In Hammer of Math, we tackle key statistical questions and issues in Warhammer 40k. This week we’re looking at modifiers, re-rolls, and how to make decisions around using these in games.
Something we’ve talked about before – but not necessarily in Tenth Edition – is the math around re-rolls, modifiers, and abilities. Given that it’s been a long time since we last discussed those, now feels like a good time to go back over some of the basics with regard to each, and talk about how you can make better decisions around using those abilities.
Let’s start with a simple one: Modifiers vs. Re-rolls, specifically:
Is +1 to Hit Better than Re-rolling Hit Rolls?
This is a good one. While there aren’t a ton of situations in the game where you can explicitly choose which of these abilities you want for a specific unit, there are often times you’ll have to choose between units with these abilities, and understanding how these abilities impact your chances matters. Also note that while we’re talking about hit rolls here, the same principles apply to wound rolls as well.
The short answer is: It depends on what you need to roll.
Let’s dive into the long version, and use hit rolls as an example. For any given To Hit roll, there are five possible values we can be trying to hit, i.e. WS 2+, 3+, 4+, 5+, and 6+, with rolls of 1 always being a failure. Each of these states gives us different odds and results depending on the modifier we’re applying so let’s go through each.:
WS 2+
In this situation a +1 to hit is meaningless unless we’re being affected by other modifiers, and a re-roll of a 1 is identical to the ability to re-roll any hit rolls. So re-rolls are always better if your target number is 2+. This is also the only case where re-rolling 1s is better than +1 to your roll. Note that at a 2+ with re-rolls your odds of success are 97.2%, so it’s not uncommon to turn all of those into hits. We’ll come back to this.
WS 3+
At 3+, re-rolling all hits gets us to an 89% conversion rate on our rolls, which is slightly better than a +1 to hit, which will give us 83% odds. You’re not going to feel the difference between these most of the time – it amounts to a difference of one hit per 20 attacks. Likewise, +1 to hit is slightly better than re-rolling 1s to hit on a 3+. Again, not something you’re going to feel most of the time as it amounts to one hit less per 20 attacks.
WS 4+
At 4+ we have an interesting result; this is the widest gulf between re-rolling all hits and +1 to hit, and the place where you most want full re-rolls. The difference still isn’t huge – 1.7 hits this time in 20 attacks – but it’ll be noticeable.
WS 5+
At 5+ the differences between re-rolling all hits and +1 become more slight, though the value of re-rolling 1s drops much faster.
WS 6+
At WS 6+ we finally see a reversal and the reason the answer to this question is “It depends” – at this point, +1 to hit is a slight improvement over full re-rolls and nearly twice as good as re-rolling 1s to hit.
Special Abilities and Fishing for Results
Of course, there are other major factors when it comes to these abilities, and the most notable of these are the weapon abilities, specifically SUSTAINED HITS, LETHAL HITS, and DEVASTATING WOUNDS. These abilities are good on their own for various reasons – we’ve talked about Sustained hits vs. Lethal Hits before in this Hammer of Math, but it’s worth revisiting this question: When do you want to re-roll successful results to “fish” for better results?
Again, this depends on what your target hit roll is, and the ability you’re using. Let’s start with the easiest one – SUSTAINED HITS. For these I’m going to use some concrete examples, because they give a more immediately applicable result.
Sustained Hits and Re-rolls
Chaos Space Marine units can use the Dark Pact ability to get SUSTAINED HITS 1 or LETHAL HITS on a unit in either the Shooting or Fight phase. A unit of 5 Legionaries with two heavy melee weapons and an attached Master of Executions charges an enemy unit on an objective and completes a Dark Pact, gaining SUSTAINED HITS 1. The enemy unit has sustained casualties, and as a result, they can re-roll the hit roll when attacking the enemy unit. Does it make sense to re-roll hits for The Master of Executions? What about the attached unit?
Let’s start with the unit. The two heavy melee weapons each have 3 attacks which hit on a 3+. That’s six attacks, and on average, we’d expect four of those to hit, with one result of a 6 to trigger SUSTAINED HITS 1, giving us an expected total of five hits. If we re-roll the two misses, on average giving 1.3 additional hits and two chances for another sustained, giving me an additional expected 1.7 hits total. So if I re-roll misses, my expected total is 5.7 hits. Now what if I re-roll all of my non-Sustained results? well in that case, I re-roll five of the six attacks, and this time around I generate an expected 4.2 hits, bringing my total to 6.2 with the two I’d already generated on my first six. That’s slightly better than just rolling failures, and this pretty much holds any time you have Sustained Hits in play, regardless of your target hit roll. The same will hold true for the rest of the unit’s attacks.
That said, you won’t always want to re-roll successful hits – it’s definitely a volume play, and will likely disappoint you if you’re re-rolling successful hits with say, a pair of meltaguns. But for high volume shots, take the chance.
Devastating Wounds
Another common situation where we’d want to fish for results is when we can combine re-rolls to wound with the [DEVASTATING WOUNDS] ability. This is fantastic anywhere it appears, and worth building around – the most common places you’ll find this are on Forgefiends, Chaos Lords with Thunder Hammers, and Infernal Masters in the Thousand Sons.
The Infernal Master with the Arcane Vortex Enhancement is one of the game’s most lethal units, able to combine a S7, AP-2, 2 damage, Psychic Torrent weapon with the Devastating Wounds ability thanks to the Detachment rule, and when paired with a unit of Rubrics, can either re-roll 1s to wound or all wound rolls. On top of that, once per turn you can change one of his hit, wound, or save rolls to a 6, getting an automatic 2 damage boost.
Against a target you’re wounding on a 3+ (most infantry targets), you generally want to re-roll failed wounds instead of fishing for 6s. Doing so gets you slightly better results against most targets, though it’s worth noting that against units with a very good save pushing through more devastating wounds might be a better play.
Final Thoughts
That wraps up this week’s Hammer of Math but hopefully you have the tools you need now to make more informed decisions about how to use these abilities and evaluate them on units. If nothing else, it should hopefully help you understand the mechanics around fishing for 6s and how you can best use re-rolls to kill things in games.
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