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.

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…

Paper Mario TTYD Stats! (The Sequel)

The new, improved Paper Mario stat sheet is here, now with heart / flower drops, item drops and drop rates, and much more!

Download the new stat spreadsheet here: Link

Explanations of the various stats in the sheet:

  • HP, ATK, DEF – Self-explanatory; based on tattle information (except in cases where it is obviously wrong like Red Spiky Buzzies).
  • EXP Level, EXP Bonus – Determine the amount of Star Points an enemy rewards. If it has a higher level than Mario, it awards (M * (EXP Level – Mario Level) + EXP Bonus) Star Points, rounded down, where M = 0.5 normally, 0.55 if there were three enemies at the start of the battle, 0.65 if there were four, and 0.75 if there were five. If its level is equal to or lower than Mario’s, it awards 0 Star Points regardless of its Bonus value.
  • Coin Base, Coin Bonus, Coin Ex% – Determine the coins an enemy drops after defeat; they drop the Base amout by default, and every additional Bonus coin has an Ex% chance of dropping.
  • HP / FP Drops – Determine the maximum number of hearts or flowers the front enemy in a battle can drop (see the link above for more details).
  • Item / Badge Drops – The items / badges an enemy can hold in-battle or randomly drop after battle, and their hold / drop weights (relative frequency of being held or dropped, with “nothing” having a hold weight of 200 and drop weight of 300). See this post for how to convert these into the absolute chance of an item drop.
  • Status Susceptibility – The likelihood of the enemy being subjected to various status ailments:
    • Sleep – Chance of being put to sleep.
    • Stop – Chance of being immobilized by a Stopwatch (Clock Out has a x1.27 multiplier to this if fully charged).
    • Dizzy – Chance of being made dizzy.
    • Confuse – Chance of being confused.
    • Burn – Chance of being burned. Is always 0 or 100+.
    • Freeze – Chance of being frozen.
    • Shrink – Chance of being shrunk.
    • Soft – Chance of being softened.
    • Fright – Chance of running away from a Fright Mask.
    • Gale – Chance of being blown away by Gale Force. Note that there is an additional factor based on the player and enemy’s relative level; for instance, a level 22 player against a Hyper Goomba (level 15) has an additional 22-15 = 7% chance of inducing the effect (assuming the chance was non-zero to begin with), and a level 10 player would have a 10-15 = -5% chance subtracted from the base chance.
    • OHKO – Chances of being defeated by Showstopper.
    • PB Cap – The “soft cap” for Power Bounce / Multibonk; i.e. the first bounce to have a 67% chance of ending the attack. The attack is forced to end at twice this number of bounces. If this value is not present, the soft cap is 9,999, which is basically infinite.
    • Dark Koopatrols seem to have a 100% susceptibility to all effects when flipped; I don’t think this applies to any other enemies, so it’s worth noting as a weird exception.

The only notable omission, which I may add at a later time, is that some Glitzville enemies have different item drop sets than their non-Glitzville counterparts; you can find those in my GameFAQs item drop guide.

That pretty much wraps up my new coverage of TTYD stuff; hope this is a good reference for aspiring badge hunters, Pre-Hooktail runners, or whomever else!

Paper Mario TTYD: To the Victors Go the Spoils

Well, this article’s been a long time coming.

For as fleshed-out as the Thousand-Year Door’s battle system is, it’s perhaps no surprise that its battle rewards are as hard to predict as they are various. So in this post, I’ll endeavor to explain exactly how the amounts of every battle reward are determined, one by one. I know my old enemy stats guide is a little out-of-date on some of the variables that go into these calculations, so I’ll probably be updating that in the very near future.

Let’s start with the most straightforward:

Coin Drops

Whereas Paper Mario 64’s enemies each had a fixed number of coins to drop, plus some extras for the enemy in front, in TTYD, each enemy drops coins in the exact same way.

