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A concept that I've been working with lately is the Dakka/Choppa per point of a model. Simply put, if your spending 150 points on models A, B, and C, do they deliver the same damage as 150 points spent on models X, Y and Z.

This post will cover ideas behind these differences and how to calculate them.


Algorithm
I've been striving for a algorithm that produces numbers similar to my RPP values (Resilience-Per-Point). As such, this my current formula.
((To Hit) * (To Wound) * (Failed Save) * (Failed FNP) * (Number of Shots)) / (Unit Cost) * 1000
....Or.....
(Models Killed) / (Unit Cost) * 1000

When running this formula, you should compare the entire units cost and the entire units capacity with weapons. This is because you need to give a fair assessment of the upgrades and overall costs of the unit. Some units have hidden fee's inside, such as a champion you must buy. Other units have 'mandatory' upgrades that are bought with them. One example would be a ghostwalker matrix on wave serpents.

I run this formula 3 times for each unit. One for GEQ, MEQ, and TEQ. This is because some weapons are better vs specific targets than others. MLs are better vs MEQ but useless vs TEQ. PGs don't produce the shots to be scary to GEQ, etc...


Wave Serpent
Lets look at a wave serpent vs GEQ
Scatter Laser = (.88889) * (.83333) * (.666667) * 1 * (4) = 1.96
SC = (.88889) * (8.3333) * (.666667) * 1 * (3) = 2.222
Scatter Laser = (.88889) * (.83333) * (.666667) * 1 * (4.5) = 2.222

Lets look at a wave serpent vs MEQ. You see we have 2 entries for the SC -- one for the non-rending wounds and one for the 1/6 of the time when it rends.
Scatter Laser = (.88889) * (.83333) * (.333333) * 1 * (4) = 0.987653333
SC = (.88889) * (.66667) * (.333333) * 1 * (3) = 0.592592
SC = (.88889) * (0.1666) * 1 * 1 * (3) = 0.444444444
Scatter Laser = (.88889) * (.83333) * (.33333) * 1 * (4.5) = 1.11111

This means that the serpent is killing 3.14 MEQ a turn and 6.42 GEQ a turn.
Lets assume the serpent has a ghostwalker matrix and a holo field, putting the cost at 155 points. This means the DPP value vs GEQ is 41.412 and DPP vs MEQ is 20.23.


DA TACs
Lets look at a DAs vs GEQ. For arguements sake, lets say they dropped down and are within rapid fire range.
Bolters = (.0.666666667) * (0.666666667) * 1 * 1 * (16) = 2.370368
PGs = (.0.666666667) * (8.3333) * 1 * 1 * (2) = 2.222

When shooting at MEQ, this is how the DA TACs do.
Bolters = (.0.666666667) * (.5) * (1) * 1 * (16) = 1.77776
PGs = (.0.666666667) * (8.3333) * 1 * 1 * (2) = 2.222

The DAs cost 170 (assuming PGs are 15 a piece, I don't have my book here). This means the overall DPP values for the DA squad are 45.52 against GEQ and 23.53 vs MEQ. If they are taking a drop pod, these values drop to 22.40 against GEQ and 19.51 vs MEQ.


What does it mean?
When shooting up close, DA drop pod tacs are actually roughly as good as serpents. If you can manage to get the bolter banner near, they can actually get a lot better.

Serpents also have a huge area of effect, so they can bring to bear all of their force, where marines dropping down will be limited. They are also more resistant to shooting, they are faster, and they can carry troops. Wow, serpents have a lot of perks.

DA troops have one other difference. They have ablative wounds instead of the vehicle damage chart. Vehicles are almost a binary in their ability to effect the game. They work or they don't. Sometimes you might damage them and knock off a gun, or immobolize them, but usually its a binary situation.
Units with wounds, however, don't have that. They are whittled down and as they take wounds they lose punch.
How does this make a difference? 5 bad dice rolls for you, combined with 5 extremely good dice rolls for your opponent will make a serpent army crumble. Those same dice rolls won't make a DA tactical army crumble.


