:

• The Attack FX badges and W Emblem / L Emblem are merely cosmetic and cost nothing to equip, so they’re obviously a matter of taste (even if W Emblem alone is the clearly supreme stylistic option).
• Seeing as TTYD gives you many options to optimize strategies to minimize or maximize focus on HP, FP, SP, items, etc.;  HP and FP Plus are an invaluable convenience for adjusting your stats as you see fit, without needing to ever level up anything but Badge Points.  However, as they’re functionally equivalent to level-ups in HP or FP at any given time, they’re not really possible to rank alongside the majority of badges with unique effects.
• Timing Tutor is useful for building mastery of Stylish Action Commands for a nominal BP cost, and on the other hand, freely skippable if you are well suited to perform them.  An excellently designed badge for beginners with no use (but no downside, other than slightly clogging Charlieton’s inventory) to experts.
• Double Pain is good for adding extra challenge, and rarely (but occasionally) for manipulating Mario’s HP value.  No major positives, but it’s free BP-wise and is really only meant to be an extra challenge.
• Finally, Slow Go is obviously meant as a joke, nothing more.  Only shame is that it’s not hidden somewhere needlessly cryptic like its predecessor in Paper Mario.

As for the rest of the badges, I initially grouped them roughly into four categories – well above average, above average, below average, and well below average usefulness.  I then tweaked their scores slightly, adding more granularity, and comparing badges with similar niches against each other.  Eventually, I ended up with a fairly balanced seven-tiered setup – Tiers F, E, D, C, B, A, and S.

Coincidentally, the higher and lower tiers ended up being clearly delineated by the middle tier (Tier C).  Most of the ones in that tier are decently generally usable badges with modestly useful effects, whereas ones above it (S/A/B) are much more frequently usable and/or heavily useful, and ones below it (D/E/F) are only usable in special cases (and often less useful even in those cases).

Of note, I generally didn’t consider stacking more badges than are naturally obtainable in the game (assuming only one of each available badge – and no Power Rushes – are bought from Pianta Parlor).

Without further ado, here are the tiers from bottom to top (badges in each tier ordered alphabetically):

### F TIER

Generally badges I’d never dream of using seriously in a battle.

• Bump Attack is really placed this low largely out of spite; it’s undeniably of some use by the time you get it, but that’s really a symptom of going through the Pit leaving you unfortunately overleveled.  Furthermore, it makes a very unsatisfying reward while in the Pit, especially considering the difficulty jump between the floors 61-79 and floors 81-99.  Arguably, First Attack is just as usable anyway for much less BP (and badge setup churn), and is available from the shop about as early as it’d be usable.
• Chill Out is useful for dodging a very few enemies’ First Strikes (basically just Z-Yuxes and maybe Chain Chomps / Moon Clefts), and being in Dazzle’s shop with many useful badges as alternatives doesn’t do it any favors.
• Head Rattle is a big missed opportunity. Confusion is a very fun status, but it only targeting the frontmost grounded enemy limits its use considerably.  Not only are you taking out most of that enemy’s potential weaponization in dealing damage to it, but you’re then unable to use a number of moves afterward (including all Hammer moves save for Hammer Throw) without doing further damage to it.
• HP Drain and HP Drain P are massively nerfed from the former’s Paper Mario incarnation; dropping attack power by 1 in exchange for at most 1 HP restoration per turn is virtually never worth it when there’s so many other ways to mitigate damage.
• Peekaboo is a waste of both BP and Star Pieces.  Experienced players should have enemy HP values memorized and keep track of them, whereas inexperienced players already have access to Goombella’s Tattle for the exact same information.  Knowing Koops’ Shell Shield and Doopliss’s partners’ HP is the only unique benefit it provides, and that is questionably useful at best.
• Pity Flower is not the worst badge in concept, but unless you’re sponging a good deal of low-damage hits on Mario specifically, the 1 FP you’ll regain 30% of the time is not worth the HP you lose.  If the FP restoration was guaranteed, or the amount restored was tied to the damage taken, it could see a bit more use, but otherwise it’s filler for Pre-Hooktail Pit Bonetail setups at best.
• Return Postage is of minimal use for much the same reason, on top of being a somewhat lackluster reward for defeating the Pit.  At least it’s highly salable (not that that is likely to be a concern after a Pit run anyway).
• Simplifier‘s hit to Star Power regeneration far outweighs its use for easier Action Commands in general.  It is useful for scouting in the Pit of 100 Trials as it makes the run-away meter much easier to fill.  It’s also debatably useful for getting an extra bounce or two out of Power Bounce, but rarely does the difference between 8 and 9 hits equal night and day (and if you have good timing you’ll end up capping at the same point on bosses anyway).
• Tornado Jump‘s tornadoes do fixed damage (depending on the number of badges equipped), and doesn’t do enough ancillary damage to aerial enemies (which are rare in the first place) to be worth it over a battle item, or Fiery Jinx, or Earth Tremor, or what-have-you.  It is useful for clearing out Mini-*-Yuxes or Grodus Xes, but that’s about it.

### E TIER

Badges I find occasionally worth considering (or consistently in specific cases, but with relatively small effect).

• All of the P badges (Defend Plus P, Feeling Fine P, Happy Heart P, HP Plus P, P-Down D-Up P) are in this tier for pretty much the same reason; partners are generally tanky enough on the whole that it’s not worth the BP to make them safer. Not really a lot to say beyond that.
• Hammer Throw is outclassed in nearly every situation it could be potentially useful.  Swoopers are just as easily hit with Earth Tremor or Quake Hammer, as well as some partner attacks.  Spiky Parabuzzies have far too much DEF for it to be viable.  For virtually everything else, a standard Jump or Hammer will suffice.  It can theoretically have a niche against airborne Ruff or Ice Puffs, but I’ve yet to be in a situation where there wasn’t some reasonably inexpensive alternative.
• Lucky Start‘s effects are too short-lived, underwhelming and unpredictable to be worth the BP it costs.  It can be used to farm HP/FP by repeatedly running away if you really hate your “A” button (and Sweet Treat).  It’s particularly unusable if planning to use Danger strats, given the chance of getting the HP-Regen status.
• Refund doesn’t yield all that much salvage since it rounds 75% of the item cost down rather than up (as in Paper Mario).  Nonetheless it can be a decent fill-out badge if you have a spare BP and a packed inventory.
• Soft Stomp is reasonably useful (though not 100% reliable) on some very late-game bosses, but certainly not indispensable.

### D TIER

Mostly badges that fairly typically get use, but aren’t all that useful, or are very useful in a very limited set of use cases.

