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…

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3 thoughts on “Power Bounce Caps: Not Quite Infinity+1

  1. mainunderscoregi

    Nice info! I want to contribute to the intro a bit though. I think a few people noticed that a system-capped Power Bounce was capped because in TTYD, if you correctly time it, it will still show “EXCELLENT” and zoom the camera out instead of acting like you missed the attack. I believe it’s similar in PM64 – if I recall, if you get capped in 64, instead of “falling” down, Mario will bounce backwards. I don’t think 64 had a system that would still show “SUPER”.

    Reply
  2. Pingback: ’00s Mario RPGs’ Item Drops: Weights? Rates? Let me Elucidate… | The Super Mario Files

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