Why tell me all this labmouse?
What I want to ask you all is this. Given the DPP measuring stick, we can run a number of analysis on differnet units. We can ask questions like "How much of an improvement do CMLs make in terminator squads" "Does the buff that prescience can give a squad really worth the 65 point investment for a librarian" "How much damage can CSM termiantors actually do". "Is it really a disadvantage to bring plasma guns in SW squads when your facing GEQ?

My question is this to ask the community. What other questions do you want to ask? What would you like to know wen comparing two units.

The good questions I'll answer here, or put them on an upcoming simhammer segment on the 11th company podcast. Thanks!

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!

I like it! I think most people already do something like this in their heads (I know I do), but it's nice to see numbers. I think the real usefulness comes in comparing units from the same codex, so comparing terminators vs tac marines would be good as an example.

I've done that earlier. Terminators shooty damage output is really lacking.

C:SM terminators really benefit from the CMLs. I did some tests and half their damage potential to MEQ comes from the CMLs. This leads for a lot of possibility of wolf guard termies who are not paying a premium for those power fists.

I'll do some more detailed analysis for you. Thanks for the reply.

Wave Serpants cannot be taken without another choice. With jetbikes being so good, i often have a problem fitting a squad of infantry into my list to take wave serpants

Exergy, I don't understand what your looking for. Are you wondering what the DPP + the DPP of guardians/avengers averaged out would be?

That is true. Dedicated transports have another hidden cost: passengers.

 SoloFalcon1138 wrote:
but ultimately, it's a waste

Why be such a nay-sayer? This guy has taken the time to put together a pretty well organized math tool to further analyze a game he is interested in. For those looking to make decisions based on the numbers and results this is perfectly viable.

So I dont think it's a waste and salute him for his math. However my mathing is horrible and this information is far beyond my comprehension.

I'd like to see the GH/CSM/PM standards of dual specials with bolter backup.

Part of that is selfish as I believe CSMs will actually out perform the other "better" choice in straight shooting.

Also, any work you can do with blast weapons would be great. Maybe compare a Vindicator to LC Predator or Oblits.

 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!

No, its not a waste. The analysis tells us which units to point at what. THEN the dice fail. But, if you made good decisions, the threshold for dice failure is more forgiving.

Also, I don't necessarily shoot a land raider. Or, if I do, I line up the best shot and try to have some love left over for its occupants. Admittedly, I'm a pretty cold player.

Serpents also have a huge area of effect, so they can bring to bear all of their force, where marines dropping down will be limited. They are also more resistant to shooting, they are faster, and they can carry troops. Wow, serpents have a lot of perks.

I don't think it's as bad as all that. Drop pods mishapless deepstriking also have a huge area of effect, and can also concentrate their firepower very well, while not allowing your opponent to shoot at them without interceptor before they get a chance to shoot, and drop pods also carry troops.

Anyways, let's see lasguns. S3 Ap- rapid fire 5 points per model.

I've been on both ends of drop pods, and I don't think they're all that. Space Wolf drop pods work primarily because of GH, not because of drop pods.

 Ailaros wrote:
Anyways, let's see lasguns. S3 Ap- rapid fire 5 points per model.

Yea, I'll do that for you.

I'll also check out blobs, blobs with SM ICs joining them and casting prescience on them.

Ill also check out vets in chimeras for you.

I've already done some of these calculations myself. I scale to 100 points, so interpret these numbers as: "How many points of the target will 100 points of the model/squad in question kill in 1 turn's shooting?"

I assume a GEQ target costs 5 points, a MEQ target 16 points, and a TEQ target 40 points. All targets are out in the open, have no FNP, etc.

Some highlights:

Ailaros' request: 33.3 GEQ/35.6 MEQ/44.4 TEQ
Grey Hunters (5 man squad, 1 Meltagun 16.5 PPM) 24.9 GEQ/28.0 MEQ/39.5 TEQ
Ravenwing Squad with SoD (30 PPM due to SoD tax) 39.5 GEQ/31.6 MEQ/39.5 TEQ
Guardians with Scatter Laser (11 PPM) 34.0 GEQ/69.0 MEQ/98.3 TEQ

Given that a typical TEQ squad will have some sort of upgrade, like a Cyclone Launcher, it's worth noting that a standard Guardian squad can expect to almost earn its points back in 1 turn of shooting at TEQ.