• Charge and Charge P pretty much never see use outside of boss battles, and quickly fall on the massive-overkill side if they are used flippantly, essentially adding 2 damage per hit per charge in the turn their charge is expended for negligible FP (and you’ll have plenty of multi-hit options from early in the game).  Arguably these could be placed in a higher tier on those grounds, but they’re really nearly wholly unnecessary considering the existence of power / Danger badges, Power Punch, and Power Lift.
• Damage Dodge P is generally a bit more useful than the rest of the defensive partner badges, since it’s cheap to equip, available early, and combining it with the Defend command offers a lot of control over partner HP values.  It won’t do any good against some late-game bosses due to piercing attacks, though.
• First Attack isn’t quite as convenient as Spin Attack from Paper Mario, but it isn’t as inconvenient to get or equip as Bump Attack, and its effect is appreciated when backtracking through previous chapters’ areas, especially in completionist playthroughs.
• Hammerman‘s extra point of power comes at the expense of Mario’s generally more versatile and powerful Jump moveset.  Could be more useful depending on your preference of partner strategy and HP/FP consumption.
• Ice Power is completely invaluable against Lava Bubbles, useful against Grodus and Bowser in Chapter 8, and completely pointless otherwise.
• Ice Smash‘s status ailment can be devastating if it works, but the Frozen status doesn’t last too long without two copies, and there aren’t a lot of targets that it can hit and work reliably on that can’t be dealt with more easily in other ways. Clock Out is generally a far better choice for reliability, or Sleepy Stomp / Sheep for turn count.
• Money Money is too expensive and appears too late in the game to be as useful as it should be, but it can be useful for farming extra Pianta badges or recipe ingredients for a completionist playthrough nonetheless.
• Pretty Lucky P can be useful for mitigating partner health loss in the long term, or bolstering their evasion rate in Danger, but isn’t generally as useful as Heart Finder for the former purpose.  Can be helpful or actively harmful if it activates against moves that hit the front and back player-controlled actors in sequence if they’re in front, as Mario will be forced to perform the last defensive action taken (including a miss) even if it would be undesirable.
• Shrink Stomp can be fairly useful on the handful of bosses it works on, and perhaps particularly tough enemies, depending on the player’s preference. However, Mini-Egg has the same chance of working and gives you multiple attempts, so it’s almost always a better option.
• Super Appeal P can help make the most of an unspent or otherwise-unspendable partner turn, but only one copy appears naturally, and by the time you have it, the extra 0.25 SP units restored aren’t of much consequence.
• Unsimplifier is sometimes effective in boosting SP restoration, but makes a handful of moves, as well as Superguarding, a much less viable option due to the increased difficulty of their Action Commands.

### C TIER

Also the middle tier, and now we’re definitely in the realm of generally useful badges.

• Defend Plus is a solid, obvious, but slightly BP-expensive way to mitigate damage. Particularly useful against fast multi-hit attacks like Magnus 2.0’s audience launcher and the like, and particularly useless against some very late-game bosses with mostly piercing attacks.
• Double Dip and Double Dip P are incredibly versatile tools, particularly for efficiently strategizing boss battles. Their FP cost (especially with Triple Dip) is fairly high, but that can be mostly mitigated by using at least one FP restoration item.  Late-game this can remove the need for Charge badges entirely, and earlier in the game it allows setup with Power Punch, Point Swap, Trial Stew, etc. in combination with recipe items to hit pretty much any stat breakdown you want.  Their biggest drawback is being located fairly late in the Pit and in the main story.
• Happy Heart is a decent filler badge for picking up occasional extra health in long battles (for instance, in Pre-Hooktail Pit), particularly if you prioritize heavier-hitting in-battle badges to the Finder badges.  Their effect is negligible in comparison to a Slow Shroom if you can afford the inventory space (and detour to the Deepdown Depot), though.
• P-Down D-Up is the only defensive badge (alongside its partner variant) to work against piercing attacks – including all stage effects and enemy items – which can be a game-changer against a number of enemies if you can afford the loss of attack power (or the badges to offset it).
• Piercing Blow is invaluable for Pre-Hooktail Pit runs against anything highly defensive and immune to fire (particularly Chain Chomps and Moon Clefts), or as a low-FP alternative even if Fire Drive does work.  It is generally overshadowed by Earth Tremor, Quake Hammer, or various item / partner attacks, and is equivalent to or worse than Power Smash for enemies with 2 or less defense.
• Power Jump and Power Smash are the go-to very-early game options for dealing a lot of damage in a single blow, and remain effective for that purpose during the entire game if you have the FP to spare for a double- or triple-stacked version of the move.  They fall behind the upgraded boots’ Jump moves quickly on low-DEF enemies, though.
• Spike Shield makes Spiky Parabuzzies tremendously easier to deal with, as well as allowing you to use Jump’s often superior firepower (and Jumpman) against lower-defense spiky foes.  It also makes Bristles approachable, though Quake Hammer is plenty effective at neutering them on its own.  Plus, there are spiky enemies it’s not terribly effective at dealing with (notably Clefts).
• Super Appeal is nice for quickly regenerating Star Power, particularly early in the game or when stacked.  It’s particularly nice for dealing with Dull Bones audience against Bonetail, as it guarantees a 1.00 SP fill-up in no more than two Mario Appeals (and often one Mario and one partner Appeal).
• Zap Tap completely blocks leeching attacks, and is a good failsafe in Pre-Hooktail Pit, particularly for direct attackers that would be otherwise impossible to kill if you’re inconsistent at Superguarding them.  It also has an edge-case use in allowing you to use contact attacks on enemies with the Electric status (not charged Puffs, though).

### B TIER

Getting into the upper tiers. These badges are generally fairly potent and usable a sizable amount of the time.

• Close Call P is a great, very inexpensive safety net for Danger/Peril partner strats, activating nearly a third of the time (or over half the time with both copies).  It’s not the best way of ensuring their safety, though.
• Damage Dodge is another inexpensive defensive boost if you’re not opting to Superguard everything to oblivion, and a fantastic tool for targeting specific HP amounts with Mario.  Naturally, still it’s of no use against piercing attacks.
• Feeling Fine is far more useful on Mario than his partner, removing the need to worry about nearly all potent status effects (Freeze being the notable exception), and freeing you to go for Superguards on nearly anything.  It’s only available very late in the game, but it’d be most particularly useful on late-game bosses anyway.
• Flower Finder‘s 1-3 guaranteed FP drops per battle are fantastic at maintaining high FP across multiple field battles.
• Heart Finder is useful for the same reason, and is unique (as opposed to Happy Heart / Lucky Start) in being able to restore HP to Mario and his partner at once.  Being able to choose when and whether to pick up each individual drop also means being able to target specific HP values for Mario or specific partners, so you can keep partners in Danger or Peril as desired. Furthermore, it can uniquely (aside from items) bring 0-HP partners back to life in a Peril (or Danger) state.
• Item Hog is useful for the fairly substantial increased chance of held and random items dropping, but perhaps better for the ~5% chance of a Dried Shroom dropping from a battle with no enemy held items, allowing for resuscitating a 0-HP partner to Peril.
• Last Stand P is useful for targeting partner Peril, and more generally for allowing partners an additional attack or two after reaching Danger status.  Unlike Paper Mario‘s Last Stand, it (and the Mario variant) takes effect last in damage calculation and rounds up, so it won’t outright prevent damage unless none would have been taken before it factors in.
• Mega Rush is obviously incredibly potent in dealing damage, but it’s relatively risky to attempt maintaining it through enemy attacking turns.  It’s at its best if you can manipulate Mario’s HP and use it to finish out a boss battle.
• Lucky Day isn’t quite as cost-efficient as Pretty Lucky (and nowhere near as much as Close Call if in Danger), but without farming extra evasion badges it’s still a decent evasion boost.  Where it obviously shines is in Pre-Hooktail Pit runs, substantially lowering the average damage taken on floors 91-99 and against Bonetail.
• Multibounce is useful for grounding multiple winged enemies in a single turn, or dealing modest damage to all enemies in a set for minimal cost (or more than modest, with sufficiently increased attack power).  Also likely the go-to cheese badge for unambitious Danger Mario “strategists”.
• Quake Hammer, despite a none-too-flattering fixed damage and FP cost compared to Paper Mario‘s array of similar badges, is nonetheless especially effective against a set of high-DEF enemies, particularly if they’re flippable and/or immune to fire (Beetles, Bristles, Clefts, Chomps, Koopatrols).  It can still be decently potent in general with sufficiently increased attack power, but there are likely better options.
• Sleepy Stomp is unparalleled for taking a single enemy out of commission for an extended period of time.   It’s available very early in the game, and particularly indispensable for Pre-Hooktail Pit runs.  Typically loses out to Clock Out for general utility later in the game.