Every enemy has three variables that go into coin drop calculation: a Base amount, a Bonus amount, and an Extra Coin Drop Rate (Ex%). The drop amount starts at the Base, and each Bonus coin has an independent, Ex% chance of dropping. For example, here’s an example of how Amazy Dayzee’s (Base 5, Bonus 5, and Ex% 70) coin drops might be calculated (the number under each bonus coin is a randomly generated number from 0 to 99, and has to be less than the Ex% for its coin to be dropped):

amazy-coins

After all the coin drops are determined, the total count is multiplied by the number of Money Money badges equipped + 1. At the end of the day, the maximum number of dropped coins is 32.

HP / FP Drops

Back in my Paper Mario 64 days, these precious hearts and flowers were the most desirable of drops (to be supplanted by badges in the sequel). Though it was far from a guarantee, it always seemed to me that taking damage, or using a ton of FP in-battle would slightly increase the amount of HP and FP I earned. Turns out in TTYD, this isn’t at all far from the truth, and in fact, it’s much simpler than that – the chances of HP / FP drops are directly tied to Mario’s current percentage of his max HP / FP:

Current HP/FP Percentage Overall HP Drop Rate Individual HP Drop Rate Overall FP Drop Rate Individual FP Drop Rate
Up to 20% 70% 50% 40% 40%
Up to 30% 60% 50% 40% 40%
Up to 50% 50% 40% 40% 40%
Up to 80% 40% 40% 40% 40%
More than 80% 30% 30% 30% 40%

So say that Mario ends a battle with 3 / 10 HP and 6 / 10 FP:

  • First, the game checks to see if any HP should drop at all (60% chance);
  • If it does, then the game checks M times to see if it should drop a single heart (50% each).
  • Next, the game checks to see if any FP should drop at all (40% chance);
  • If it does, then the game checks N times to see if it should drop a single flower (40% each)…

where M and N are determined by the type of enemy leading the battle, and can range from 2 to 6. For example, most early-game enemies have (2,2), Spiky Parabuzzies have (4, 2), X-Nauts PhD have (2, 4), and Elite Wizzerds have a whopping (5, 5). Needless to say, those constants will be in the next version of my TTYD enemy stats guide.

After those HP / FP drops are determined, if Mario has any Heart Finder badges on, the game adds some random additional heart drops – 1 to 3 of them if one badge, or 1 to N+3 of them if more than one. Likewise, Flower Finder will grant equivalent bonus FP drops. Both heart and flower drops cap at 32 apiece, just like coins. (Although you’d have to have a ridiculous number of Finder badges to exceed that!)

And now for the main event:

Item / Badge Drops

Back in 2011, I uploaded a guide to GameFAQs that contains the drop tables of every enemy in the game. Although these tables had some numbers alongside them, I could only proffer some vague speculation as to how those translated into their actual drop rates. Fast-forward to April 2016 and the discovery of Palace Skip; I finally had an excuse to get my hands dirty in assembly code again, and I successfully figured out everything that goes into these calculations! Here’s the dirt…

Item Hold Chances

The first thing to find out is how likely enemies are to hold items in battle, since those are observably a ton more likely than random drops. For the rest of this section, we’ll look at Crazee Dayzee’s drops as an example (for no particular reason, other than 900 failed attempts at getting a Flower Saver drop…)

crazee-drops

These are all the items Crazee Dayzees can hold / drop, with their respective hold / drop weights. Anything without a hold weight indicated actually has a hold weight of 0.

Upon determining an enemy’s held item, it basically chooses between all the options at their respective weights, with an additional weight of 200 for no item at all. Practically, this means that the chance of a particular item being held is its hold weight divided by (200 + the sum of all items’ hold weights). For example, a Super Shroom has a 10 / (200 + 10 + 10) = 1/22 chance of being held by a Crazee Dayzee.

This same function is used when determining what item Ms. Mowz steals from an enemy with no held item, only with her stealing a coin in the case of no item being chosen, rather than nothing. (Notably, if she would normally steal an item / badge, but Mario’s item / badge inventory is full, she misses the enemy rather than stealing a coin.)

All held items being determined, here’s what happens at the end of a battle:

Drop Type Determination

There are three things that can happen at the end of a battle – the game can try to roll for a random item from the front enemy (henceforth, “random drop”), drop an enemy’s held item (“held drop”), or drop nothing at all. The chances of these events happening are weighted as follows:

item-weights-0

If Mario has Item Hog badges equipped, this adds an additional “weight” per badge equipped to the random and held drop cases:

…and so forth. As the number of Item Hog badges increases, the chances of the Random / Held drop cases approach 50%; however, their effect visibly has pretty sharply diminishing returns after the first couple of badges.

