Cut the BS

My last analysis on rerolls brought up a couple of questions from the audience, with comments mainly focusing on Ballistic Skill.  One in particular about the merits of the Vindicare assassin got me thinking about the how to evaluate shooting ability.  In line with my usual form, here’s a question:

A lowly guardsman stands in the open, he faces on one side, the mighty Eldar Phoenix Lord Fuegan Burning Lance (BS7) and on the other side Krazy Kullen (BS4) the weapon operator on a Chaos Rhino.  Fuegan’s melta weapon is obviously more potent than Kevin’s twin-linked bolter.  But who is more likely to miss?

So my earlier treatise on rerolls only considered ‘normal’ rerolls where whatever you needed to get the first time was the same for the reroll.  Cunning commenter Caolan pointed out that at very high BS the shooter gets a reroll on a miss, but it’s not the same as the initial roll.  So a BS of 6 gets you a hit on a 2+, and  a 6+ reroll if you miss; BS7 gets the same 2+ to hit, with a 5+ reroll on a miss; BS8 is 2+ 4+; BS9 is 2+ 3+; and finally BS10 is 2+ 2+.

Rather than running the numbers in this post, have a look at my response to his comment at the bottom of this post.  But where I took it a step further this time is to calculate the odds to hit for BS1 to BS10 and for BS1 to BS5 with rerolls.  This gives us an interesting ranking of the relative accuracy of the BS values, and the impact of rerolls.  I’ve highlighted the rerolls in green to set them apart from the regular BS values.  The dark blue is the additional accuracy provided by the reroll (so under the dark blue is the basic odds to hit, the dark blue is the reroll, and the whole bar is the total accuracy).

Lo and behold the answer to our starting question appears before our very eyes.  It turns out that Eldar Phoenix Lords at BS7, are only as accurate as Chaos Rhinos with BS4 twin-linked bolters.  They are equally accurate. Who knew that Krazy Kullen was such a marksman?

What really comes through for me is how good BS4 rerolls are.  I’m known to have a fondness for Obliterators, and with twin-linked plasma AND melta at BS4 you can really see why.  More generally we can see that a reroll is better than a 1 point improvement (or more!) in BS for all cases except BS1 – but I think that’s a fairly well known thing already.

That said, you now have the definitive list from BS10 to 1 with rerolls, use it well my friends.