### A TIER

These are generally incredibly potent at their best or very solid general choices.

• FP Drain is an incredibly underrated badge.  For a single BP and at the cost of a single point of attack power, it effectively acts as a Flower Saver that works on any of Mario’s attacks that deal damage, even 0- or 1-FP moves, so long as you can foot that extra point in advance.  The lost attack power is very easily recuperated in late-game, given the many cheap attack power-raising options that exist.
• Happy Flower is similar in appeal to Happy Heart, without the potential to screw up HP targeting if you’re planning to employ Danger / Peril strats.  Again, Gradual Syrup blows its inflow out of the water if you can afford to carry one (or two, if you have both Mario and his partner both use one).
• Last Stand is great as a last gasp to survive an additional attack or two, similarly to Last Stand P, though again not nearly as potent as Paper Mario‘s equivalent.
• P-Up D-Down is the cheapest way to get extra attack power without cutting off strategic attacking options (Jump / Hammer moves or intentional missed Action Commands), at the expense of taking an additional point of damage from everything, including piercing attacks.  Naturally, that downside can be mitigated with extra defensive setup, evasion, exploiting enemy AI, or Superguarding, or even be exploited to reach Danger/Peril earlier.
• Power Plus and Power Plus P are the most BP-hungry and blunt way to raise your attacking power, but are nonetheless effective and generally not too expensive to be worth considering.
• Power Rush P is doubtlessly useful, but is really the “poor man’s” Mega Rush P, as keeping partners in Danger is barely easier than keeping them in Peril for substantially lower gain.  The extra damage on top of Mega Rush P can be useful in theory, but is often unnecessary, especially with the existence of non-badge sources of increased attack power.
• Pretty Lucky is a fairly useful badge for filler (particularly with two equipped), or in conjunction with stronger evasion badges.  It often isn’t advantageous in cases where you need to deal damage to direct attackers with counterattacks or Zap Tap, as Sweet Treat should often be sufficient on its own to mitigate the lost health from failed Superguards if your partner Appeals.
• Quick Change‘s primary function is to preserve a partner’s status (be that Peril health, or Charge / other positive status effects) indefinitely by switching to another partner before the enemies’ attacking turns.  Aside from that, there aren’t many compelling use cases for it, and it has a steep BP and Star Piece cost to boot.  It’s not all that necessary for partner Peril strats in Pre-Hooktail runs either, unless you have extra restrictions (such as a speedrun or low-Mario health run).

And finally,

### S TIER

The best of the best; unmatched in utility and/or viability.

• All or Nothing is a cheaper Power Plus with virtually no downside; you lose only the ability to strategically omit Action Commands (or the damage from the last, unsuccessful jump in a Power Bounce).  Obviously it is not a good choice if you’re not solid on Mario’s Action Commands in general, but most of them are fairly straightforward and easy to land, even with Unsimplifiers equipped.  Its only flaw is its only being obtainable terribly late in the game.
• Close Call is a cheap and effective safety net when Mario is in Danger, particularly when stacked in duplicate (~55.1% misses), or in duplicate with the other evasion badges (upward of 70% misses).  Adding Last Stand(s) to the mix can allow near impenetrablility of Mario’s defenses in Danger, for a measly handful of BP.  Both natural copies are available very early in the game, and they can be farmed (albeit not terribly effectively) basically at the start of the game as well, if you want to truly overkill your evasion.
• Fire Drive is nearly always a viable attacking option for non-aerial enemies, and is absolutely indispensable (daresay, the linchpin) in Pre-Hooktail Pit runs.  In addition to doing massive damage early-game, it can inflict the burn status on pretty much anything that isn’t immune to fire attacks, dealing ancillary damage and completely confounding lingering Dark / Elite Wizzerds.  Stacking both copies is virtually never a good idea, by comparison; the boost in attack power is negligible for the whopping 10 FP and 3 extra BP cost.
• Flower Saver is the single most generally useful badge in the game, for my money; it is available incredibly early in the game via Dazzle, and there is virtually no time (especially after obtaining Spin Jump) that bringing Mario’s 2-FP moves to 1-FP is not useful.  The second badge can be useful as well, bringing Quake Hammer and Power Bounce to 1 FP and Fire Drive to a modest 3.  Combined with FP Drain and/or Gradual Syrup(s), nearly all of Mario’s moveset, natural and badge alike, can become virtually free.
• Flower Saver P isn’t quite as mind-blowingly useful as the Mario variant, but it brings down the cost of several key moves (notably Power Shell, and all of Goombella’s and Yoshi’s moves) substantially, especially if worn in duplicate.
• Jumpman‘s extra point of power comes at the cost of his defense-piercing, harder-hitting, and multi-target hammer moveset, but given most Jump moves have at least 2 hits, it raises damage dealt by at least 2 points for a negligible BP cost.  Star Powers and partner attacks can fill the void of multi-target and piercing attacks, and additional power-increasing badges (or Power Jump) fill the more-damaging niche of the Hammer reasonably well.
• Mega Rush P makes Pre-Hooktail Pit runs considerably less daunting (though it is by no means essential).  Using it with Heart Finder works wonders at maintaining partner Peril across multiple field battles, whereas Quick Change often makes it near-impossible to lose the status within a single battle.  In conjunction with Goombella’s Multibonk or most of Yoshi’s attacking moves, it is arguably the most broken badge in the game.
• P-Up D-Down P, in particular if stacked via Elite X-Naut farming, is essentially equivalent to having permanent Danger / Peril partner strats.  Even a single copy paired with Power Plus(es) P turns partners into destructive powerhouses, at a relatively nominal cost to defense for an Ultra-Ranked partner.
• Power Bounce can, as expected, take advantage of Mario’s slightly wider array of attack-power raising options than partners to blast through pretty much any foe.  It’s also (arguably more sportingly) useful for tackling annoying enemies in Pre-Hooktail Runs as soon as possible, often in conjunction (for high-HP enemies) or parallel (for multiple moderate-HP enemies) with Goombella’s Multibonk.
• Power Rush is a cheap and a safe option (compared to Mega Rush) to maintain raised damage output in repetitive field battles, as well as an easier and safer damage boost than Mega Rush to target from initially max HP in a boss battle.  Obviously stacking multiple copies from the Pianta Parlor, and/or using it in conjunction with perma-5 HP Mario, makes it the most boringly broken badge in the game, but it doesn’t deserve all the stigma it gets for that if it’s used creatively.

