Wolf Standard: A Statistical Analysis

This article is here to determine the viability of paying 10 points for a wolf Standard. First, let's take a look at the exact wording of the item:

Once per game, a unit that includes a Wolf Standard may call upon the power of the wolf. For the duration of the next assault phase, all models in that unit may re roll any dice rolls of one.

Seems pretty simple, even seems like a bad wolf priest at first thought since you can only re roll 1's. BUT, you can re roll all dice thrown that assault phase...think of all of the die rolls you make in an assault phase. You can re roll 1's for difficult terrain on your charge move, to hit rolls, to wound rolls, armor saves, armor pen rolls, and sweeping advance just to name the main ones.

We're going to focus on the main rolls we care about...hitting and wounding. Instead of hitting with 50% of your attacks against models with a 4-8 WS, you'll hit with 58.33%. 8.33% doesn't seem too serious, especially for just one round...is it really worth 10 points? Well, let's say you have 8 Grey Hunters in the first round of combat when you use the banner. Because of counter-charge, you'll have 3A each regardless of if you or your opponent charged. That is 24 Attacks. Assuming you're going up against 4WS 4T opponents (and usually you are), you're going to get 12 hits and 6 wounds before armor saves without the banner. When you roll your 24A with the banner, however, math-hammer says 4 will be 1's. You just increased the number of attacks in your unit, effectively, by 4 since you get to roll 4 additional attack dice. Well, now that you've hit 14 times (12 initial hits, and 2 off of your 4 bonus attacks). With those 14 dice you'll get 2.33 1's and 7 rolls of 4+. The 2.33 re-rolls will net 1.17 wounds. This is a total of 8.17 wounds. Based on our hypothetical opponent, you would need to make 32.67 attacks to cause 8.17 wounds without the banner. Essentially, we got 8.67 additional attacks for one turn for 10 points. The more important thing to note is that we increased our wound output by 36.11% against 4WS 4T opponents for one turn with our basic attacks. So, 5 Grey Hunters would cause 5.1 wounds instead of 3.75 and 10 Grey Hunters would cause 10.2W instead of 7.5W.

Well, that's fine for when I'm fighting Marines and Orks, but what about IG, Eldar, Nids? What about when my Wolf Guard with a Power Fist is attached to the unit? What about when Ragnar is in the unit? Heck, that's a lot of calculations to have to do to figure out if we want to know Wolf Standard's viability across the board...or is it?

Here the a list of the percent chances of rolling a certain number or higher, right next to it I've put the percent chance of rolling that number or higher while re rolling 1's.

6+ 16.67% 19.44%
5+ 33.33% 38.89%
4+ 50.00% 58.33%
3+ 66.67% 77.78%
2+ 83.33% 97.22%

Notice a pattern? In every case, the ratio that the percent chance went up by was 1/6. In retrospect, it seems painfully obvious that this would be the case since we're going to be always re-rolling 1/6 of our dice. Well, that is good and fine for a single roll (and also good for pointing out that we'll be making 77.78% of our armor saves instead of 66.67%), but we're re rolling our "to hit" AND our "to wound" dice. Again, I first put the chance of causing a wound with a single attack and followed it by the chance to wound with a single attack re rolling all 1's. I've included the most common instances we'll come across, but take note that 4+ to hit and 3+ to wound is the same as 3+ to hit and 4+ to wound mathematically so I have only included it once here for brevity's(HA!) sake. If you try and do some of these calculations, please note that I originally took everything out to 10 significant figures and have rounded to 2 decimal places for ease of reading.

3+ to Hit and 3+ to Wound - 44.45% 60.50%
4+ to Hit and 2+ to Wound - 41.67% 56.71%
4+ to Hit and 3+ to Wound - 33.33% 45.37%
4+ to Hit and 4+ to Wound - 25.00% 34.03%
4+ to Hit and 5+ to Wound - 16.67% 22.68%
4+ to Hit and 6+ to Wound - 8.33% 11.34%

Once again we have a pattern across the board; you're getting a 36.11% increase in output when you incorporate both the "to hit" roll and the "to wound" roll.

In conclusion, we know that we're going to increase the success of all single rolls by a ratio of 16.7% and increase our total wounds caused by 36.1% for one turn with Wolf Standard, regardless of who is making the attacks or who they're attacking. Based on this, if you have any intention of your Grey Hunter squad getting in close combat, it should be more than worth the extra 10 points to increase your effectiveness by so much for one crucial turn...and all for the cost of a single Hunter-Killer missile.

If you guys enjoyed my article on Space Wolves tactics, then I'd suggest you check out Space Wolves Grey. I mentioned it last entry, but this site is everything you want out of a website dedicated to a particular army. They have painting and converting tutorials, really good tactics articles, army lists, pictures of their painted armies, and they're going to very soon start posting battle/tournament reports. In the mean time, next time I'll be posting some info on my Sapce Marine chapter, The Sons of Euclid.