Detailed Dice Analysis of THE REMATCH

The following analysis was provided by @IsYitzack, who has contributed odds and other calculations on Twitter. Below is his mathematical analysis of the dice for The Rematch between Kern and Grog.

I’ve worked out the odds of how many hits Grog and Kern can expect with the number of hits given and under the conditions given. I understand that Grog has an attack bonus of +10. I’ve guessed that Kern is at +8 based on the rolls in this match. Taking the first match into consideration would improve knowledge of his attack roll.

Grog attacked with advantage 4 times, even 22 times, and disadvantage 3 times. He applied inspiration to 2 disadvantaged attacks. He hit 16 times. We would expect that he would hit 18.43 times with a standard deviation of 2.53. He hit poorly to .96 standard deviations.

Kern attacked with disadvantage 3 times and even 22 times. Cutting Words was applied to an even roll. He hit 16 times. We would expect that Kern would get in 12.73 hit with a standard deviation of 2.46. He rolled hard by 1.33 standard deviations.

There were 5 contested athletics skill checks. 4 were initiated by Grog. That detail is important as tied contested rolls go to the status quo. Since we’re in a fight, the status quo is a default win by the defender giving the defender better odds. We were told that Grog’s athletics modifier is +7. We are also told that Kern’s athletics modifier is +8. When Grog defends an athletics contest, he will win 47.5% of the time. When he initiates the contest, he will win 42.75% of the time. Grog initiated 4 athletics contests and defended 1. He won 3 of them. We would expect that he wins 2.185 of them under these conditions. He has a standard deviation of 1.11. He rolled hard by .735 standard deviations.

All in all, the dice did not roll in Grog’s favor for the fight. But it wasn’t extreme. It wasn’t so far out of whack that I’d be wondering if Matt’s dice were loaded or otherwise faked.

I understand that there was some discussion as to what Kern’s last move should have been. There is an objectively correct answer. He could have attacked once and dodged or attacked 3 times. Since the single attack happens in both cases, we’ll only consider what happens after that, dodge or attack twice.

Kern will hit with 55% probability. Grog has +4 constitution modifier. The second relentless rage will succeed 40% of the time. The third will succeed 15% of the time. There is not a fourth relentless rage, the DC is out of Grog’s range. Grog did have inspiration at the time that could be applied. Since the application of inspiration is conditional on the player and the roll, I decided it would be better to ignore it here and apply it the strikes.

If Kern attacks twice more, Grog would go down 58.14% of the time. Grog would then have a 97.76% chance of hitting him. If Kern defends, Grog has a 89.96% chance of hitting him. In the end, if Kern attacks, he wins or gets another turn 59.07% of the time. If he defends, he gets another turn 10.04% of the time. The objectively correct answer is to attack. However, for the story and character of Kern, dodging is correct answer as he is now scared shitless that he may lose yet and that he should dodge instead.

If you’d like to see the rest of his notes for the calculations, they are available here. Thanks for the analysis, IsYitzack!