With that, this is my complete Paper Mario: TTYD badge tier list as it currently stands, in a single image for brevity:

Feel free to discuss your opinions on the matter (and no doubt lambast my disservice to Quick Change such-and-such badge) in the Glitz Pit Discord server or my own personal Discord server, Club Jdaster64; I’m generally around both frequently, and there’s plenty of Paper Mario series discussion to go around.  If you’re interested in this sort of qualitative discussion of Paper Mario mechanics in addition to my usual technical fare, Kappy (organizer of the Glitz Pit and Paper Mario wizard) has a blog for this sort of stuff that you can check out here.

Of course, if you’d like my take specifically on more stuff like this, feel free to shout out suggestions for similar topics in the comments here, or on my Discord server.  Might be worth pooling together some of the top challenge runners’ minds to form a “Paper Mario Back Room” badge tier list in the future, or something; who knows.

# The Trick Is To Not Get Hit – Evasion Badges in TTYD

So luck badges.  Years ago I tried doing research into the likelihood of Close Call, Pretty Lucky, and Lucky Day causing enemies to miss Mario in TTYD, taking thousands of samples for each, and summarized the badges’ effects among a bunch of others in my Badge Hunting + Stacking series.  Then after getting back into TTYD assembly reverse-engineering in the wake of the Palace Skip discovery last year (at that point having 2+ years actual software engineering experience), I found the exact rates of the badges, updated that post, and left it at that.

But for the 4 years since that initial post (and 5+ years since the initial statistical research), I took for granted that given evasion rates for each badge, it would be obvious how those ought to be combined into one evasion rate when stacked or combined.  Subsequent recent experience with a larger community of Paper Mario players has shown that not to be the case, so let’s do a deeper dive, shall we?

Brief note – all of the principles in this post could be applied to the evasion badges in the original Paper Mario as well, except the miss probabilities are a bit different (10/101 for Pretty Lucky, 20/101 for Lucky Day, and 30/101 for Close Call).  And there aren’t multiple copies of each to stack, obviously.

### Calculating Evasion Rate (Independent vs. Disjoint Probability)

The crux of the issue comes down to badges’ evasion chances being independent of one another, and the fact that the math involved with that is un-intuitive compared to just adding disjoint probabilities together.

Illustrated here is a representation of what disjoint treatment of badges would look like, and the independent probabilities they actually have (assuming you have one Pretty Lucky, one Lucky Day, and one Close Call badge on in TTYD):

That’s a lot to take in, so let me elaborate in text form.

If badges represented disjoint probabilities of being missed, then you would just sum their evasion rates to get the total evasion rate; i.e. PL+LD+CC = 10 + 25 + 33% would be 68%, and the odds of getting hit would be 32%.

In actuality, though, evasion is calculated by multiplying the indepedent probabilities of the badge resulting in a hit; i.e. PL+LD+CC = 0.90 * 0.75 * 0.67 = 0.45225 = 45.225% chance of hit, or 54.775% chance of a miss.

This extends to multiple badges of the same type; i.e. each Pretty Lucky multiplies your chance of getting hit by 90%, every Lucky Day by 75%, and every Close Call by 67%; i.e. your total evasion rate is:

1 – (1 – 0.10)PL * (1 – 0.25)LD * (1 – 0.33)CC

### But which of the evasion badges is the best?

(hint: it’s Close Call.)

So that settles the question of how badge evasion is calculated, but how do you compare the effectiveness of each of the three evasion badges, particularly Pretty Lucky and Lucky Day?  You cannot divide the rates by their BP cost to get an idea of “evasion per BP”, since that’d essentially be falling back on the incorrect disjoint-probability model.

Instead, since you already multiply the probabilities of badges together, you need to see what number needs to be multiplied by itself N times to produce the proper hit rate for an N-BP badge.  Thankfully, math has a helpful name for that concept, the radical / Nth root, but we can do one better and use logarithms to convert all the messy multiplication (for multiplying the effects from each of the types of badges), exponentiation (for getting the term for a number of a specific badge), and radicals (for getting the effect per BP) into much nicer addition, multiplication, and division respectively.

So, let’s take and compare the log base 0.5 of each of the badges’ hit probabilities, then (i.e. how many times you would have to multiply 0.5 by itself to get the hit rate).  The choice of 0.5 is admittedly arbitrary, but this way we can compare it to something meaningful; Repel Capes / Dodgy Fog (or enemy Dizziness) cause a 50% chance of evasion.

 Badge Hit Rate log0.5(Hit Rate) Pretty Lucky 0.90 0.152 Lucky Day 0.75 0.415 Close Call 0.67 0.578

This gives us some concrete insight into the badges’ real relative worth; Pretty Lucky is 15.2% of the effect of a Repel Cape, Lucky Day is 41.5%, and Close Call about 57.8%.  But we can do one better, and divide the log-transformed rates by the BP cost to compare the badges’ worth per BP.

 Badge Hit Rate log0.5(Hit Rate) log0.5(Hit Rate) ÷ BP Cost Pretty Lucky 0.90 0.152 0.076 Lucky Day 0.75 0.415 0.059 Close Call 0.67 0.578 0.578

Yikes, no contest now; Pretty Lucky is a good deal better than Lucky Day per BP (7.6% of a Repel Cape per BP vs. 5.9%), and Close Call destroys them both.

### The Power of Math!

Rephrasing the effects of the badges this way means we have another way of representing overall evasion:

1 – (0.5)(0.152 * PL + 0.415 * LD + 0.578 * CC)

While not perhaps easier to calculate this way, it does make one fact perhaps more obvious; that being, there’s no way to get 100% evasion, as no matter how high the exponent gets, nothing will make 0.5N equal 0.

Except, technically that’s not actually true; since all RNG calls for badge evasion happen back-to-back, and Paper Mario: TTYD has a finite number of RNG states, technically it could be possible to wear enough badges that there’s no string of consecutive RNG states that do not result in at least one “miss”.

If using just Close Calls, this is actually possible to achieve at 52 badges; using the formula about 0.5(0.578 * 52) = 0.5(30.0) = about a 1/1,000,000,000 chance, but in fact no successive run of 52 out of the 4,294,967,294 RNG states produces all non-misses.  Not practical in purpose, as a “mere” 17 badges already results in a miss 999 out of 1,000 times, but interesting as a curiosity.

### The Mega-Comparison Chart of Awesomeness

Rather than grab a calculator every time you want to get the exact evasion rate for an arbitrary combination of badges, here’s a helpful chart that compares the evasion rate for various combinations of 1-3 Pretty Luckys, 1 Lucky Day, and 1-3 Close Calls:

You can extrapolate past the end of the chart by imagining more copies of the bars at the top added to the end, bearing in mind that adding another span of the marked length halves the hit rate.  (Of course, as a rule of thumb, if you’re bothering to badge hunt for more than 2 Close Calls, you’re probably going to get missed often enough (70%+) that you don’t really need to care about exactness.)

Hopefully this doesn’t end up being more confusing than the original blurb in the badges article, but I’ve said my piece at this point. Close Call master race!

# ’00s Mario RPGs’ Item Drops: Weights? Rates? Let me Elucidate…

Random enemy item drops have long been a focus of my Mario-RPG stat-gathering and what-not – there’s just something satisfying about getting extra items or missable equipment when it’s not guaranteed, and I always thought it’d be nice to know the odds.

