Main Gun vs MG DPS, what matters more?

MGs versus Cannon – Which matters more?

This is gonna be one of these ‘wall of text’ posts that may be quite a chore to read till the end, so be warned. There’s a TL;DR at the bottom, so in case you’re not into the more theoretical part, feel free to skip to the conclusion. Now with this out of the way, let’s go.

Preface
There’s been quite some debate about the anti-infantry power level of medium tanks in the Balance Preview feedback threads recently, with some putting the Cromwell on the bottom of the tier list due to its “shitty” MGs, and others complaining about the T-34’s alleged sub-par AI performance as a result of the 76 mm gun being trash against infantry and tanks alike.
I think much of the controversy (beside the obvious “nerf red – buff blue” faction bias) stems from the fact that there’s no real benchmark combining main gun and MG AI performance into a handy indicator that would allow objective conclusions to be drawn. This shouldn’t be too surprising, since the interaction of scatter and AoE profiles make the main gun AI notoriously difficult to assess, as compared to the more accessible, accuracy-based MG DPS. The latter being single target, while AoE damage obviously affects multiple entities at once doesn’t really help the case, either.
Having tried to work out the main gun AI part of the equation recently, I was wondering how much the various hull/coax/pintle MGs actually provide to the total damage output of a given tank and if both could possibly be combined into a single DPS indicator.

Methodology
In order to calculate such a combined DPS value, it is of course necessary to first obtain the total DPS output of the MGs and that of the main gun. Luckily, the former is quite handily accessible from this awesome site, so I didn’t have to go through the hassle of figuring out how to calculate these myself. (Note that in lieu of actual numbers I’ve taken the liberty to “guesstimate” the DPS values at 5, 20 and 35 m from the displayed charts. This may not be 100% accurate to the last digit, but should suffice for simplicity’s sake).
The second part is a bit more tricky, as the main gun damage output is inherently random and varies significantly with distance to target, formation and model spacing to name a few. Furthermore, the AoE of the explosion typically affects multiple entities at once, so it will scale with the total model count of the target squad as opposed to that of an MG, which naturally is single-target only.
To get a rough number for the theoretical single-target DPS of the main gun I’ve therefore taken the combined HP of 6 full-health entities (480 HP) and divided it by time-to-kill values against a 6-man squad in either clumped or wide formation at a distance of 5, 20 or 40 m calculated here. This gives an average “squad-based” DPS value (i.e. the damage each squad member receives per second) that, when multiplied by 6 for the model count, yields a single target DPS equivalent that can now be combined with the MG DPS.

Results
Now, with these two values in hand, how do they fit together and what does that mean for the AI performance of a given medium?
The answer is, unfortunately, a tad bit more complex to be represented by a single number. Both scatter (main gun DPS) and accuracy (MG DPS) scale with distance, and other modifiers like target size (or received accuracy) bonuses from veterancy or abilities as well as from cover will dilute the MG DPS (technically, also the main gun DPS, but the effect is negligible) even further. Therefore, let’s have a look how the Ostheer Pz IV, British Cromwell, Soviet T-34/36 and, as the true benchmark for anti-infantry potency, the USF M4 Sherman tank equipped with HE shells perform in three different scenarios.

1) Target size = 1, no cover

In the first example, let’s assume the target squad (6 members at full health) does not receive any reduction to target size through vet or cover, assumes either a loose or a clumped formation and is attacked from 5, 25 and 35 m distance. The following table sums up the respective contributions of the main gun, MGs (assuming both hull and coaxial MGs are facing the target and pintle mount upgrades, if available, are purchased), total resulting DPS and the percentage the MGs contribute to the overall damage output:

DPS Table for Target Size = 1, no cover.

Obviously, the difference in main gun/total DPS against wide and clumped formations is huge, since for loose spacing only 2 or 3 models can be caught in the AoE at a time, while all members of the tight formation easily fit into the blast radius of any of the tank cannons. Hence, these two cases can be regarded as the respective minimum (i.e. roughly single target) and maximum bounds for AoE DPS. Squad spacing has no influence on the MG DPS output, but due to the scaling of scatter as well as accuracy and other MG DPS-related stats (e.g. burst length, cooldown, aim time, etc.) with distance, both MG and main gun DPS decline rapidly with increasing distance to target.
Concerning the overall DPS, it comes to no surprise that the HE Sherman with its powerful MGs and large AoE easily beats every other tank in any possible scenario. Behind the top spot it gets interesting though: Despite having lower main gun DPS, both the Pz IV and the T-34 perform similar or better than the Cromwell at close range thanks to dishing out almost double the amount of MG DPS. However, this advantage diminishes quickly at longer distances where the lower reliance on MG DPS lets the Cromwell almost climb to 2nd spot.
What’s also apparent is that, especially against clumped targets and at point blank range, the contribution of the MGs to the total DPS is relatively small, but non-negligible (10-20%). Only against spread out targets and for the Pz VI and T-34 it starts to become really significant (up to 45%).
But wait… there’s more!