The numbers also show people who have issues playing Marines against Eldar have reason to complain. The effectiveness of Shuriken Catapults against MEQ/TEQ is nuts. For comparison's sake, 100 points of Marines with Plasmaguns (31 PPM) will kill 57.3 points of MEQ. And that's ignoring Gets Hot!. If you give the target 4+ cover the Guardians do ~54 points worth of kills against 28.5 for the Marines.

I really didn't need a rigourous analysis to tell that shuriken catapults own teqs, but it was a very good analysis anyway

Thanks.

You're right, it's pretty obvious, but I didn't expect them to be that strong on paper. They're almost 50% better on a per-point basis than Black Knights, for example. It's crazy that a basic troops unit can outperform a theoretical hard counter.

By the way, I just checked, and having a Scatter laser actually drags down the Guardians' efficiency pretty severely. Their numbers are 37 GEQ/ 79 MEQ/ 115 TEQ if you run them naked (9 PPM).

Terminators complete inability to live up to the fluff is one of the more disappointing aspects of 40K. Especially because terminators big liability is the T4 that they can't do anything about. The mighty terminators die miserably to the lasgun wall.

It's interesting, and yes,a drop pod of guys in your face should do as much to an enemy squad as a serpent sitting 24" away.

I think you really need a way to combine the resiliency and damage together to make this mathematical model work, along perhaps with some way to quantify versatility.

The Drop Pod unit, for example, can be dropped off and hammer one target, after which, it gets shot and/or charged. The Wave Serpent can avoid many threats simply by staying further away. If can re-position as the battle demands.

Not saying that making a model to represent this stuff is a bad idea, but it's important to make comparisons between units with similar roles.

I get a lot wins off C:SM drop pod lists. And that's with BA. Drop pods don't impress me unless they are filled with cheese, er Grey Hunters.

I think DPP combined with a similar equation for average survivability per point (I am assuming more math is required for armor, T, W, cover avg) would be a awesome useful tool.

 MrEconomics wrote:
By the way, I just checked, and having a Scatter laser actually drags down the Guardians' efficiency pretty severely. Their numbers are 37 GEQ/ 79 MEQ/ 115 TEQ if you run them naked (9 PPM).

There is one reason to buy at least one long range weapon. It allows the entire squad to kill past the 12" range. Otherwise they can only kill enemy models within 12".


Automatically Appended Next Post:

 Redbeard wrote:
I think you really need a way to combine the resiliency and damage together to make this mathematical model work, along perhaps with some way to quantify versatility.

That's an excellent point. What defines the overal effectivness of a unit? In my experience I have defined the following values that define 'overall effectivness'
- Dakka (or Choppa) Per Point (DPP)
- Resilience Per Point (RPP)
- Area of Influence (AoI)
- Scoring
AoI is a different than just range. Swooping hawks, for example can move 12", run another 4" then shoot 24" (40" total). The difference of overall AoI between the two are huge! This is because the area of a circle is defined by (radius squared * pi). The 24" static AoI has 452.16" in the AoI, while the hawk has 1256" in the AoI. Yep, t
hat means that the hawk can effect around four times as much of the board as the static 24" gun.
So in my view, you add the total threat range.

What makes the most effective unit? Well, a lot of that will be based upon your personal preference. Is DPP or RPP more important? Do you want to have troops with huge AoIs? Doing these exercises can help explain which units have the best values based upon your desire, giving you the best advantage in the game.

This is because humans arbitrarily assigned point values to units. These values were not mathematically based, so we can determine using math which are more effective. Since we all have a limited resource when we play (points) this helps us to have an advantage when playing the game.

 labmouse42 wrote:

 MrEconomics wrote:
By the way, I just checked, and having a Scatter laser actually drags down the Guardians' efficiency pretty severely. Their numbers are 37 GEQ/ 79 MEQ/ 115 TEQ if you run them naked (9 PPM).

There is one reason to buy at least one long range weapon. It allows the entire squad to kill past the 12" range. Otherwise they can only kill enemy models within 12".