Here’s a breakdown of what happens in each of these cases:

Random Drop

So you’re lucky enough to get a shot at a random item drop! Don’t celebrate just yet though, because the odds are stacked further against you. Similarly to the formula for determining held item chances, the chance of an item being randomly dropped is its drop weight divided by (300(!) + the sum of all items’ drop weights).

For example, the chance of a Crazee Dayzee dropping a Point Swap would be a none-too-great 15 / (300 + 10 + 10 + 10 + 15 + 10 + 2 + 1 + 1) = 15/359 ≈ 1/24, and the chance of a Flower Saver drop is a mere 1/359!  Taking into account the 25% chance of getting the “Random Drop” case to begin with (or 33.3% with an Item Hog badge), that chance plummets to an abysmal 1/1,436! (or 1/1,077 with an Item Hog.) Blech…

To reiterate, only the front enemy in a battle can drop items this way, so unfortunately you won’t be getting any Amazy Dayzee random drops.

Held Drop

Things are far brighter for this case; you simply get one of the items that were held by the enemies at the start of the battle (excluding ones you stole with Kiss Thief, you monster). If there aren’t any items to be dropped this way, you’re out of luck. However, if that’s the case when you have at least one Item Hog badge equipped, you have a 50% chance of picking up one of the following items at random:

item-hog-list

Yes, Dried Shrooms are three times as likely to drop; in fact, factoring in the chance of the “Held Drop” case being chosen, with one Item Hog, your total chances of getting a Dried Shroom from a battle with no enemy held items are a none-too-shabby 33.3% * 50% * 30% = 5%. Rejoice in that, Mega-Rush-P-using Pre-Hooktail-Pit-Runners!

No Drop

You don’t get an item drop in this case. Thought that’d be self-explanatory…

Final Thoughts

And finally, that wraps everything up! Again, I’m hoping to compile all the drop tables, HP / FP drops, and existing enemy stat info into a single doc in the near future. In the meantime, enjoy your well-earned rewards (and revel in your RNG fortune if you manage to get any of the rarer badges!)

Oh, one more note about item / badge drops; if you scare all the enemies in a battle away with Fright Masks, items can still be dropped in the same way as always. This could be potentially useful for enemies with really high susceptibility to Fright (e.g. Dayzees – 100%!) Who knows?

Paper Mario TTYD: No Holds Barred

Hey, long time with no updates, but I’m back, bearing more Paper Mario: TTYD badgey goodness! Before getting to the real skinny (actual drop / hold rates, rather than baseless speculation), I thought I’d do a short bit on messing around with enemies’ held items.

Interestingly, even though the enemies’ drop tables prevent too many weird / useless held and dropped items, the game actually has a failsafe to prevent enemies from holding anything but one of these 32 items, using internal item IDs 0x80 – 0xA0 (128 – 160):

enemy-items-ok.png

Astute readers might have noticed that’s actually a range of 33 IDs rather than 32; the one in that range that isn’t allowed is “Trade Off”, a dummied-out item that raises the EXP of enemies. Some of the items that are allowed seem a bit odd; enemies have no use for the FP-restoring items, and they don’t seem to be programmed to use the Hot Dog, or the unused Cake item (restores 10 HP) either. Still, they are completely capable of holding these items in-battle:

enemy-held-items-totally-normal.PNG

Also notably, this list does exclude some in-battle items that one might consider “normal”, but for usually understandable reasons:

  • Point Swap: Can’t have enemies swapping their HP with nonexistent FP, after all.
  • Fright Mask: Although it would be humorous if enemies could force Mario to run away from battle, I can imagine why this doesn’t work.
  • Mystery?: Not really sure, as I never used this item much myself. Maybe some of the effects wouldn’t work properly on enemies.
  • Spite Pouch: Interestingly, this one is programmed into some enemies’ drop tables, but cannot in fact be held.  I suspect this is because the Counter status was never programmed properly for some enemies / attacks; more on that later…
  • Gold Bars: Yeah, you wish.