2) Target size = 0.75, no cover

So far we’ve only covered the ideal scenario in terms of MG damage: high target size and no benefit of cover. Naturally, things change a lot as the game progresses and infantry squads start to vet up, making it much more difficult to be hit by non-explosive weaponry. Assuming a modest gain in received accuracy, the target sizes of several units can drop significantly below the 0.75 threshold arbitrarily picked in the next example shown below:

DPS Table for Target Size = 0.75, no cover.

Now the chunk of the total DPS the MGs provide gets noticeably lower, making the Cromwell look even better in comparison.
But again, that’s not the end of the road. We still have more to… well… cover!

3) Target size = 0.75, light cover

As mentioned before, there’s another source of target size – and hence MG DPS – reduction that also gets more and more abundant the longer the game progresses: light cover. Craters of all sizes and shapes will be plentiful in the late game and cut MG DPS in half for every model hiding inside. As a result, the contribution of MGs gets marginalized against clumped squads in the majority of fights with typically over 90% of the DPS being dealt by the main gun.


DPS Table for Target Size = 0.75, no cover.

Conclusion or TL;DR

While MGs bring a lot of nominal anti-infantry power to the table, the main source of AI DPS remains the tank gun under realistic in-game conditions (i.e. abundance of yellow cover, reduced target size). Notable exceptions are fights against spread-out entities, for which the effectiveness of AoE damage drops significantly, as well as early engagements with unvetted squads out of cover.
Furthermore, the combined main gun and MG DPS value should allow a more accurate and straightforward comparison of AI strength than juggling with blast radii, AoE profiles, scatter values and MG DPS curves.

Any thoughts or comments, let me know!

-MMX-

Thanks for the great great work and a good analysis.

Think this work will put some myths to rest.

Where you using Okw or Ostheer PzIV values because I think they are different.

Nice work, even if its just putting actual numbers behind an obvious truth, but I feel like it is in response to some people thinking panther is a generalist tank from yesterday.

As much as I appreciate your theoretic work, I am not sure that these calculations yield usable data in this case.

The first issue is that the gun damage is calculated with a 6 model squad (you maybe know the formation/spacing style), which only approximates for Soviets, but 4 men grenadiers might behave differently. However I have a vague memory of you also saying that formation and spacing would matter more than the number of models, which also makes sense but I don't know to which extend this is true between Conscripts and Grenadiers for example. Back when I did my alpha damage calculations (basically answering how much damage the first shot does), I even saw a difference between Volks and Riflemen, but maybe this effect nullifies over multiple shots.
What will also happen though is that your approximation of the main gun damage yields a lower value than in the game, because from my understanding the original data includes also the shots at the last model(s), where main gun damage is less effective. There will be multiple instances of tanks trying to finish off a low health model but missing or dealing marginal damage, while in game an MG would solve this quickly. Also, squads with few members will usually be retreated from tanks and not participate. Maybe this could be solved by taking only the damage that the first (arbitrary number) 5 shots do and then calculate it on a per shot basis.


And one last note because I already see people tearing these numbers out of context:
In the end the MG serves a quite important task: It finishes off models. Shooting a full squad down to 20% health is nice, but if you don't kill anyone you have won only map presence. Shooting it down to 40% health but killing half the models is usually worth more.


EDIT: small addition
On the other hand moving should affect the MG less worse than the gun. The MG damage should get halved approximately, while both angular and horizontal scatter get doubled. Doubling the angular scatter alone already doubles the scatter area (or halving the hit chance so to say), so the horizontal scatter further reduces that.

As much as I appreciate your theoretic work, I am not sure that these calculations yield usable data in this case.

The first issue is that the gun damage is calculated with a 6 model squad (you maybe know the formation/spacing style), which only approximates for Soviets, but 4 men grenadiers might behave differently. However I have a vague memory of you also saying that formation and spacing would matter more than the number of models, which also makes sense but I don't know to which extend this is true between Conscripts and Grenadiers for example. Back when I did my alpha damage calculations (basically answering how much damage the first shot does), I even saw a difference between Volks and Riflemen, but maybe this effect nullifies over multiple shots.
What will also happen though is that your approximation of the main gun damage yields a lower value than in the game, because from my understanding the original data includes also the shots at the last model(s), where main gun damage is less effective. There will be multiple instances of tanks trying to finish off a low health model but missing or dealing marginal damage, while in game an MG would solve this quickly. Also, squads with few members will usually be retreated from tanks and not participate. Maybe this could be solved by taking only the damage that the first (arbitrary number) 5 shots do and then calculate it on a per shot basis.


