Spider-Man has a really interesting defensive stat-line, with 3s across the board, but the ability to reroll two dice, so long as they don’t come up skulls. But how does that compare to, say 4 dice with no rerolls?

It’s fairly obvious that 3-reroll-2 is strictly worse than 5 dice. With 5 dice you roll the same number of dice, but have a higher possible total of blocks and more chance of getting extra dice from criticals. But it is nowhere near as obvious how it compares to 4 dice.

A typical defensive dice has three successes out of 8, but you get an extra dice if you roll a crit, which has another 3 out of 8 chance of a defensive success. So a typical single dice should produce about 0.42 blocks. That means a typical pool of 4 dice, you would “expect” 1.69 blocks.

The maths of Spidey’s defences are significantly more complex. Some binomial analysis is required, but it is complicated both by the crits and the inability to reroll skulls. In the end, I resorted to brute forcing the maths, which you can can find here, but it comes out to expecting to block 1.78 damage per roll. That puts it very slightly (0.09 damage) better than 4 dice. There will be less upside (maximum damage blocked is 6 rather than the possibility of 7 or 8 with 4 dice), but the distribution will be more skewed towards the right because of the effect of the rerolls.

So when evaluating Spider-Man, you can consider all his defensive stats to be 4, and you are about right. That is until Venom gets his tongue on Spidey…

[…] good is Spider-Man’s Spider Sense? I had a quick look at the maths here, but I’ve had time now to do the complex maths around crits, fails and […]

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