Category Archives: Paper Mario

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…

Badges, Part 1: An Introduction.

For my first official post on the Super Mario Files, I’ll once again revisit my favorite aspect of one of my favorite Mario games, badges in Paper Mario: The Thousand-Year Door.

Badges played a massive part in the original Paper Mario, allowing for amazing diversity in strategies, and if utilized correctly, completely mitigating the need for any other stat. Despite the large part badges played in PM64’s gameplay, the system was rather limited, with a set number of available badges and a horribly restrictive maximum BP of 30.  In the Thousand-Year Door, these limitations were all largely removed, with over triple the available BP, a larger number of badges available through normal means, a system for selling and re-buying badges easily, and most striking, a handful of ways that collectively allow one to collect practically infinite amounts of almost every badge in the game. This system is massively improved over the original’s; whereas there were at most three of any one badge in the original game, Thousand-Year Door provides you with the ability to hyper-focus your strategy on virtually any aspect of the battle system. A naïve player that doesn’t realize BP’s potential might reach the endgame with roughly 60 HP and FP; with all but 20 of that HP and FP being put into BP instead (totalling 51 BP), you can:

  • Restore an average of ~8 HP or FP every turn with 25 Happy Heart or Flower badges,
  • Get a straight extra 8 Attack or 10 Defense power for you or your partner with the respective numbers of Power/Defense Plus,
  • Increase ALL of your partners’ HP by 40 with HP Pluses P, giving you 300+ HP’s worth of meat-shields,
  • Gain back over three times the selling price of every item you use in-battle with Refunds,

and so on, and so on; you get the idea.  However, despite all these massive additions, the game makes little to no mention of how to get infinite copies of badges, or exactly how wearing multiple badges of the same type changes their effects. That’s where my research comes in; in the next couple of posts, I will pin down the effects of every badge in the game in single and multiple copies as accurately as they can be conceivably known, as well as detailing the exact methods for obtaining extra copies, whenever possible.  Stay posted for these updates in the near future!