Weirdly, unlike items, not only is there nothing preventing enemies from holding arbitrary badges, a good number of them that can’t normally be held do in fact work, at least to some extent:

  • All or Nothing: Gives the enemy +1 Attack (apparently they know about Timed Hits!)
  • Feeling Fine: Works as advertised. Presumably not used since Mario wouldn’t have any use for a second one.
  • Zap Tap: Same deal. Rather obnoxious to deal with, too.
  • Lucky Day: Works, rather unsurprisingly. Pretty Lucky is objectively better anyway, though…
  • Double Pain: Works, and is in fact stackable. Yeesh.
  • Happy Flower, Pity Flower: Shows visible FP gain, though it doesn’t seem to do anything.
  • HP Drain, FP Drain: These don’t really work; they do lower the enemy’s Attack by 1, though.
  • Lucky Start: Humorously, works exactly as it does for Mario:

enemy-held-badges-all-the-fp

 

(Not so lucky in that case, bud…)

Finally, Return Postage does grant the Counter status, but with some… interesting side effects for some moves…

enemy-return-postage-mowz-2

Uhh…

enemy-return-postage-mowz-4

Right.

If you want to see some of these crazy badges in action, check out MilesLuigi’s video of most of the effects!

Tune in again soon, where I detail how to calculate item drop rates exactly, as well as explaining the rest of after-battle rewards in depth!

Super Smash Bros. 4 Equipment – All the RNG!

So, I was totally fed up with dealing with huge variance in Super Smash Bros. 4’s much-maligned custom equipment drops. Clearly data-mining held some answers, and in either case, I had 2000+ pieces of equipment (most from an ongoing quest to get a Critical Hitter Brawn Badge from Smash Wii U’s Crazy Orders) to back my findings.  And for the most point, I pretty much got what I was looking for; here’s the process the game uses to generate random equipment, as far as I can tell:

  • A positive stat value is determined from 10 to 85. Based on this number, the item is given a tier ranging from 1-7 (see the table below for details).
  • A negative stat value is determined, which ranges from 50 to 70% of the positive stat’s value.
  • If the equipment has a helpful (“positive”) bonus effect, subtract its effect’s stat modifier (see the table below for these values) from the previously generated positive stat; likewise, if it has a harmful (“negative”) effect, subtract its effect’s stat modifier from the previously generated negative stat.
  • After these calculations, any equipment generated will not have either stat with a value below 5.
  • “Generic” badges (Brawn, Protection, Agility) have both stats multiplied by 0.72.
  • Both stats are rounded down, if necessary.

Additionally, the sell price of equipment is pretty simply calculable by the following formula: (1.0p - 0.6n + 1.1pb - 0.4nb) * t, with the variables representing the following quantities:

  • p = Positive stat
  • n = Negative stat
  • pb = Positive stat modifier, if equipment has a positive bonus effect
  • nb = Negative stat modifier, if equipment has a negative bonus effect
  • t = Price multiplier based on item’s tier (see table below)

Here’s a table determining what tiers correspond to what ranges of stats:

Tier Positive Range* Negative Range* Price Multiplier Equipment Class
1 10 – 20 5 – 14 0.36 Normal
2 21 – 30 10 – 21 0.58 Normal
3 31 – 40 15 – 28 0.97 Super
4 41 – 50 20 – 35 1.22 Super
5 51 – 60 25 – 42 1.35 Super
6 61 – 70 30 – 49 1.44 Rare
7 71 – 85 35 – 59 1.71 Rare

* Before applying effects’ stat modifiers or “generic badge” modifier.

As an aside, the fact that the sell price formula uses the final stats, but the sell price tier of the original positive value before any modification, means that two generic badges on the Tier 4-5 or 5-6 boundary can have the same stats, but differing sell prices. For example, two Super Brawn Badges with (+36, -20) that started out as (+50, -28) and (+51, -28) would sell for 29G and 32G, respectively.

