Figureing out the Golaith Barbarian: How Good is the Re-Rolled Attack?
The Goliath Barbarian, with it's reroll attack ability, poses a rather interesting number crunching problem when analyzing the statistics of a warband, just how good is it's ability? Clearly the piece is worth more than the +10/+5 (20) that is listed on the card, but just how much more? This is also useful to star wars players, since you can spend a force point to re-roll an attack roll you missed on.
To answer this question, I am going to resort to what amounts to applied elementary probability and statistics, and if it makes your head hurt just skip down to the chart. I call it elementary because I don't do this stuff for a living and it makes sense to me, therefore it can't be all that difficult. What I did was convert the "roll needed" to hit to a probability of hitting, at a simple 0.05 probability per side that can hit. Then I squared that probability to get the odds that I will miss twice. Once on the normal attack and once on the re-roll. The rest of the probability, split basically 50/50 is the odds I hit on the normal roll or the re roll. But I just calculated those together. Then I figured what an equivalent "hit number" would be for those odds, the difference between the two is the benefit from using the re-roll. Here is a chart summarizing the numbers.
Armed with this information we have our answer, about +3/+4 on most attacks. Against a Large Silver dragon it's like having a +14/+5 attack (+13/+5 if buffed). Against an Orc Champion it's +10/+10 (+13 on a single attack), against an Ogre Ravager it's +10/+10 or +14 on a single attack. Against a Frenzied Bezerker it's +10/+8, not so special there. Between the primary and secondary attacks it is most effective against ACs between 15 and 23, i.e. most of the beaters!
Here is a quick comparison chart for a Goliath re-rolling an attack against a particular AC.
To answer this question, I am going to resort to what amounts to applied elementary probability and statistics, and if it makes your head hurt just skip down to the chart. I call it elementary because I don't do this stuff for a living and it makes sense to me, therefore it can't be all that difficult. What I did was convert the "roll needed" to hit to a probability of hitting, at a simple 0.05 probability per side that can hit. Then I squared that probability to get the odds that I will miss twice. Once on the normal attack and once on the re-roll. The rest of the probability, split basically 50/50 is the odds I hit on the normal roll or the re roll. But I just calculated those together. Then I figured what an equivalent "hit number" would be for those odds, the difference between the two is the benefit from using the re-roll. Here is a chart summarizing the numbers.
| Roll Needed | 2x Miss Odds | Effective Roll Needed | Net Bonus |
|---|---|---|---|
| 20 | 0.098 | 19.05 | 0.95 |
| 19 | 0.190 | 17.20 | 1.80 |
| 18 | 0.278 | 15.45 | 2.55 |
| 17 | 0.360 | 13.80 | 3.20 |
| 16 | 0.438 | 12.25 | 3.75 |
| 15 | 0.510 | 10.80 | 4.20 |
| 14 | 0.578 | 9.45 | 4.55 |
| 13 | 0.640 | 8.20 | 4.80 |
| 12 | 0.698 | 7.05 | 4.95 |
| 11 | 0.750 | 6.00 | 5.00 |
| 10 | 0.798 | 5.05 | 4.95 |
| 9 | 0.840 | 4.20 | 4.80 |
| 8 | 0.878 | 3.45 | 4.55 |
| 7 | 0.910 | 2.80 | 4.20 |
| 6 | 0.938 | 2.25 | 3.75 |
| 5 | 0.960 | 1.80 | 3.20 |
| 4 | 0.978 | 1.45 | 2.55 |
| 3 | 0.990 | 1.20 | 1.80 |
| 2 | 0.998 | 1.05 | 0.95 |
Armed with this information we have our answer, about +3/+4 on most attacks. Against a Large Silver dragon it's like having a +14/+5 attack (+13/+5 if buffed). Against an Orc Champion it's +10/+10 (+13 on a single attack), against an Ogre Ravager it's +10/+10 or +14 on a single attack. Against a Frenzied Bezerker it's +10/+8, not so special there. Between the primary and secondary attacks it is most effective against ACs between 15 and 23, i.e. most of the beaters!
Here is a quick comparison chart for a Goliath re-rolling an attack against a particular AC.
| Primary | Secondary | ||||
|---|---|---|---|---|---|
| 30 | +11 | 25 | +6 | ||
| 29 | +12 | 24 | +7 | ||
| 28 | +13 | 23 | +8 | ||
| 27 | +13 | 22 | +8 | ||
| 26 | +14 | 21 | +9 | ||
| 25 | +14 | 20 | +9 | ||
| 24 | +15 | 19 | +10 | ||
| 23 | +15 | 18 | +10 | ||
| 22 | +15 | 17 | +10 | ||
| 21 | +15 | 16 | +10 | ||
| 20 | +15 | 15 | +10 | ||
| 19 | +15 | 14 | +10 | ||
| 18 | +15 | 13 | +10 | ||
| 17 | +14 | 12 | +9 | ||
| 16 | +14 | 11 | +9 | ||
| 15 | +13 | 10 | +8 | ||
| 14 | +13 | 9 | +8 | ||
| 13 | +12 | 8 | +7 | ||
| 12 | +11 | 7 | +6 | ||
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