Automatically Appended Next Post:

 Redbeard wrote:
I think you really need a way to combine the resiliency and damage together to make this mathematical model work, along perhaps with some way to quantify versatility.

That's an excellent point. What defines the overal effectivness of a unit? In my experience I have defined the following values that define 'overall effectivness'
- Dakka (or Choppa) Per Point (DPP)
- Resilience Per Point (RPP)
- Area of Influence (AoI)
- Scoring
AoI is a different than just range. Swooping hawks, for example can move 12", run another 4" then shoot 24" (40" total). The difference of overall AoI between the two are huge! This is because the area of a circle is defined by (radius squared * pi). The 24" static AoI has 452.16" in the AoI, while the hawk has 1256" in the AoI. Yep, t
hat means that the hawk can effect around four times as much of the board as the static 24" gun.
So in my view, you add the total threat range.

What makes the most effective unit? Well, a lot of that will be based upon your personal preference. Is DPP or RPP more important? Do you want to have troops with huge AoIs? Doing these exercises can help explain which units have the best values based upon your desire, giving you the best advantage in the game.

This is because humans arbitrarily assigned point values to units. These values were not mathematically based, so we can determine using math which are more effective. Since we all have a limited resource when we play (points) this helps us to have an advantage when playing the game.

And they can take away HPs from light vehicles as well before catapult range.

 hazal wrote:
I think DPP combined with a similar equation for average survivability per point (I am assuming more math is required for armor, T, W, cover avg) would be a awesome useful tool.

Resilience-Per-Point (RPP)


Automatically Appended Next Post:

Martel732 wrote:
And they can take away HPs from light vehicles as well before catapult range.

Agreed. It gives two AoI ranges for the guardians, which can be worth the loss of DPP vs MEQ.

Let's be honest here, the Eldar have meqs over a barrel already.

 labmouse42 wrote:
Exergy, I don't understand what your looking for. Are you wondering what the DPP + the DPP of guardians/avengers averaged out would be?

I just dont think you should compare apples to oranges. DT have to take passengers somewhere. Waveserpent to Venom to Psyback is fine. Tactical Marines to Shoota Boyz to Firewarriors is also fine.

thats too much math for my weak mind to handle. i just grab dice assume the worst and start throwing see which works better lol

 minigun762 wrote:
I'd like to see the GH/CSM/PM standards of dual specials with bolter backup.

Grey Hunters
Assuming that you have 10 grey hunters with 2 PGs. The GH get the first PG for 10 points and the second is 10.
The GH will also want the wolf banner for 10 points. They will also want a drop pod, clocking in the entire unit at 205 points.
This will assume your in rapid fire range.
GEQ DPP : 49.86449864
MEQ DPP : 20.5961084
TEQ DPP : 12.10478771

CSM
Lets say your taking 10 CSM. CSM are limited by their capacity in trasports. In this case, were going to assume 10 CSM in a rhino.
The CSM will have a bare bones champion, and dual plasma guns. The cost for the unit is 205 points.
This will assume your in rapid fire range.
GEQ DPP : 51.30984643
MEQ DPP : 21.43923686
TEQ DPP : 13.48991075
Why are the CSM marginally better given that the squad costs are the same? The rhino has a combi-bolter which is TL when in 12", while the storm bolter is assault 2.

PM
I'm going to mirror the PMs to the other 2 units, taking 10 of them with 2 PGs. They will need to have a rhino with them to get them across the board.
The total cost for the unit is 305 points.
GEQ DPP : 31.89637596
MEQ DPP : 15.13856903
TEQ DPP : 9.431287917

If you bring 5 man PM squads with 2 PGs and a rhino, the values change to this.
GEQ DPP : 28.56189309
MEQ DPP : 17.75104625
TEQ DPP : 11.94527648

Takeaways
CSM can be on par with GH for shooting ability. GH are still better overall due to an extra CC weapon, ATSKNF, the wolf banner and counter attack. Sorry.
PMs are much weaker in shooting ability. Even going with 5 man squads does not really improve the damage output that much, and greatly lowers the RPP values.
When your going with PMs, your trading damage output for durability.

