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Labmouse, have you thought about factoring survivability/fear factor into the equation somehow?

I'm not quite sure how that would be possible mathematically...

And what about random rolls resulting in improved/decreased DPP?
For example, giving my DP three rolls on Biomancy makes it much more likely that he will get Warp Speed, which makes him have more attacks. But that costs 75pts, as compared to the 25pts I COULD spend and still luckily get Warp Speed. OR the 75pts I could spend and NOT get it, thus making him no more better than a DP with no powers.

 xole wrote:
I knew it. Those laser pointers are deadly. I no longer feel about bad about throwing wave after wave of guardsmen to their death.

They are not deadly. They are cost-effective. There is a difference

You can't throw 300 guard onto the table and call it a day. They would not all be able to shoot, therefore would not be able to use that firepower.


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 Elric Greywolf wrote:
Labmouse, have you thought about factoring survivability/fear factor into the equation somehow?

I'm not quite sure how that would be possible mathematically...

And what about random rolls resulting in improved/decreased DPP?
For example, giving my DP three rolls on Biomancy makes it much more likely that he will get Warp Speed, which makes him have more attacks. But that costs 75pts, as compared to the 25pts I COULD spend and still luckily get Warp Speed. OR the 75pts I could spend and NOT get it, thus making him no more better than a DP with no powers.

Look up the words Resilience Per Point on the last page. I link to an article I wrote earlier this year describing the same point. I talk about this a lot in the simhammer segments on the 11th company podcast.

For your biomancy rolls, you would need to caculate the values for your prince with iron arm or warp speed. They would change to the base value. It would take some thinking to come up with a way to determine if its worth the rolls. You would need to figure out the chances of you getting the powers you want.

Awesome thread, I've checked out your site too as well. Very interesting stuff.

40k being a game of dice is in essence a game of probabilities. Having a deep understanding of the probabilities will make you a better player. Not only will it allow you optimise your army list but allow you to form more optimised tactics and strategies against your opponents.

If possible I'd like to see the numbers for dire avengers, guardians, wraithguard, kroot and fire warriors please.

Hey labmouse, really liked your previous writeup "Abbadon Will Take Your Lunch Money"

I was wondering if you could do some DPP analysis for some Tau units. Crisis suits, the rip tide, Sky Ray, and Fire Warriors with Plasma rifles!

Thanks for any help you provide.

-From

Thanks Lab, I'm ok with how the Chaos Marines performed.
Just reinforces the idea that they are best utilized as cheap shooters.

Labmouse,

Your numbers are great, but I think you should tweak your formula a little. The issue I have is that it isn't very meaningful to compare your vs. GEQ numbers against your vs. MEQ numbers, etc. This is because you are calculating the number of models killed per point, and then scaling up by a factor of 1000 so the numbers are easier to read. So your numbers can be interpreted as "Number of target (GEQ, MEQ, or TEQ) models killed by 1000 points of unit X".

To me, what you should do is also multiply by the value of the models you're killing. That's what I did in my numbers. If you use a scaling factor of 100, you can interpret the numbers as "Number of points killed of GEQ (or whatever) models by 100 points of unit X shooting".

I think this makes the numbers a bit more useful, as you get a better sense of specialization. It also helps with scenarios like "Is it generally worth it for my Guardians to hop out of their Wave Serpent to paste those Terminators, even if they get wiped out the following turn", because a number over 100 indicates a good exchange, all else being equal.

Anyway, I want to reiterate that I think your numbers are great, and useful, and thanks for starting the thread.

So, in the end, guardsmen with lasguns are better than like everything.

I suppose that that's the limitation of looking at efficiency instead of effectiveness.

 SoloFalcon1138 wrote:
Don't forget to calculate the psychological factor of certain units. When people see a Land Raider on the table, they shoot it. When people see a tactical squad, it's not much of a threat till it hits an objective.

