Week 4 Session: Most Randomness Is There to Be Removed

The roll — variance, critical hits and hit chance, and how to tell a random element that is doing work from one that is only adding noise

15 March 2027

Once the formula is written down, the rolls around it stop being atmosphere and become a design choice you can price.

Three rolls that do different jobs#

Damage variance. Pokémon multiplies final damage by a uniformly random integer from 85 to 100, floor-divided by 100. Sixteen outcomes, 6.25% each, expected multiplier 0.925. It spans about 15% and it decides almost nothing on its own — but it’s what makes a two-hit knockout sometimes take three, which is what makes the difference between a 99% and a 105% damage roll worth planning around. This roll exists to make thresholds fuzzy.

Critical hits. From Generation VI a crit multiplies by 1.5, and from Generation VII the base rate is 1/24. So the expected contribution is 1 + (1/24 × 0.5) = 1.021 — about two percent. Two percent. If crits were there to raise damage, they’d be indefensible; you could delete them and re-balance with a 2% bump nobody would feel. They’re there for the tail, and the tail is the point: the fight you nearly lost and didn’t.

Hit chance. A miss doesn’t scale damage, it deletes a turn. In a system where turns are the currency — and after week 2 you know exactly what a turn costs — a 90% accurate move is a 10% chance of paying full price for nothing. That’s a much heavier tax than the number looks, and it’s why accuracy-lowering effects feel worse than damage-raising ones of the same size.

Three rolls, three jobs: blur a threshold, fatten a tail, destroy a turn. When you’re asked whether a fight needs its randomness, that’s the question — which job, and does the fight want it done?

Expected value is the honest way to argue#

Arguments about randomness go nowhere on vibes. Expected value at least makes people disagree about something specific.

Take a move that does 100 damage with a 1/24 crit at 1.5×. Expected damage is 102.1. Now give the same move a flat 102 and no crit. Same average, different game: the first one occasionally ends a fight a turn early, the second never does. If you can’t say which you want and why, you haven’t finished designing the fight.

The same arithmetic tells you when a roll is pure noise. If removing a random element changes the expected value by under a percent and doesn’t change the shape of the distribution anywhere that matters, it isn’t doing a job. Cut it. Most JRPG randomness is like this, inherited from tabletop where the dice were doing a job the computer now does invisibly.

Task: price one boss’s crit chance#

Pick a boss from the provided saves. Using your week 3 formula, compute the expected damage per turn of its main attack with its crit chance, and again with crits removed and the average held constant. Then compute the chance it kills a full-health party member in one turn, under both.

Write one paragraph: does this fight need its crits? Defend it with the two numbers, and name what you’d have to change elsewhere to remove them. There’s no right answer here and there are several wrong ones, all of which start with “it feels better”.

One page worth reading#

Bulbapedia’s Critical hit page has the rates and multipliers by generation, which is more interesting than it sounds — the multiplier dropped from 2× to 1.5× and the base rate from 1/16 to 1/24 within a few years, and both changes are the designers deciding the tail was too fat.