Finally, here’s a table of all of the bonus effects and their associated stat modifiers (negative / red ones signify negative effects, but the modifiers should be considered as positive values). For reference, I’ve also included the best possible stats for generic and non-generic badges with the highest positive stat for each effect:

Effect Name Stat Modifier Best Non-Generic Best Generic
Sprinter 25 +60, -42 +43, -30
Stroller -30 +85, -12 +61, -8
Glider 25 +60, -42 +43, -30
Antiglide -38 +85, -5 +61, -3
Leaper 34 +51, -42 +36, -30
Antileap -36 +85, -6 +61, -4
Speed Skater 34 +51, -42 +36, -30
Hi-Jump 27 +58, -42 +41, -30
Lo-Jump -35 +85, -7 +61, -5
Double-Jump Boost 34 +51, -42 +36, -30
Double-Jump Drag -43 +85, -5 +61, -3
Thistle Jump 19 +66, -42 +47, -30
Anchor Jump -43 +85, -5 +61, -3
Speed Walker 12 +73, -42 +52, -30
Meanderer -8 +85, -34 +61, -24
Lingering Edge 10 +75, -42 +54, -30
Hasty Edge -5 +85, -37 +61, -26
Gluey Edge 27 +58, -42 +41, -30
Tough Edge -32 +85, -10 +61, -7
Hard Braker 5 +80, -42 +57, -30
Perfect-Shield Helper 40 +45, -42 +32, -30
Imperfect Shield -35 +85, -7 +61, -5
Shield Regenerator 21 +64, -42 +46, -30
Shield Degenerator -22 +85, -20 +61, -14
Air Defender 27 +58, -42 +41, -30
Air Piñata -38 +85, -5 +61, -3
Nimble Dodger 22 +63, -42 +45, -30
Dodgy Dodger -33 +85, -9 +61, -6
Smooth Lander 33 +52, -42 +37, -30
Crash Lander -36 +85, -6 +61, -4
Quick Smasher 28 +57, -42 +41, -30
Hyper Smasher 29 +56, -42 +40, -30
Air Attacker 15 +70, -42 +50, -30
Air Scrapper -35 +85, -7 +61, -5
Meteor Master 40 +45, -42 +32, -30
Desperate Attacker 27 +58, -42 +41, -30
Desperate Defender 18 +67, -42 +48, -30
Desperate Speedster 20 +65, -42 +46, -30
Desperate Specialist 33 +52, -42 +37, -30
Desperate Immortal 36 +49, -42 +35, -30
Unharmed Attacker 24 +61, -42 +43, -30
Unharmed Speedster 8 +77, -42 +55, -30
Unharmed Speed Demon 26 +59, -42 +42, -30
Trade-off Attacker 16 +69, -42 +49, -30
Trade-off Defender 25 +60, -42 +43, -30
Trade-off Speedster 21 +64, -42 +46, -30
All-around Trade-off 27 +58, -42 +41, -30
Moon Launcher 29 +56, -42 +40, -30
Vampire 43 +42, -42 +30, -30
No-Flinch Smasher 30 +55, -42 +39, -30
Critical Hitter 58 +27, -42 +19, -30
Insult to Injury 25 +60, -42 +43, -30
First Striker 9 +76, -42 +54, -30
Countdown 23 +62, -42 +44, -30
Speed Crasher 27 +58, -42 +41, -30
Shield Exploder 30 +55, -42 +39, -30
Shield Healer 33 +52, -42 +37, -30
Shield Reflector 15 +70, -42 +50, -30
Escape Artist 18 +67, -42 +48, -30
Item Hurler 40 +45, -42 +32, -30
Item Lobber -21 +85, -21 +61, -15
Item Hitter 35 +50, -42 +36, -30
Item Pitcher 15 +70, -42 +50, -30
Item Shooter 33 +52, -42 +37, -30
Quick Batter 26 +59, -42 +42, -30
Star Rod 12 +73, -42 +52, -30
Lip’s Stick 11 +74, -42 +53, -30
Super Scope 14 +71, -42 +51, -30
Ray Gun 14 +71, -42 +51, -30
Fire Flower 6 +79, -42 +56, -30
Beam Sword 12 +73, -42 +52, -30
Home-Run Bat 22 +63, -42 +45, -30
Bob-omb 12 +73, -42 +52, -30
Mr. Saturn 4 +81, -42 +58, -30
Food Lover 17 +68, -42 +48, -30
Picky Eater -7 +85, -35 +61, -25
Crouch Healer 30 +55, -42 +39, -30
Caloric Attacker 26 +59, -42 +42, -30
Caloric Speedster 16 +69, -42 +49, -30
Caloric Defender 16 +69, -42 +49, -30
Caloric Powerhouse 27 +58, -42 +41, -30
KO Healer 22 +63, -42 +45, -30
Caloric Immortal 32 +53, -42 +38, -30
Auto-Healer 42 +43, -42 +30, -30
Smash Ball Attractor 16 +69, -42 +49, -30
Pity Final Smasher 5 +80, -42 +57, -30
Smash Ball Clinger 6 +79, -42 +56, -30
Super Final Smasher 20 +65, -42 +46, -30
Final Smash Healer 16 +69, -42 +49, -30
Double Final Smasher 23 +62, -42 +44, -30
Sudden Death Gambler 16 +69, -42 +49, -30
Safe Respawner 28 +57, -42 +41, -30
Risky Respawner -33 +85, -9 +61, -6