Over analyzing data is great when you have the time, but ultimately, it's a waste. Dice fail and strategies fall apart. That's what happens. And units, from book to book carry different points values and units have different roles to play. Instead of making overly complicated algorithms, just play!

You talk about "The psychological factors of certain units." and then go on to discredit analyzing probability going as far as to claim it's a "waste". We're suppose to keep it civil here so I'll attempt to point out to you that your logic is ing irrational as .

Perhaps in your playgroup people are affected by the psychological impact of a toy tank. Where I play and in tournaments people don't follow this thought process, 40k is a game of dice, and thus probability. Taking the average of dice, while not perfect, is the best way to figure out the potential outcome of a situation on average. When you're going to make a tactical decision and you happen to know "On average the two TL devourers on my Flying Hive Tyrant are going to bring down this Stormraven." it helps you select a target with confidence.

Knowing what units combat others with a statistical advantage will help your target priority a TON, which saves time, which helps you plan ahead, which helps you play out your game in allotted amount of time, which helps you win games. In my experience Warhammer is not a game of picking fair fights, you want to have a general idea of what the tools in your army can massacre not beat by a small margin. When you pick the correct targets you can really see probability come into play.

The main thing that you don't get out of the statistics is movement, positioning of models, and the general lay-of-the-land(board). Which in itself is a huge part of the game, but the above paragraph explains what you can apply the math to and it WILL help.

I know that dice fail and some times a strategy falls apart because of it. But claiming that probability is a waste of time when it literally is the only thing we have to go on and is what the game is designed around is foolish and insulting to anyone who has put some thought into it.

MY apologies for calling you out here. I've read many of your posts and you're welcome to call me a WAAC jerk for it. But to some people doing well at a game is the fun, not just the game itself.

For the record, I agree that playing will teach you more than mathhammer, but I completely disagree that it's a waste.

If two players are equally skilled at pushing the plastic, all that's left is mathhammer anyway.

 Ailaros wrote:
So, in the end, guardsmen with lasguns are better than like everything.

I suppose that that's the limitation of looking at efficiency instead of effectiveness.

Nope, the takeaway is that Guardians are better than like everything. (Although Ravenwing with the Banner are slightly better at killing GEQ)

That's a turnabout for sure. Kill the guardians before they reach 12"!

Yeah, at least it's somewhat fluffy. The Guardian has a stat line that's almost as weak as a Guardsman, but the Eldar technology lets them slaughter genetic supermen as long as they're in range.

Conceptually I don't mind it. It's just that meqs in general are getting into the joke territory, instead of being balanced out.

Totally agree. I remember back in 5th when the Vanilla Space Marine codex only had a few viable, niche builds (Bikers and Vulkan). Now that state of affairs pretty much covers all Marine codexes.

The real sad thing is that my raw numbers say the Guardians have somewhat better CC offense too, on a per-point level anyway. The extra +1S doesn't make up for the nearly double price tag.

Tactical marines need to look like grey hunters minus the counter attack for starters. THEN they will be more like functional marines.

I think range of weapon and AoI not to mention LoS, throw a spanner I this theory hard..
And measuring only AoI is haphazard at best..
Say you do look at jump infantry.. Moving 12" with 12" weapon does not equal moving 6" with 18" weapon..
Your far more exposed at worst case.. And can shoot at units an 18" weapon can't see best case..
This also does not take into account JSJ...
I think range/ cover and LoS, to name a few variables, makes maths hammer unreliable at best.. Bum-steer in the wrong direction at worst..
And in an edition of cover saves, flyers and strange rules galore.. MH is even less reliable than before..
If MH really could win battles.. We wouldn't need models/ terrain or dice...

Mathhammer is as reliable as it has always been. It tells you what kind of damage to expect from each unit. It never did tell you how to push the plastic.

Martel732 wrote:
That's a turnabout for sure. Kill the guardians before they reach 12"!

