Rerolling 1’s bias?

[darranh1]

I’ve noticed unless my maths wrong, rerolling 1 to hit gives 18% increase in wounds. However rerolling 1 to save as in standard spell benefits units with better saves. A unit with Standard saves of 5 only benefit from 9% less damage when rerolling 1s whilst units with save 3 benefit from more than 50%. 

Does this mean mystic shield is bias towards certain units dependant on their save or have I extrapolated something from nothing?

 

[King Taloren]

Really it’s just the fact of scaling number bias. 6sided dice are way too swingy to give any proper scale for statistical purposes. Each step up on the scale is a 18% jump in power. So any kind of reroll granted to a 3+ will always be way better than anything a 5+ roll will ever see even rolling all failed saves on a 5+ won’t be as good as rerolling 1s on a 3+ .

[Nighthaunt Noob]

You're right but there are still some assumptions in play here like which unit will be targeted more.

Edited May 8, 2019 by Nighthaunt Noob

[amysrevenge]

(Aside: You have to be careful how you talk about percentage increases.  There are two things you could be comparing against - the total number of attacks, or the total number of hits.  If you compare against the total number of attacks, you get a misleading sense of the actual impact of the reroll.)

As far as the math claim in the OP, "rerolling 1 to hit gives 18% increase in wounds", that's a close enough off-the-cuff approximation to what is actually 1/6 = 16.6667%.  If you are comparing number of hits with and without rerolling 1s, it doesn't depend on the To Hit characteristic.   The reason why Saves are screwy is that the math is inverted, and you are counting fails rather than counting successes, so it doesn't scale the same way.  If you were comparing "successful hits" to "successful saves" it would all work out identically.  But since the actual outcome we care about is successful hits and failed saves, the math is different.

(Do 36 attacks to make the math easier). 

If you hit on 2+ (or better), you go from 30 to 35 hits, for 5/30 = 16.7% more hits.  If you hit on 3+, you go from 24 to 28 hits, for 4/24 = 16.7% more hits.  If you hit on 4+, you go from 18 to 21 hits, for 3/18 = 16.7% more hits.  If you hit on 5+, you go from 12 to 14 hits, for 2/12 = 16.7% more hits.  If you hit on 6+, you go from 6 to 7 hits, for 1/6 = 16.7% more hits.  Ratio-wise everyone comes out equally  at 1/6 improvement (although distribution-wise, the higher To Hits will benefit more from a reduced chance for outcomes that are abnormally poor)

If you save on a 2+ (or better) you go from 6 fails to 1 fail, for 5/6 = 83.3% fewer fails.  If you save on a 3+, you go from 12 fails to 4 fails, for 8/12 = 66.7% fewer fails.  If you save on a 4+, you go from 18 fails to 9 fails, for 9/18 = 50% fewer fails.  If you save on a 5+, you go from 24 fails to 16 fails, for 8/24 = 33.3% fewer fails.  If you save on a 6+, you go from 30 fails to 25 fails, for 5/30 = 16.7% fewer fails.  Ratio-wise this doesn't come out fair at all.

[AaronWilson]

Mystic shield is better on some units then others for sure.