Statistical Analysis of Sigurd's Injury Rule

The following is from a mail posted to the Blood Bowl Mailing List (bbowl-l@cs.utk.edu) by Mike Reeder
I've done a little simple statistical analysis on blood bowl injuries, and I figured you folks on this list might want to see it (if you don't, no one will). I figured the stats using 3 different common injury tables: First, the regular Blood Bowl injury table, where all modifiers apply; second, the Natural 12 rule, which is the same except modified 12's count as SI's, not kills; and third, the new rule introduced by Sigurd G. (and adapted by the Big Man himself, Jervis Johnson). I'll call this one "Sigurd's Rule," just to give credit where credit is due.

If you missed it, here is Sigurd's Rule, in his own words.

I calculated the odds of getting knockouts, badly hurts, serious injuries, and kills under each of the three injury systems. I calculated the odds for normal injury rolls (with no modifiers), as well as injury rolls with +1 or +2 modifiers (with mighty blow, dirty player, razor sharp claws, etc.). Then I arranged the numbers into handy, easy to read tables. Without further ado, here they are:

Regular Injury Rules


KO%BH%SI%Kill%Casualty%
No modifier25.08.35.62.816.7
+1 modifier30.611.18.38.327.8
+2 modifier30.613.911.116.741.6

NATURAL 12 RULE


KO%BH%SI%Kill%Casualty%
No modifier25.08.35.62.816.7
+1 modifier30.611.113.92.827.8
+2 modifier30.613.925.02.841.6

SIGURD'S RULE


KO%BH%SI%Kill%Casualty%
No modifier25.08.35.62.816.7
+1 modifier30.613.99.34.627.8
+2 modifier30.620.813.96.941.6

Comments: First, notice that a normal injury roll, with no modifiers, is the same under all 3 systems. Also, the total KO rate and overall Casualty rate (BH+SI+Kills) are exactly the same under all the systems, no matter what the modifier. Therefore, the only difference between the systems is the way casualties are distributed, when modifiers are added.

Under the Regular Rules, there are too many kills. Mighty Blow, and especially Dirty Player are way too powerful, causing deaths. But everyone already knew that.

The Natural 12 Rule fixes that problem, but goes too far. Now, deaths are very rare, and serious injuries are way out of whack. Mighty Blow and Dirty Player help you get opponents off the field, but add nothing to the death rate.

That brings us to Sigurd's Rule. Looking at the tables, this is by far the most sensible injury rule. Deaths go up with the modifiers, but not obscenely. This is the only one of the systems where casualties occur in a logical manner, with badly hurt being more common than serious injury, which is more common than deaths.

Hey, good job Sigurd! It's nice to see a rules modification suggestion on this list that is simple, and actually adds something to the game. I'm going to lobby to add your injury rule to our league, immediately.

Mike

(p.s.- I'm not a mathematician, feel free to check my numbers and correct any mistakes. I think I got them all right.)


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