And one last note because I already see people tearing these numbers out of context:
In the end the MG serves a quite important task: It finishes off models. Shooting a full squad down to 20% health is nice, but if you don't kill anyone you have won only map presence. Shooting it down to 40% health but killing half the models is usually worth more.

I concurre with this point as well.
In game you don't keep a unit with 1/2 models fighting against a tank. What matters is the performance in the first 5/10/15s of engagement most of the time.

MGs performance on tanks is hard to gauge cause you are not always using 100% uptime for the hull MG.

Thanks for the work MMX! The nominal DPS numbers look good. Theoretically, Crommy has the best max range DPS besides the blap gun of the Sherman.

Just how that DPS converts to kills/bleed is the next step (if it ain't dead, doesn't count). That way leads to AoE profile madness and MG uptime assumptions.

I applaud the effort, (and agree with the conclusions) but I'm dubious that a ton of useful info can be gleamed from this.

The raw number of variables involved make this a nightmare of a question to answer. And even a few tiny changes to 1-2 values (how close together the models are, how far the shot scatters affecting how much incremental damage the squad takes for the next round of shots, etc) can skew the results hard to one side or the other.

From just a pure game experience PoV, I agree the main gun always going to be the most relevant weapon, while MGs are there to kill off models the cannon damaged. But how much each contributes is a nightmare to figure out.

Assuming its a real game and people actually retreat their damaged squads, those first 1-2 cannon shots have the best chance of killing multiple models outright, and are the only weapon that has the possibility to outright wipe the squad, while the MGs really need time for their DPS to shine.

That being said, the MGs are excellent at finishing off models damaged by the main gun, and *can* be a major source of the tanks DPS against squads spread in the open or support weapons that more naturally spread out. A Pintle will also add a lot of residual damage to infantry over the course of a big dive. I'm never unhappy to have a 3rd Pintle MG for one of my tanks.

thanks a lot everyone for the feedback, much appreciated!

i agree with the sentiment that the usefulness of the combined DPS data is inherently limited, since the interaction of the continuous MG damage with the huge damage chunks delivered by the main gun (e.g. finishing off low-health models) can only be very roughly approximated by just adding their respective DPS values. to get a more realistic picture, it would be necessary to simulate both at the same time, but i'm afraid this would be far too complex (at least for me using excel / vba as the only tool) to realize.

i've also thought about relying the initial, or alpha damage for the main gun DPS estimation, but didn't have the data readily available unfortunately. taking the TTK as a base, as pointed out by Hannibal and elchino7 inevitably yields to a lower cannon DPS, but i was somewhat happy with this as it would be a more accurate estimate for long encounters with significant models drops. however, on second thought i must concur that this is a somewhat flawed assumption since most people would retreat way before only one or two low-health entities are left.

that being said, what would you think would be a more appropriate indicator for AI performance than raw DPS? I was thinking about something like average number of model drops or OHKs during the first 5 or so shots may paint a clearer picture than just measuring the accumulated squad HP left, although this still wouldn't fit the MG contribution into the equation?

Thanks for the great great work and a good analysis.

Think this work will put some myths to rest.

Where you using Okw or Ostheer PzIV values because I think they are different.

that's correct. i've been using the ostheer pz iv here, which should use the same mg profiles, but has higher scatter on the main gun than the okw version.

snip

If we should go for a test which gives values closest to what one would expect in game then it should be something like this:


-Considering the first shot from the main gun been at T=0s you should just take the DPS of total 4 shots, which would roughly be 17-20s?
I think that's a more realistic time frame for most "prolonged" engagements in the game.

-If possible, half the shots while static and the other while on the move.

-Finally for Hull MGs, i would say that the uptime should be around 50% and 60% respectively for those who have a 5 and 10 fire cone angle.

If we should go for a test which gives values closest to what one would expect in game then it should be something like this:


-Considering the first shot from the main gun been at T=0s you should just take the DPS of total 4 shots, which would roughly be 17-20s?
I think that's a more realistic time frame for most "prolonged" engagements in the game.

-If possible, half the shots while static and the other while on the move.

-Finally for Hull MGs, i would say that the uptime should be around 50% and 60% respectively for those who have a 5 and 10 fire cone angle.

yeah i think cutting down the timeframe of the engagement would be a good idea indeed.
having half the shots fired while moving might be a bit difficult to implement, but possible with a bit of tweaking of the simulator code.
however, might be better to just separate both conditions from each other into two individual tests.
talking about the mgs, i've given this a bit of thought lately and it might be possible to approximate their dps contribution in the spreadsheet if they're treated like a constant source of single target damage, kind of like a steady HP drain. that way it would't be necessary to calculate the odds of every single bullet or burst, which would simplify things greatly. uptime of individual mgs could also then be simulated via a simple multiplier.

i'll be giving this a try when i find the time.