|Number muching. It's a tough job, but somebody's gotta do it.|
I've put together this article as a summarized introduction to Nikephoros' 40k Metrics system. 40k Metrics is a benchmarking system designed for the evaluation of the effectiveness of lists. I'll state right now that this isn't a guaranteed method of designing winning lists. It's designed as a tool to compare lists together that are of the same army and a similar type/theme. It won't work for comparing Space Marines to Dark Eldar, for instance, as the armies function with vast differences from each other and their units serve different purposes, as well. So what does it do? It allows you to compare, let's say, two different Imperial Guard gun line lists to see if a newer list can match similar firepower to a list that has established effectiveness or something similar. Let's take a closer look.
The system itself is quite simple, though it does require a lot of tedious math. Fortunately, 40k works in fractions of sixths and elevenths, so you see a lot of common numbers. You'll use all of these numbers to find out statistics for 4 different categories. Each of these categories is calculated for each unit in an army list, and then the sum of all the units respective categories are combined to produce the list's total rating. This rating is where you can garner a degree of how useful the list will be. The 4 categories are as follows: Dead MEQ Shooting (DMS), Dead MEQ in Close Combat (DMCC), Dead Rhinos Per Game (DRPG), and Dead Land Raiders Per Game (DLRPG). As you've no doubt noticed, these are all based around marine units. This is because MEQ armies are currently the most common army you'll fight (supposedly) at any given time, and it's also generally accepted that any list that can handle an MEQ list with ease should do suitably well against GEQ lists as well. So, let's break down what each category means...
Dead MEQ Shooting (DMS): This is how many marines a unit could kill in one round of shooting from 12" away. So, we'll use a unit of tactical marines as an example. They all have bolt guns and bolt pistols, except the Sgt. who has a Combi-Melta and a Power Weapon. So, in one round of shooting, you have 20 shots (the Sgt. would reserve the Melta for vehicles) at BS4 which means 3+ to hit which translates to 66% of the shots hitting (20*.66) = 13.2 hits. Now in order to wound you need 4+ because of S4 vs T4 meaning you wound 50% of the time (13.2*.50) = 6.6 wounds. Of the wounds you've generated, only 1/3 make it past the 3+ armor save so, (6.6*.33) = 2.18 DMS for the unit. You'd calculate the DMS for every unit in your list and add them together to find the total potential for your whole army.
Dead MEQ in Close Combat (DMCC): This is how many marines a unit could kill in one round of close combat when they have the charge. I'll be using the unit described in the entry above to work out an example. Try to keep up. So, 18 regular attacks and 3 Power Weapon attacks at WS4 vs WS4 means you need 4+ to hit or 50%, so you'd get (18*.50) = 9 regular hits and (3*.50) = 1.5 Power Weapon hits. To wound, you need 4+ or 50% so you'd have (9*.50) = 4.5 wounds and (1.5*.5) = .75 unsavable wounds. From there, you'd subtract the armor saves from the regular attacks taking out 2/3 of them for the 3+ save. This would give you (4.5*.33) = 1.49 unsaved wounds plus the ones from the Power Weapon (1.49+.75) = 2.24 DMCC for the unit. Again, you apply this across your whole list to determine your close combat effectiveness.
Dead Rhinos Per Game (DRPG): This is how many penetrating hits a unit can get on a rhino (since it's a common sight and equivalent to most light armor) through the course of a game. That last part is important. Unlike the other 2 numbers, this is how effective a unit can be against light armored targets throughout a whole game. So, again, using the unit described above, we'll figure out the number. Now, it's important to remember here that only units solely dedicated to fighting transports in close combat will use a close combat score (ie: Terminators with Chain Fists, Monstrous Creatures, Etc.) and also do so in lieu of shooting, while normal units will use their shooting capability. Since the unit from above has a Combi-Melta, we'll be using that and we'll also assume that the player was able to get it into range for it's bonus. So, we have 1 shot at BS4 (1*.66) = .66 hits. Here's where it gets a little tricky, now we need to figure out what we'd have to roll for a penetrating hit. The armor value is 11, but with the Melta we get 2 d6 for our roll as opposed to 1. You'd need to roll 12+ and since you can't roll 1 with 2 dice, the denominator of the fraction is instead, out of 11. So, you'd have [.66*(7/11)] = .42 penetrating hits. Now, with other weapons that could be fired more than once, you'd multiply this final number by 5 to get the number of penetrating hits for the game, but since we have a Combi-Melta in this unit, the number of dead Rhinos (penetrations, NOT destroyed results) stands at .42 for a game.
Dead Land Raiders Per Game (DLRPG): This is how many penetrating hits a unit can get on a Land Raider (since it's probably the most common AV 14 vehicle you'll come across in play) through the course of a game. Much like DRPG, the final score for DLRPG is multiplied by 5 at the end to find the number of penetrating hits that could be scored against a Land Raider during an entire game. Again, only units solely dedicated to close combat can count that score and would do so in lieu of shooting. So, let's get cracking, and again, with the squad from above. So, you'd start with 1 Combi-Melta shot at BS4 (1*.66) = .66 hits and again, you'd work out what you'd need to roll on the armor table to get a penetrating hit and get (.66*4/11) = .24 penetrating hits. Again, while this number would normally be multiplied by 5 to get a result for the whole game, the Combi-Melta can only be used once, so the number of dead Land Raiders stands at .24 per game for this unit.
So, this Tactical squad's score when tallied up would look like this:
However, when you take 5 Grey Hunters with a Melta and a Wolf Guard with a Combi-Melta your get this:
As you can see, this is a powerful means for comparing the effectiveness of units. You can tell from the numbers, the Tactical Marines have a slight advantage against infantry (due to greater numbers) while the Grey Hunter's have a lot more reliability against varying target types (due to how they're kitted out). This gives a great base comparison between these 2 units. Normally, you wouldn't compare units from different armies, but because they're both Space Marine units of a sort and because I don't feel like doing the math, there you have it.
This should give you the gist of how the numbers are crunched and how you can build up some very interesting benchmarks to be used across different lists. I can say that the one common thing I've seen among successful lists is a very high DRPG (some over 60). I believe this relates more to the current meta of mechanized lists more than anything. So go ahead and start going over your own numbers. You'll be very surprised at what you find and may even save yourself the effort of testing lists that cannot be competitive just by their stats. First, there are a couple guidelines.
Templates: For the sake of preserving your sanity, let's assume that small blasts hit 3 models each time, while large blast and flame templates hit 5 models each time.
CC against Vehicles: Since you can get a ridiculously high number of penetrating hits on vehicles with units like Meganobs, the number of penetrations that a unit can get against vehicles in close combat through the course of a game is limited to 15. This is to prevent the statistic for the army from being skewed as it's unlikely a close combat unit will damage than that many vehicles in 5 turns. Also, assume vehicles have moved at combat speed when working out the number of hits. This provides a fair average.
Again, I'd like to remind you that this system was developed by Nikephoros at Bringer of Victory. For more introductory information and some more examples, you can check out his initial article here. He's also got an FAQ page for 40k Metrics that you can check out here, though I'd like to think I addressed most of those concerns in my article.
I've gone through and done the tonnes of math for last falls local 'Ard Boyz for the top placing lists as well as the lowest placing lists and will be doing an article on my discoveries in the near future. In the meantime, I'd be open to hearing any one's thoughts, questions, or even how their lists came out when all of the math was done. :)