Right..well, that's why I mentioned area of influence as the values you get from a unit. Sure, when guardians are within 12" of enemies they are hell on wheels on a point-for-point basis, but they are fragile and they have a limited AoI (area of influence)

That's the balancing factor of the unit. Does the first value (DPP) outweigh the AOI and RPP values? Well, that's really up to you when selecting the army and is not the primary goal of this exercise. The goal of this exercise is to ask "Is X better than Y for damage" or "Does it actually help if I add melta guns to vet squads".

That's not entirely true Martel732. The limits of "how many X will Y kill this phase" will not tell you how to win a game.

However, there is more math to the game than just casualty figures. Advanced mathhammer can tell you exactly when you should start moving instead of shooting. It can tell you where your best choices are to be made.

Just like people ignored math in baseball for years, it doesn't mean there's no math there, it just means you're not using it yet. And, as seen in the movie Moneyball, when you start using more advanced math, you get good results.

You can create a mathematical model for the entire game, and, if we ever see a computer AI player, this will be how it works. Every possible move can be said to move your overall position in this model either closer to victory or closer to defeat. Computing the expected change in position for all these moves and then selecting the one that increases your chance of victory the most is at the core of mathhammer.

 MrEconomics wrote:
Your numbers are great, but I think you should tweak your formula a little. The issue I have is that it isn't very meaningful to compare your vs. GEQ numbers against your vs. MEQ numbers, etc. This is because you are calculating the number of models killed per point, and then scaling up by a factor of 1000 so the numbers are easier to read. So your numbers can be interpreted as "Number of target (GEQ, MEQ, or TEQ) models killed by 1000 points of unit X".
.

I've been chewing over your forumla as well. One of the worries I have is assigning point values to GEQ, MEQ or TEQ. CSM TEQ are 13 points cheaper than deathwing, for example. When you upgrade MEQ with a special weapon, a heavy weapon, a rhino, and a PF wielding searg the point per model goes well over 16. What happens if someone brings bare bones DA instead?

Its really a tough situation. In a perfect world, I would have a program that would just do this for me, but I don't want to handle all the loads of data entry to a database to make it happen. At my last check there were over 600 different units in the game, each with different stats, different equipment, etc. That's more data entry than I wish to handle.


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 Redbeard wrote:
Just like people ignored math in baseball for years, it doesn't mean there's no math there, it just means you're not using it yet. And, as seen in the movie Moneyball, when you start using more advanced math, you get good results.r.

QFT.

Math does not mean your going to win a game. Going over the math means that when you play you will have a better understanding of the odds.

Why do we do the math instead of just play more warhammer? Well, I don't have a 40k table here in the office. When I'm waiting for people to show up at a meeting, I can play with numbers on excel and mathhammer.

In a perfect world, the game designers would use a formula like this in order to appropriately cost their units.

It would also include weighting by how much you'd expect to see of each type, and what it's intended purpose is.

For example, the formula used to price an infantry unit expected to engage other infantry might be something like:

Point cost of model X = .35*(resiliency vs small arms) + .15*(resilience versus big guns) + .20*(damage output versus light infantry) + .20*(damage output vs heavy infantry) + .05*(damage output versus MC) + .05*(damage output versus vehicles).

The modifiers could be tweaked too so that an anti-tank unit's price is based more on how well it hits tanks, and gives less weight to how it hits infantry.


As a player, if you want to use these numbers to decide what's efficient to bring, you need to weight what you expect to see in a tournament setting. You might have the most cost-effective unit in the game at killing AV14 vehicles, but if you know that no one in your meta is running them, that unit really isn't that valuable, and needs to be weighted down as a result.

Redbeard wrote:In a perfect world, the game designers would use a formula like this in order to appropriately cost their units.

Except they wouldn't.