As a side note, the stats of equipment obtained from challenges and such are fixed, and do not necessarily follow the same rules as random drops. Notably, the Critical Hitter Brawn Badge received as a reward for getting 300 KO’s in Super Smash Bros. 3DS has +7 Attack, -40 Defense, which is impossibly bad for a random generic Critical Hitter equipment (the negative range for +7 Attack would normally range from -24 to -34 Defense). So that’s a bit of a pain.

Smash Run – Not Kirby Air Ride 2, but meh, close enough.

So I’ve been playing a bunch of Super Smash Bros. for 3DS’s single player recently, for the first time in a while, and naturally I’ve been doing some data-mining. In light of that, here’s a list of all of the Smash Run enemies’ stat drops.

The types of patch dropped are based on a weighted distribution unique to each enemy type. By default, normal stats have a weight of 10; stats in the “stat strengths” section have a weight of 100 instead, and if All is in the section, it has a weight of 10 rather than the default of 0.  The “stat points” is the approximate range of the total worth of the patches dropped (with All counting only for how many points it grants to a single stat, not all six); individual patches come in fixed size increments, worth 3, 10, 30, 100, or 200 points. After the halfway point of a run, this amount is cut in half for all enemies (except Souflees and Clubberskulls, which always drop max-sized stat boosts).