Well, over time, I’ve gotten proficient enough in memory hacking and assembly to be able to interpret the routines and/or RNG calls responsible for item drops in the first three Mario & Luigi and Paper Mario games (since those are the ones that I’m the most experienced with, and whose systems have widely-accessible emulation), and the ways they represent the possible item drops in data form, and then use that data to determine what items to drop and when, vary wildly from game to game.  Hence, I’ll go into detail in how it works for each of these six games (links to the actual drop data will be at the end of the post).

### Paper Mario (64)

This is the Mario RPG I’d been curious about drops for the longest, and somewhat ironically, it took me the longest of these six to find out anything concrete about how item drops are determined; these findings here are the first I’ve gathered on the matter.

Let’s take a look at Pleasant Path Koopa Troopas’ item drop list, since they’re one of the first to be able to drop multiple types of items:

 Global Rate Item 1 Weight 1 Item 2 Weight 2 5 Mushroom 3 Koopa Leaf 7

This means that 5%* of battles against enemy sets led by a Koopa Troopa will drop an item, and of those items, Mushrooms and Koopa Leaves appear with frequency 3 and 7, respectively (30% and 70% of the time there is a drop, or 1.5% and 3.5% including the overall drop chance).

* Note: As alluded to in my Power Bounce article, Paper Mario 64’s RNG is weird in that it generates numbers from 0 to N inclusive (ergo, N+1 different values) when called with rand(N), meaning there are a lot of cases where there’s one extra value than intended. This is no exception, so the global drop rate is actually 5 out of 101, and though I haven’t checked, it’s possible that the weights between different items might get slightly messed up as well (probably giving the last item +1 weight, if so).

Also of note, both Paper Mario and Paper Mario: TTYD’s drop tables are assigned by encounter, not by enemy type, so it’s possible I missed a couple more battles where the drop tables are different the ones listed for the enemy type.

### Paper Mario: The Thousand-Year Door

I’ve already gone over this at length in a previous article, but I might as well have it here too for completeness’s sake. While most enemies only have one or two possible drops in PM64 (aside from a few weird ones like Shy Guys that have up to five), a good number of enemies in TTYD have up to five items + three badges that can be dropped.

Here’s a sample drop table (take a guess what enemy’s, at this point):

 Item Hold Weight Random-Drop Weight None 200 300 Super Shroom 10 10 Maple Syrup 0 10 Thunder Bolt 10 10 Point Swap 0 15 Fright Mask 0 10 Happy Flower 0 2 Flower Saver 0 1 Flower Saver P 0 1

Notably, all enemies have the same “None” weights, normal items’ weights are either 5, 10, 15, or 20, and badges’ are 1 or 2.

The hold weights are used to determine whether an enemy will hold an item/badge in battle (or have Ms. Mowz steal an item/badge, if they are holding nothing).  For example, in this case, the enemy will hold a Super Shroom 10/(200+10+10) = 10/220 = 4.54% of the time.

For drops, there are three possible scenarios; the game will either try to drop a held item, a random drop item, or nothing.  The relative probabilities of these cases are as follows:

 Held Drop Random Drop No Drop Normal battle 1 1 2 Normal battle (N Item Hog badges equipped) 1+N 1+N 2 Pit of 100 Trials battle 1 1 3 Pit battle (N Item Hog badges equipped) 1+N 1+N 3

If the held drop case is selected, then one of the items the enemies were holding in battle is dropped at random (items used by enemies are considered, but not ones stolen by Ms. Mowz); if no enemies were holding items, nothing will be dropped.

If the random drop case is selected, a random drop is selected from the front enemy’s random drop column, weighted accordingly.  For example, the chance of a Flower Saver being chosen is 1/(300+10+10+10+15+10+2+1+1) = 1/358.  Given there being such a high weight for no random item, in addition to having to have the random drop case selected in the first place (a 1/3 chance with an Item Hog, or 2/7 with an Item Hog in the Pit of 100 Trials), getting any random drop is pretty rare, especially badge drops.

If the “no drop” case is selected, or neither of the above cases result in a drop, Item Hog has a 40% chance of dropping one of the following items (Dried Shrooms being three times as common).  (* In the Japanese version of TTYD, the chance is 50%, but only if the held drop case was selected.)

### Super Paper Mario

Compared to the wealth of complication in TTYD’s system, SPM’s is much more straightforward; essentially the same as the original Paper Mario’s.

Here’s the drop data for a normal Goomba:

 Global Drop Rate 4% Item Name Weight Dried Shroom 100 Cake Mix 100 Big Egg 100 Honey Jar 100 Shroom Shake 200 Catch Card 50

Pretty straightforward.  Notably, poison-inducing enemies often have 100% global item drop rates (as might be pretty evident when playing the game).  Doesn’t mean you can’t get unlucky in a pinch and get a Catch Card, though.

### Mario & Luigi: Superstar Saga

Unlike the Paper Mario series, M&L games have been pretty consistent about the pools of items enemies have to draw from from the very beginning – at most one standard drop, one rare drop, and every enemy in a battle can independently drop one of its items. Superstar Saga is a bit of an oddball in how it handles those two drops, though.

Here’s Bob-omb’s data, for an example:

 Normal Item Weight Rare Item Weight Nuts 6 Red Pepper 10

Uniquely to the series, only the “normal” item can drop under normal circumstances, and the chance of it dropping is just the normal item’s weight out of 31 (yes, 31; they only had five bits to spare, I guess).  So Bob-ombs drop Nuts about 19.3% of the time.

If you equip the Gameboy Horror SP accessory, then you always receive the Rare Item if the enemy has one, no matter what the weight is (even 0, which does happen; Troopeas in the US version have Super Nuts as a 0-weight Rare Drop).

Swing Bros. Advance is where it gets interesting; here, and only here, are both items treated as weighted item drops.  In Bob-ombs’ case, then, you’ll get Nuts 6/16 (37.5%) of the time, and Red Peppers 10/16 (62.5% of the time).  Note that Woo Beans cannot be stolen in this way, but their weight does contribute (so Tanoombas with their “Woo Bean, 20 / Green Pepper / 10” table only drop Green Peppers a third of the time, and nothing the other two-thirds), and there’s no way to get an item with a 0 weight.

### Mario & Luigi: Partners in Time / Bowser’s Inside Story

Only recently did I discover how these rates are actually calculated, but it’s consistent between these two games (and possibly later games in the series as well, but I have no experience with their data).

Here’s Shroob Rex’s pair of items:

 Normal Item Global Item Rate Rare Item Rare Item Rate Mix Flower 15 100-Point Pants 15

Until recently I’d been interpreting these as each having a 15% chance, since nothing in Partners in Time had more than a 50 for either (although some enemies in Bowser’s Inside Story did, leading to confusion on my part about enemies whose “rates” summed to over 100, but no further research).

As it turns out, though, the numbers are misleadingly ordered in the data; it turns out this means that Shroob Rexes drop an item 15% of the time, and 15% of those items are 100-Point Pants (thus meaning 12.75% / 2.25% overall rates for the items, respectively).  Equipping the Treasure Badge skips the first check entirely when the enemy is defeated by a Bros. Item, meaning 85% of Rexes drop Mix Flowers, and 15% drop 100-Point Pants.