This metric only measures efficiency, and efficiency is a tiny factor in 40k. Effectiveness is really what is important, and durability is a close second. Also other lesser things like mobility and other special rules the model has. And the kinds of access it has to which kind of upgrades, and what its role is relative to the rest of the codex it's in, and now allied armies.

Using a single metric, or even a couple of metrics alone would horribly skew the game beyond reason. Using just the results of these numbers, every player would play eldar, and every player would play an army of more or less only guardians. But think practically for a moment - would an army of only guardians win? No, not even close.

That's because things are way more complicated than a numerical representation of efficiency of firepower against certain target types. Not that that information can't ever be useful, of course, but it shouldn't be relied on as the only, or even primary way of judging units.

Really great stuff Labmouse.
Comment about scatter laser actually decreasing DPP of guardians made me reconsider some choices, especially expensive character upgrades. Would You be so kind and run the math for striking scorpions with and without tooled up exarch? I am mostly positive that DPP with him gets worse vs GEQ and better vs TEQ...not sure about MEQ as his price is really steep. Once more thanx for this food for thoughts :-D
Cheers.

 labmouse42 wrote:


I've been chewing over your forumla as well. One of the worries I have is assigning point values to GEQ, MEQ or TEQ. CSM TEQ are 13 points cheaper than deathwing, for example. When you upgrade MEQ with a special weapon, a heavy weapon, a rhino, and a PF wielding searg the point per model goes well over 16. What happens if someone brings bare bones DA instead?

Its really a tough situation. In a perfect world, I would have a program that would just do this for me, but I don't want to handle all the loads of data entry to a database to make it happen. At my last check there were over 600 different units in the game, each with different stats, different equipment, etc. That's more data entry than I wish to handle.

You make a good point here. I guess our different formulas do better for our different purposes. I keep mine in a spreadsheet to do hypotheticals, so it isn't too hard to tweak the point values if I want.

What you're doing is more systematic, so I think you're making the right call for your purpose. By the way, if you have plans to do something beyond tabulating these figures, like trying to use them to predict point costs for units (or put another way, try to find objective evidence for which units are over/undercosted, hit me up. I've always wanted to do something like that, but I just can't justify spending the time when I could be trying to write something I can publish to help my career. (I'm an applied microeconomist) In particular, I'd love to be able to quantify codex-creep in a way that works across all codexes. It would also be interesting to see how well the formula would fit.

 Ailaros wrote:

Redbeard wrote:In a perfect world, the game designers would use a formula like this in order to appropriately cost their units.

Except they wouldn't.

This metric only measures efficiency, and efficiency is a tiny factor in 40k. Effectiveness is really what is important, and durability is a close second. Also other lesser things like mobility and other special rules the model has. And the kinds of access it has to which kind of upgrades, and what its role is relative to the rest of the codex it's in, and now allied armies.

Using a single metric, or even a couple of metrics alone would horribly skew the game beyond reason. Using just the results of these numbers, every player would play eldar, and every player would play an army of more or less only guardians. But think practically for a moment - would an army of only guardians win? No, not even close.

Did you completely fail to read the rest of my post? If you looked at the sample I put in, you'd see that resilience was a factor, as was effectiveness versus a range of targets.

Mobility (or, more importantly, Area of Control, as LabMouse pointed out) should also be part of the general equation. You don't need to be mobile if you're equipped with a weapon with a 60" range that ignores LoS...

Great stuff labmouse.
I do think vehicles + MC should be included here, as well as flyers, otherwise some units cannot be compared effectively on their efficiency.
I may at some point come around to programming something for this, it shouldn't be too hard.
PM me if you're interested?

The biggest challenge to such a project is data entry. There are over 600 different units in the game, so building that database is daunting work.

If we have volunteers to enter those values -- about one volunteer for every army, then it would be very feasable.
All people would need to do is get a excel sheet mailed to them with the proper template and then fill it out and return it.

Any takers?