Allow me to derp for a moment. Do you want these numbers to be high or low?

 Ailaros wrote:
Anyways, let's see lasguns. S3 Ap- rapid fire 5 points per model.

10 Guard
Lets take 10 guardsmen, bare bones. Their sergeant will only have 1 shot, as he is using a laspistol.
GEQ DPP : 63.3333365
MEQ DPP : 21.11110689
TEQ DPP : 10.55551228

What happens if we add a melta gun?
GEQ DPP : 54.16666903
MEQ DPP : 22.68518204
TEQ DPP : 10.55551228

So what happened here? Well, oddly enough the DPP of the guards decreased when adding a melta gun, due to the fact that the guard are so cheap.
By adding the single melta gun, we increased the overal cost of the guard squad by 20%, which did not make up for the melta gun damage.
Now, this does not mean "You should not take melta guns". What this means is that melta guns don't increase your DPP, but give you some options.
They also increase the amount of firepower you have in the same footprint on the board.

What happens if they are in a chimera?
GEQ DPP : 31.15942558
MEQ DPP : 19.80673063
TEQ DPP : 14.85506285


10 Guard Vets
Lets try the same exercise with guard vets. These are bare bones
GEQ DPP : 60.31749349
MEQ DPP : 20.10582614
TEQ DPP : 10.05287386

Now lets add 3 melta guns.
GEQ DPP : 43.33335689
MEQ DPP : 18.1481547
TEQ DPP : 16.29630378

What happens if you have plasma guns?
GEQ DPP : 42.51210019
MEQ DPP : 20.61192438
TEQ DPP : 17.39131407

Why did the vets with plasma guns not get much more effect on the marines? Well, the answer is simple, because the costs shot up dramatically.
Adding 3 PGs to the squad increases the cost from 70 points to 115 points. Like before, it increases the overall effect of the squads.
If I were to spam 10 man vet squads, I would give them 3 melta guns, as that gives them a lot of threat and keeps them at 100 points.
Remember, this is a per-point value of damage.

Chimera Vets
What happens when you have 10 chimera vets? This is with no special weapons. The chimeras have a multi-laser and heavy bolter.
GEQ DPP : 32.44445856
MEQ DPP : 20.5925987
TEQ DPP : 17.6296233

Now lets add 3 melta guns. After all, who runs naked vets?
GEQ DPP : 28.31542421
MEQ DPP : 17.5029934
TEQ DPP : 10.54360271

What happens if you have plasma guns?
GEQ DPP : 39.06811776
MEQ DPP : 28.25568695
TEQ DPP : 17.71206866

What effects do we see here? The effect against MEQ is static, yet the effect against GEQ is much less.
Since your only getting 5 shots out of the hatch, your GEQ DPP stays pretty low.
You will also see how the vets in chimeras shine more than the non-vets in chimeras.
This is because when your adding the chimera cost, the extra 20 points for the upgrade to vets is fairly small.

Compared to Wave Serpents
A post was recently made on BOLS about how one wave serpent was as deadly as X chimeras. Lets look at the DPP of chimera vets to the Wave Serpent.
Chimera Vets
GEQ DPP : 39.06811776
MEQ DPP : 28.25568695
TEQ DPP : 17.71206866

Wave Serpent
GEQ DPP : 41.41776185
MEQ DPP : 20.23096631
TEQ DPP : 8.363201593

What does it mean? That post was incorrect. It assumed that the chimeras did not use heavy bolters.
It assumed your running bare bones wave serpents -- which you will NOT be doing. It assumed you had no troops inside.
The reason I'd take serpents over chimeras is that the serpents have better armor, better speed, and better Area of Influence. They are NOT better on a DPP basis.
Even if you ran your serpents without ghostwalker matrix' or a holo field, this is what your looking at.
GEQ DPP : 49.38271605
MEQ DPP : 24.12153675
TEQ DPP : 10.35138082


Automatically Appended Next Post:

 Ailaros wrote:
Allow me to derp for a moment. Do you want these numbers to be high or low?

Higher is better. Higher = more killy.

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