I don’t offhand know exactly how the Item Gloves work in BIS, but I imagine it might cap some enemies’ global drop rate so as not to get an item every attack from bosses (though notably, likely not Shroobs‘); might be worth looking into in the future.

### Item Drop Data Resources:

Paper Mario (64)
Paper Mario: The Thousand-Year Door
Super Paper Mario (data reverse-engineered / extracted by aldelaro5)

That’s all for this post, stay tuned soon (hopefully) for an in-depth look at evasion badges in Paper Mario: TTYD.  In the meantime, join my Discord server if you have suggestions for other mechanics you’d like to see get a deeper dive, or just want to chat Paper Mario or what-have-you.

# Superstar Saga’s Stateside and Overseas Stats – A Side-by-Side Size-up

Well, this post has certainly been entirely too long in coming, and hearing a credible rumor of a potential upcoming remake / port of Mario & Luigi: Superstar Saga for 3DS, this absolutely would be the time to get this out there.

I’ll go ahead and say it; much as I love the first three Paper Mario titles, and have done more than a fair number of playthroughs and mechanics-investigation, Mario & Luigi: Superstar Saga is easily my favorite Mario RPG, hands-down (and the rest of the M&L series doesn’t even come close to that title).  May be to some degree due to nostalgia (even though I’d already played PM64 many times by the point I was introduced to MLSS); there’s certainly nothing like playing through Superstar Saga with a sibling on a GameCube Game Boy Player w/ 2 controllers hooked up.  At any case, I’m a huge fan of its simplicity, the fast-paced action as a contrast to PM64 / TTYD’s nearly chess-like calculated strategy, and its brazenness in throwing the Mario brand’s familiar locales and art style to the breeze, while still throwing in a bunch of nods to its roots (and even some fascinating cut content doing the same with other Nintendo properties at the time!).

All that praise aside, the one thing that stood out to me as subpar about Superstar Saga, even on the earliest playthrough, was that it was hardly the best balanced game.  Items give ridiculous amounts of restoration for a casual player (no one in their right minds will have 120 HP upon reaching Little Fungitown), Mario’s Bros. Attacks dwarf Luigi’s in attack power (even with the Bros. at similar POW), the bosses’ EXP curve is all over the place (Cackletta gives 900 EXP at her first appearance, when the previous boss gives 260 and the next at most 300), and the Mush Badges deal downright ludicrous amounts of extra damage per hit, especially if you’re already good at dodging attacks.  Strangely enough, though, a good chunk of these oddities are absent in the Japanese release of Superstar Saga.  Indeed, despite the North American and Japanese versions being released only a week apart (and having been built only slightly longer apart than that), there are a staggering number of balance differences between the releases (to say nothing of the much-needed Heart Blocks in hard-to-leave areas, and a few welcome user interface upgrades; more on that on TMK’s excellent localization changes article).  Presumably the versions diverged and were developed in parallel earlier than that, but whatever the case, let’s see just how many things were altered…

Enemy Stats

Obviously there’s too many changes to note in plain text here, given that there’s over 100 unique enemy targets in the game, each with a dozen or so salient parameters.  The full sheet of stats can be found at the bottom of the post, alongside the stats for items and such; meanwhile, I’ll note some of the more notable changes here:

• Beanbean Castle Town enemies got their EXP yields shattered compared to the middling amounts in the US version.  Sharpea and Sworm both yield 2 (whereas the latter used to give 14), and the tougher ones yield 7-14 (rather than 16-20).  In addition, Lakipea got a massive SPEED increase, and Tanoombas’ stats were dramatically increased across the board (in exchange for a 20-coin reward).
• The EXP curve was smoothed considerably in most areas; notably, Bowser’s Castle enemies all yield from 90-130 EXP (adjusting the outliers 80 for Sniper Bill / 40 for Boo), and several enemies (notably “????”) from Gwarhar Lagoon give considerably less.
• EXP / coin oddities caused by improperly assigning those stats to different forms / parts of the same enemy / boss were mostly fixed.  De-winged Parabeanies and Paratroopeas give more EXP than in their winged form rather than less, Chomp Bros. no longer drop their wallets alongside their Chomps, Mom Piranha yields coins regardless of her final color, and the boss EXP curve is much saner (Cackletta gives 300 instead of the unintended 300×3, Trunkle 500 instead of 1000-1030, and Wendy and Lemmy’s fakes no longer give that odd 1 coin apiece).
• The Koopalings’ HP and DEF are a lot more variant, and their EXP climbs steadily from 550 to 850 rather than being a flat 800 apiece.
• Not stat-related per se, but Cackletta’s final form allows you to get the first turn regardless of SPEED, rather than likely killing you outright if your Bros.’ SPEED are both under (the fairly high value of) 120.
• Thankfully, for the completionists, Piranha Bean no longer has mutually exclusive one-time item drops (pawning off his rare drop on Ludwig instead).

Item / Equipment Stats

Again, a lot of changes, but these are among the most notable:

• Non-MAX Item restorations were reduced considerably; Mushrooms and Nuts both restore 25 / 45 / 75 HP, and Syrups restore 20 / 35 / 55 BP.  In exchange, the prices for the MAX items (including 1-Up Supers) and Nuts ballooned considerably.
• Red / Green Peppers’ effectiveness were halved, from a +50% boost to POW / DEF to only +25%, and sell for only 30 (to 60) coins rather than 50 (to 100).
• Turn-order affecting clothing was made preposterously more expensive; #1 Trousers and Beanstar Pants (which were for some reason made Mario- and Luigi-exclusive), as well as Peachy Jeans and Scandal Jeans were all put in the slowest-growing STACHE discount group, and their base cost is upward of 1,000 coins apiece (for comparison, nothing was sold for over 600 in the US version).
• A handful of the later “standard” equipment got bumps in price and stats (i.e. Casual Slacks got boosted from +70 DEF / +20 HP to +70 / +30, and General Badge changed from +45 POW / +15 BP to +55 / +12, in exchange for ~doubled prices).
• If First Strike was considered broken before, apparently Random G was considered worthless; both Harhall’s and Random Slacks got substantial boosts in stats (+60 HP to +100 HP, +60 DEF to +90 DEF).
• Finally, Mush Badges got a three-fold and much-needed nerf:
• The added damage from each Mushroom shrunk from ~0.20 / 0.20 / 0.25 / 0.30 to ~0.08 / 0.10 / 0.12 / 0.20 for each normal / Super / Ultra / Max Mushroom, respectively, for a total possible boost of 48 damage per hit rather than 93, most of which comes from expensive Max Mushrooms.
• The badges no longer have a base POW stat increase, but nominal increases in BP instead.
• Their prices roughly doubled (probably could have stood to be higher still, but oh, well).

On the note of STACHE, item discount rates were generally slowed across the board in the JP version, both intrinsically in the discount growth functions, and extrinsically from the Bros. getting less STACHE from level-ups (especially after 40; more on that later).