Name Series Patches Stat Pts1 Stat Strengths
Goomba Mario 3 15 – 20 Speed Attack Arms
Shy Guy Mario 3 15 – 20 Speed JumpSpecialDefense2
Bullet Bill Mario 3 15 – 20 Jump Attack Arms
Spike Top Mario 3 15 – 20 Speed Attack Defense
Koopa Mario 3 45 – 60 Speed Jump Attack Arms
Flame Chomp Mario 5 45 – 60 Jump Special Arms
Hammer Bro Mario 5 60 – 80  Jump Special Arms
Lakitu Mario 5 60 – 80  JumpArms
Spiny Mario 0 0  No Stats
Magikoopa Mario 5 100 – 125  JumpSpecial Arms
Banzai Bill Mario 7 90 – 120 Jump Attack Defense
Grand Goomba Mario 7 90 – 120 Speed AttackDefense
Tikibuzz Donkey Kong 3 15 – 20 Jump Attack Arms
Kritter Donkey Kong 5 60 – 80 Speed Attack Arms
Octorok Zelda 3 15 – 20 Speed Special Arms
Bubble Zelda 5 35 – 70 Jump Attack Special Defense
Peahat Zelda 5 45 – 60 Jump Attack Special Defense
Redead Zelda 5 60 – 80 Speed Attack Special Defense
Stalfos Zelda 5 90 – 120 Speed Attack Defense
Geemer Metroid 3 15 – 20 Speed Attack
Reo Metroid 5 30 – 40 Jump Attack Defense
Kihunter Metroid 3 45 – 60 Jump Attack Special Arms
Waddle Dee Kirby 3 15 – 20 Speed Jump Arms
Bronto Burt Kirby 3 15 – 20 Jump Attack Arms
Tac Kirby 3 15 – 20 Speed Jump Attack Special Arms
Waddle Doo Kirby 3 30 – 40 Speed Special Arms
Plasma Wisp Kirby 3 30 – 40  Jump Special Arms
Gordo Kirby 0 0  No Stats
Shotzo Kirby 0 0  No Stats
Petilil Pokémon 3 15 – 20 Speed Special Arms
Gastly Pokémon 3 20 – 25 Jump Attack Defense
Koffing Pokémon 3 20 – 25 Jump Special Arms
Cryogonal Pokémon 3 30 – 40 Jump Special Arms
Chandelure Pokémon 5 45 – 60 Jump Special Arms
Starman EarthBound 5 60 – 80 Special Arms
Monoeye Kid Icarus 3 15 – 20 Jump Special Arms
Nutski Kid Icarus 3 15 – 20 Jump Special Arms
Bumpety Bomb Kid Icarus 5 30 – 40 Speed Special Defense
Daphne Kid Icarus 3 30 – 40 Jump Special Arms
Lethinium Kid Icarus 3 30 – 40 Special Defense
Mahva Kid Icarus 5 30 – 40 Jump Defense
Zuree Kid Icarus 5 40 – 50 Jump Attack Defense
Flage Kid Icarus 5 40 – 50 Jump Attack Defense
Skuttler Kid Icarus 5 45 – 60 Speed Attack Arms
Skuttler Cannoneer Kid Icarus 5 45 – 60 Speed Special Arms
Skuttler Mage Kid Icarus 5 100 – 125 Speed Special Arms Defense
Ghost Find Mii 3 15 – 20 Jump Arms
Eggrobo Sonic 5 30 – 40 Jump Special Arms
Met Mega Man 3 15 – 20 Special Defense
Pooka Namco 5 45 – 60 Speed Jump Attack Defense
Bacura Namco 0 0   No Stats
Mite Smash Bros. 1 10 Speed Jump Attack Arms
Glunder Smash Bros. 3 15 – 20 Speed Special Defense
Glice Smash Bros. 3 45 – 60 Speed Special Defense
Glire Smash Bros. 3 60 – 80 Speed Special Defense
Roturret Smash Bros. 7 75 – 100 Special Defense
Chain Chomp Mario 7 150 – 200 Speed Attack Defense All
Darknut Zelda 7 450 – 600 Speed Attack Defense All
Metroid Metroid 5 150 – 200 Jump Attack Defense All
Bonkers Kirby 7 450 – 600 Speed Attack Special Arms Defense All
Devil Car EarthBound 7 300 – 400 Speed Attack Defense All
Polar Bear Ice Climber 7 300 – 400 Speed Jump Special Arms Defense All
Megonta Kid Icarus 5 150 – 200 Speed Attack Special Defense All
Boom Stomper Kid Icarus 7 225 – 300 Speed Attack Defense
Reaper Kid Icarus 7 300 – 400 Speed Attack Arms Defense All
Mimicutie Kid Icarus 7 300 – 400 Speed Attack Defense All
Lurchthorn Kid Icarus 3 150 – 200 Jump Special Arms All
Clubberskull Kid Icarus 3 MAX Speed Attack Defense
Bulborb Pikmin 7 375 – 500 Speed Attack Defense All
Fly Guy Yoshi’s Island 0 0  No Stats
Souflee Kid Icarus 1 MAX Speed Jump Attack Special Arms Defense
Glint Beetle Pikmin 0 0  No Stats
Sneaky Spirit Rhythm Heaven 3 36 All3
Poppant Smash Bros. 0 0  No Stats
Orne Kid Icarus 0 0  No Stats
Bill Blaster Mario 5 ???4 Speed Jump Attack Special Arms Defense
Generator Smash Bros. 5 ???4 Speed Jump Attack Special Arms Defense


Footnotes:
1. In-game data stat range. In practice, stats can vary a little bit outside of this range; for instance, enemies with a “15 – 20” range can drop either 16 or 23 points’ worth of patches.
2. Only the color matching the color of the Shy Guy has a value of 100.
3. Sneaky Spirits only give All patches.
4. In practice, this stat range is all over the place and doesn’t match up with the game values at all; I’ve seen them drop from as low as 50 to over 150.