It’s been announced that in Fourth Edition there will no longer be any rolls necessary to confirm criticals. This reduces the number of rolls in the game (I think a good thing) and increases player enjoyment (also a good thing!). However, this got me thinking about the math behind 3.5E criticals.

I’m sure everyone at one point or another has thought of the situation of a heavily armored fighter against an mob of low level foes. The fighter’s AC is such that the foers can only hit him on a very high roll, possibly a 20. This leads to the interesting question: “Because he can only be hit on critical threats, does this mean a larger portion of successful hits against him are crits?” Is the fighter invincible except when he gets crit? It seems like a strange situation.

Being a graduate student with some free time, I decided to quickly do the math. I considered all To Hit values necessary to hit the defender from 1 to 20, and a critical is threatened on a 20. (I’m looking at the percentage of hits that are criticals, not total number of critcals here.)

 
As we can see, the proportion of hits which are criticals are exactly the same if a critical is threatened only on a 20. A fighter suffers 5% critical hits from all opponents, invariant with attack bonus.

However, this changes in Fourth Edition. The proportion of hits which are criticals increases until all hits against a highly armored defender are criticals.

I don’t think this is a terrible thing, but it is an interesting consequence of the new system.

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