Here’s a comparison table of how many STACHE points are needed to make each of the six STACHE “discount groups” hit a given buy discount in the US version:

 Rate DG 0 DG 1 DG 2 DG 3 DG 4 DG 5 6% 0 20 33 36 52 81 10% 13 22 34 38 55 85 15% 14 23 36 40 57 87 20% 16 30 41 43 59 89 25% 19 32 50 46 61 91 30% 21 35 53 51 63 95 35% 25 37 55 56 73 101 40% 29 40 58 68 80 110 45% 40 47 60 81 84 122 50% 53 57 75 106 103 146

And here are the respective rates in the JP version:

 Rate DG 0 DG 1 DG 2 DG 3 DG 4 DG 5 6% 0 22 33 45 55 78 10% 15 24 36 49 57 80 15% 19 27 39 53 60 82 20% 22 33 43 58 62 85 25% 26 39 52 63 65 87 30% 31 42 55 70 78 93 35% 37 45 58 79 82 105 40% 47 55 67 89 91 122 45% 65 73 92 113 116 147 50% 90 98 117 138 141 172

Bros.’ Level Up Progression

Not a lot of huge tweaks here; in the JP games, Mario & Luigi both get a BP boost during the early levels, have slightly higher POW / DEF respectively through the mid levels, and (similar to most successive games in the series) get substantially lower stat gains after level 40.  The EXP required for level-ups wasn’t tweaked at all between versions, notably.

Here’s the sum of the Bros.’ natural level-up stats through levels 10, 40, and 99 in the US version:

 Mario HP BP POW DEF SPEED STACHE Lv. 10 20 15 29 24 34 14 Lv. 40 56 28 96 89 93 91 Lv. 99 86 45 181 166 210 193
 Luigi HP BP POW DEF SPEED STACHE Lv. 10 25 18 27 27 22 12 Lv. 40 65 37 85 98 70 85 Lv. 99 98 58 163 185 163 210

and in the JP version:

 Mario HP BP POW DEF SPEED STACHE Lv. 10 20 22 30 24 34 14 Lv. 40 56 35 100 87 93 83 Lv. 99 76 50 152 137 147 144
 Luigi HP BP POW DEF SPEED STACHE Lv. 10 25 27 27 28 22 14 Lv. 40 67 46 85 106 70 89 Lv. 99 87 62 137 155 125 149

Attack Power

Since I haven’t as of yet done a post on Superstar Saga‘s battle mechanics, here’s the base damage formula used by solo and Bros. attacks:

Solo attacks:
0.4 * (Attacker POW – 1/2 * Defender DEF) * (attack constant K)

Bros. attacks:
0.4 * (Attacker POW – 1/2 * Defender DEF) * (success constant S) * (attack constant K)

(Enemy attacks are calculated the same way as the Bros.’ solo attacks, with an attack constant of 1.)

As it turns out, all of the solo attacks have the exact same constants between versions, but for the sake of completion, I’ll list the basic attacks’ constants here as well (yes, the Hammer constants do vary based on the type of Hammer!):

 Attack Normal (Mario) Lucky (Mario) Normal (Luigi) Lucky (Luigi) Jump 1.20 2.30 1.00 2.00 Normal Hammer 0.90/1.00/1.10 2.10 1.00/1.15/1.30 2.50 Super Hammer 0.80/1.00/1.20 2.10 0.60/1.13/1.36 2.50 Ultra Hammer 0.80/1.05/1.30 2.10 0.80/1.10/1.40 2.50 Hand 1.15 2.20 1.15 2.20 Counterattack 0.50 — 0.50 — First Strike 0.50 — 0.50 —

Most of the Bros. Attacks’ base attack constants and success constants were changed between versions.  Rather than list all of the possible constants for all possible Action Command combinations for all attacks (since there are a lot, and they’re all in the doc at the bottom anyway), I’ll just list the (success constant S) * (attack constant K) products for each attack’s perfectly executed form, and whose POW is responsible for dealing the hit.

Here are those constants for the US version:

 Attack S * K (Normal) S * K (Advanced) Attacker Splash Bros. 3.60 3.17 Mario Swing Bros. 5.76 (max speed) 5.76 + a marginal amount Luigi (M+L on Advanced) Chopper Bros. 3.66 (for 10 hits) 4.56 (for 5 hits) Mario Fire Bros. 2.0 (for 8 hits) 3.60 (for 8 hits) Mario Bounce Bros. 3.00 1.20 apiece Luigi (both on Advanced) Knockback Bros. 2.88 4.90 (for 5 hits) Mario Cyclone Bros. 2.16 (for 5 hits) 2.52 (for 6 hits) Mario Thunder Bros. 0.60 2.10 Luigi

And here are the constants for the JP version:

 Attack S * K (Normal) S * K (Advanced) Attacker Splash Bros. 2.76 2.64 Mario Swing Bros. 4.80 (max speed) 4.80 + basically 0 Luigi (M+L on Advanced) Chopper Bros. 3.48 (for 10 hits) 3.96 (for 5 hits) Mario Fire Bros. 3.08 (for 8 hits) 3.96 (for 8 hits) Mario Bounce Bros. 2.94 1.56 apiece Luigi (both on Advanced) Knockback Bros. 2.40 4.08 (for 5 hits) Mario Cyclone Bros. 2.31 (for 5 hits) 2.90 (for 6 hits) Mario Thunder Bros. 1.56 2.86 Luigi

In addition to balancing the attacks, the JP fixed a bug where the fewer Action Commands were landed during Thunder Bros., the stronger the stat-dropping effect would be on its target (presumably due to setting the multiplier directly, rather than subtracting it from 1.0). Here are the (outrageously broken) effect strengths in the US version:

 First Command Second Command All Commands Normal DEF x0.0 DEF x0.12 DEF x0.333 Advanced DEF x0.0 DEF x0.275 POW x0.285

Whereas the JP version only drops stats if all action commands are executed properly (x0.7 DEF for the normal form of the attack, and x0.8 POW for the Advanced).

Lucky Chance

Finally, for one brief bit of trivia, the calculations that go into Lucky hit calculation vary considerably between the US and JP versions of the game. The formula for Lucky calculation is as follows:

luckyChance = clamp(LuckyBase + LuckyMult * playerStache / enemyStache, MinChance, MaxChance)

where the enemy’s STACHE is determined by the average of the Bros.’ natural STACHE stats at its own level, and LuckyBase, LuckyMult, MinChance, and MaxChance are constants that depend on how close the enemy and player levels are (one set for if the levels are within 10% of each other, another for less than 25% apart, and a third for more than 25% apart).

The values for those constants in the US version are as follows:

 Level Difference LuckyBase LuckyMult MinChance MaxChance Within 10% 0% 10% 6% 15% 10-25% Apart 0% 12% 10% 20% 25%+ Apart 0% 6% 4% 10%

and the values for those constants in the JP version:

 Level Difference LuckyBase LuckyMult MinChance MaxChance Within 10% -0.83% 9.17% 6% 22% 10-25% Apart -1.54% 8.46% 10% 30% 25%+ Apart -1.54% 8.46% 4% 15%

In addition, wearing a badge with the “Lucky Attack” effect increases chances of a Lucky hit by a flat 15% after the previous calculations (to a max of 25% in the US version and 40% in the JP).  But in short, the JP version has a higher cap on Lucky chances, but scales more evenly regardless of the level difference.

Also as a side note, I haven’t looked into it particularly deeply, but I suspect the JP version’s formula implementation has the potential to overflow to particularly low Lucky chances if the attacking bro’s STACHE stat is a bit more than 128 (or 128 + a multiple of 256) above the opposing enemy’s. Not likely to occur without a bunch of StarBeans drink farming, at any rate.