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 MrEconomics wrote:
What you're doing is more systematic, so I think you're making the right call for your purpose. By the way, if you have plans to do something beyond tabulating these figures, like trying to use them to predict point costs for units (or put another way, try to find objective evidence for which units are over/undercosted, hit me up. I've always wanted to do something like that, but I just can't justify spending the time when I could be trying to write something I can publish to help my career. (I'm an applied microeconomist) In particular, I'd love to be able to quantify codex-creep in a way that works across all codexes. It would also be interesting to see how well the formula would fit.

Here is how I would illustrate the codex creep.

You can create the DPP/RPP/AoI/Troop values for each army. You can get a sum total of these values, as well as the number of units that pass X threshold of the 4 values (ie, an awesome unit) . Compare these armies to each other.

If a new codex comes out and the new values are higher than the previous codex's you can quantify codex creep.

 labmouse42 wrote:
The biggest challenge to such a project is data entry. There are over 600 different units in the game, so building that database is daunting work.

If we have volunteers to enter those values -- about one volunteer for every army, then it would be very feasable.
All people would need to do is get a excel sheet mailed to them with the proper template and then fill it out and return it.

While this would be the target, it shouldn't be too difficult to create a UI that asks the end user to input the stats for the unit firing/chopping and the stats it wants to measure efficiency against.
Beyond that an algorithm could be run to measure efficiency against a pre-determined, limited number of targets, toughnesses, save values, armour values etc.
And then beyond that we fill out the profiles of every different unit.

3-stage attack.
Easy to do, but stage 3 would be tedious and time consuming.

Gorgnoob wrote:
Really great stuff Labmouse.
Comment about scatter laser actually decreasing DPP of guardians made me reconsider some choices, especially expensive character upgrades. Would You be so kind and run the math for striking scorpions with and without tooled up exarch? I am mostly positive that DPP with him gets worse vs GEQ and better vs TEQ...not sure about MEQ as his price is really steep. Once more thanx for this food for thoughts :-D
Cheers.

This is 10 scorpions with no upgrades.
We will assume that 5 scorpions are in range to use their mandiblasters.
GEQ : 44.66
MEQ : 13.07
TEQ : 6.536


This is 10 scorpions, including one exarch. This is an exarch with no special gear.
What this shows is that adding an exarch has no net output on increased DPP. It lowers your RPP slightly.
I think this is worth the trade as it allows you to focus more points in a concentrated area, in addition to letting you have a character in the unit.
GEQ : 43.83
MEQ : 13.27
TEQ : 5.71


What happens when we add a biting blade? This increases the STR of the exarch by 2, at the cost of 1 attack.
GEQ : 43.83
MEQ : 12.71
TEQ : 5.56
In every case, they lose or tie DPP. The biting blade sucks.


What happens when we add a chain sabres? This increases the STR of the exarch by 1, and gives rending.
It also gives a keen gun.
GEQ : 43.86
MEQ : 13.74
TEQ : 6.0
Given that the saber comes with an assault 2 bladestorm gun, I think its full of win.


What happens if we add crushing blow to the biting blade?
GEQ : 43.33
MEQ : 13.61
TEQ : 5.97
You can see that crushing blow lowers the DPP vs infantry. Its really not worth it with the biting blade.


This is the scorpion claw, even with its heavy investment of 30 points.
GEQ : 41.27
MEQ : 17.72
TEQ : 6.00
Its worse against GEQ and better against MEQ. There is a strong case to be made for the claw.
Crushing blow will just lower DPP values, but gives additional capacity to damage armor.


Are you curious to see how banshees stack up?
GEQ : 44.44
MEQ : 22.22
TEQ : 3.7
Their DPP is almost exactly what a scorpions is vs GEQ, but their other abilites vs MEQ are much higher. They are horrible vs TEQ.
How does it even out? Scorpions can take a bit more punishment in return.

If you're still taking requests, I'd be curious about doom siren, ubergrit noise marines compared to either dual flamer GH or PM.