Well, that pretty much sums up the stat-based changes between the US and JP releases of Superstar Saga. Given that most of the balance changes in the latter were in my opinion for the better, I’m hoping that the alleged Superstar Saga remake ends up basing its stats off of that version. We’ll have to see, anyway.

You can find a spreadsheet of all the enemy stats, item stats, attack constants, and level-up progressions in both versions of the game here. Fingers crossed that we get a bunch more M&L:SS stuff to look at in an upcoming release!

# Power Bounce Caps: Not Quite Infinity+1

If like me, you were a casual fan of Paper Mario 64 back in the day, you might have wondered why you were able to get a ton of Power Bounces on enemies normally, but always crumbled under pressure when trying to use them against a boss. Well, this’ll probably come to no surprise if you’re into the speedrunning / TAS-ing scene now, but it turns out that in both Paper Mario 64 and TTYD, there are hard limits to how many times you can Power Bounce in a row, especially on bosses.  Let’s dive into how those are determined!

Also for completion, I’ll give the frame windows for how long you have to execute the Action Command each bounce, since they do get tighter on the later bounces.

Paper Mario 64

Though not that technically complex, the way the cap is determined in Paper Mario 64 is… well, rather indirect.  Where you end up getting capped also tends to have pretty heavy variance, with most of the caps being early on, but with an arbitrarily long tail.

Each enemy/boss has a single value that gets fed into the calculation, with a max of 100 (Goombas, Fuzzies, Shy Guy, et al.), and a minimum of 50 (Final Bowser, prior to the Twink battle), which I’ll call the Cap Multiplier, or Cap% for short.

A value in memory (I’ll call it the “bounce chance”, or BC) is set to 200 on the first bounce, and for every subsequent bounce, this value is multiplied by the Cap%, then divided by 100, and rounded down to the nearest integer. For example, if Cap% is 50, the BC will take on values of 200, 100, 50, 25, 12, 6, 3, 1, and then 0 for all subsequent jumps.  On each bounce, a random number from 0 to 100 (inclusive) is generated; if that number is higher than the current BC value, then no more jumps will be possible afterwards.

This will almost always be the limiting factor of a Power Bounce on anything with a Cap% < 100, since the timing windows are fairly lenient, giving you 7 frames at 30fps for the first bounce, and 1 frame fewer each subsequent bounce until it hits a minimum of 2 frames at 30fps (2/30 seconds) on the sixth bounce, totally reasonable compared to TTYD’s 3/60-second Superguards or SMRPG’s 2/60-second Super Jumps.

Curiously, not only does Dodge Master increase the timing windows for later bounces to a downright ridiculously forgiving minimum (5 frames, or 1/6 of a second; as generous as TTYD’s jump / normal guard commands with THREE Simplifier badges), it also makes your Power Bounces get capped later!  The badge adds 7 to the enemy’s Cap%, making the values take longer to get small. For instance, a 50-Cap% enemy’s BC goes from the above values to 200, 114, 64, 36, 20, 11, 6, 3, 1, 0.

What do all these values mean practically though? Well, here’s a chart of the chance of getting capped upon reaching each of the first 10 bounces (“Cap Likelihood”), as well as the number of expected attempts to get to that number of bounces (“Expected Attempts”), for an enemy with a Cap% of 70 (typical for chapter bosses; only Hallway / Final Bowsers have worse), with and without Dodge Master.

 Jump # 1 2 3 4 5 6 7 8 9 10 w/o Dodge Master BC 200 140 98 68 47 32 22 15 10 7 Cap Likelihood 0% 0% 2.0% 31.7% 52.5% 67.3% 77.2% 84.2% 89.1% 92.1% Expected Attempts 1 1 1 1.4 3.1 9.6 42.2 267 2447 30,903 Timing 7/30s 6/30s 5/30s 4/30s 3/30s 2/30s 2/30s 2/30s 2/30s 2/30s With Dodge Master BC 200 154 118 90 69 53 40 30 23 17 Cap Likelihood 0% 0% 0% 9.9% 30.7% 46.5% 59.4% 69.3% 76.2% 82.2% Expected Attempts 1 1 1 1.1 1.6 2.9 7.3 24 101 568 Timing 7/30s 7/30s 7/30s 7/30s 6/30s 5/30s 5/30s 5/30s 5/30s 5/30s

Interestingly, given that the bounces are only capped if the generated number is higher than the current BC, but not if it’s equal, it is technically possible to get arbitrarily many bounces (up to the global cap of 101) even for the worst Cap%, so long as the random number generated is always 0.  For example, getting a 13-cap without Dodge Master on Tutankoopa (or another 70-Cap% boss) is a 1/1,000,000,000 chance.  And yet, it’s possible. (Lua scripting FTW!)

Here’s a spreadsheet of the Cap Multipliers and “Expected Attempts” for the first 30 bounces for every enemy / boss in the game.

EDIT (2017-11-16): As a side note, wearing Dodge Master does not change the cap multiplier or frame window for Goombario’s Multibonk move.  Otherwise, the logic for it is exactly the same as Power Bounce.
EDIT (2018-04-06): In addition, per a discovery by r0bd0g, Multibonk’s cap multiplier is glitched and won’t reset to 200 when you start subsequent uses of the move unless you switch him out for another partner in between uses.  Presumably a bug, and as far as I know it happens in all versions of the game.

Paper Mario: TTYD

Compared to Paper Mario 64, TTYD’s approach is remarkably simple. Each enemy/boss has a “soft cap” N. For the first N-1 jumps, you can’t get capped. For the next N (bounces N through 2N-1) you have a 67% chance of getting capped each bounce (bounces N through 2N-1), and you will be forcibly capped on bounce 2N.  Practically all enemies have a soft cap of 9,999 (e.g. effectively infinite), and bosses’ soft caps range from 5-9, much better than Paper Mario 64’s potential (and on Bowser, likely) 3-caps.

Unlike PM64, Simplifier and Unsimplifier badges do not change the cap counts or likelihood of being capped; however, that does lead to the disadvantage of TTYD’s Power Bounce – no matter how which badges you’re wearing, eventually the timing window on the bounce gets down to a single frame at 60fps, which is basically impossible to keep up for more than a few bounces.

Here’s a table of the timing windows for any number of Simplifiers / Unsimplifiers, in 1/60-second frames:

 Bounces 1 2 3 4 5 6 7 8 9 10 11+ 3 Unsimplifiers 5 4 3 2 1 1 1 1 1 1 1 2 Unsimplifiers 6 5 4 3 2 1 1 1 1 1 1 1 Unsimplifier 7 6 5 4 3 2 1 1 1 1 1 Normal 8 7 6 5 4 3 2 1 1 1 1 1 Simplifier 9 8 7 6 5 4 3 2 1 1 1 2 Simplifiers 10 9 8 7 6 5 4 4 3 2 1 3 Simplifiers 10 10 10 10 10 9 8 7 6 5 1

You can find the soft-caps for each enemy in my recently-updated PM2 Stat Guide (listed as “PB Cap”).

That pretty much covers this little-known / understood balance feature! Really, I don’t think TTYD’s cap is accomplishing all that much when you’re forced to perform frame-perfect jumps from the eighth bounce onward, but ehh…