Summary of Tank vs Tank Combat

Update v1.01, 16.05.2021
-Fixed wrong damage for Firefly (standard damage was previously set to 160 with 200 at vet. Corrected to 200 standard with 240 at vet).






This time around I'd like to suggest a different take on the comparison of vehicle to vehicle combat. Data is downloadable here.

Intro
Currently, we rely on the "time to kill" (TTK) or "shots to kill" (STK) as a measure of how quickly vehicles can kill each other. It is calculated by dividing the number of penetrations needed to kill a vehicle (e.g. 4 for most mediums) divided by the chance to penetrate and the chance to hit. This metric gives us a decent estimation how many shots it takes to kill the opponent. Since CoH2 is based on RNG, it does not tell us the chance with which the opponent will be killed.
In more extreme cases, the TTK/STK can even be misleading. Imagine two vehicles fighting. Vehicle 1 penetrates with 10% chance but only needs one penetration to kill the enemy. Vehicle two penetrates with 100% chance but needs 10 shots to kill the enemy. The STK will tell us the same value: 10 shots. Yet, vehicle one will win in almost two thirds of the fights, because a single lucky shot is all it needs. The chance for all 10 shots (after which it will be dead) to bounce is about 35%, meaning that in all other cases it will score the lucky hit before being killed itself.

We can translate this thought into CoH2 as well. As previously stated, CoH2 is an RNG based game. Vehicle fights could go on forever, with all shots bouncing or missing. The chance for this to happen is super, super low, but never zero. To this end, it is important to rephrase the question, and thus, the metric itself: Instead of asking how many shots we expect for the kill, we need to ask how many shots we need to have at least a certain chance of killing the opponent. Those shots follow a binomial distribution and can be calculated fairly easily.


Method
I have calculated the data for a most of the vehicles in CoH2 (currently 176 including veterancy) using MMX's vehicle data from his "ScatterThis" sheet (an updated pre-version was kindly provided by him) at ranges 10, 20, 30 and 40. To get somewhat normalized values, I calculated the number of shots needed to have at least an 80% chance to kill the opponent. I used 80% because first, I feel most would agree that a 4 out of 5 chance is "reliable killing" of the opponent. Second, some vehicles that always hit and pen will result in a 100% chance. It did not seem right to compare a setup with 100% chance with another one yielding a chance of maybe only 50%. Third, since a clean 100% kill chance is impossible in all setups where bounces and misses are possible, values too close to 100% will dramatically increase the numbers. An 80% chance is reachable for all vehicles in a reasonable amount of time without bloating the numbers artificially.

Without the proper means to calculate scatter hits accurately, I made the assumption that 60% of misses will still hit by scatter. However, this punishes units with naturally small scatter. This estimation could be further refined, but for the time being it is the best I could do. Nevertheless, please treat the data with thought towards that. I want to mention that this issue is also not resolved with the current metrics.

If you have thoughts, critique, ideas or what not on the matter, I'd be happy to hear.


HOW TO and download
The zip file contains 4 xlsx files termed with the respective distance that was used for calculation. Columns represent the target, rows the shooter. A cell with the row "PanzerIV_H(OST) and the column "T-34/76" represents how many shots or how long the P4 needs to kill the T-34/76- Each file contains 6 sheets:
1. Tries_htks (htk = "hits to kill"): The number of hits needed to have at least an 80% kill chance. Does not take into account accuracy and only bases the calculation on penetration values.
2. htk_chances ("hits to kill chances"): The exact kill chance for sheet 1.
3. "tries stks (stk = "shots to kill"): Similar to sheet 1, but takes accuracy into account as well. All numbers are therefore equal or larger to sheet 1.
4. stk_chances ("shots to kill chances"): The exact kill chance for sheet 3.
5. ttk_htks ("time to kill based on hits to kill"): Calculated TTK based on the needed hits. Neglects accuracy. First shot is set as time 0.
6. ttk_stks ("time to kill based on shots to kill"): Like 5, but uses accuracy as well.

The last two sheets are probably the most valuable ones, but use those and the others how you want.
Since there are a ton of data points, visualization is hard. I personally like to display them as a heatmap as shown below.


You could also use it to answer the question of "what is the best counter to the IS-2?" (it is the vet3 Elefant in case you wondered. But a vetted StuG is doing very, very well too, followed by the Panther).


Similarly, you could flip the question upside down and check against which units your Puma performs best against, how large the difference is between vet levels and many more.

Data is downloadable here.




Comparison with current TTK
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Other notes
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didn't have the chance to look into the data yet, but this looks like awesome stuff once again, kudos!

just one question; how did you come up with the 60% hit value from scatter? is it an educated guess or approximated from some in-game or calculated data?

cool stuff! great work

didn't have the chance to look into the data yet, but this looks like awesome stuff once again, kudos!

just one question; how did you come up with the 60% hit value from scatter? is it an educated guess or approximated from some in-game or calculated data?

I checked for some units with different scatter profiles (Panther, Stug, T34/85 and Su85) with how many shots they hit a P4 at their max range. I modded their accuracy to 0 so there would be scatter shots only.
Panther had about 45%< the Stug about 70%, and the two others somewhat 55-60% or so when I counted ~40 shots each. So it is more a semi-educated estimate.
Refinement could be to increase the chance with shorter distance and also use the target size as an indicator for the model size to increase scatter hit chances (as a rule of thumb large models have large target size). But this would need more testing since I currently have no idea how the curves would look like, so it would be mostly arbitrary.

I checked for some units with different scatter profiles (Panther, Stug, T34/85 and Su85) with how many shots they hit a P4 at their max range. I modded their accuracy to 0 so there would be scatter shots only.
Panther had about 45%< the Stug about 70%, and the two others somewhat 55-60% or so when I counted ~40 shots each. So it is more a semi-educated estimate.
Refinement could be to increase the chance with shorter distance and also use the target size as an indicator for the model size to increase scatter hit chances (as a rule of thumb large models have large target size). But this would need more testing since I currently have no idea how the curves would look like, so it would be mostly arbitrary.

ah i see... yeah i guess without the correct size of the hitboxes it's gonna be pretty difficult to get an accurate value for scatter hits. i've been trying to come up with a way to measure these in-game that isn't overly time-consuming but so far to no avail. really too bad that these don't seem to be accessible from the modding tools...

Update v1.01

-Fixed wrong damage for Firefly (standard damage was previously set to 160 with 200 at vet. Corrected to 200 standard with 240 at vet).

This made the Firefly look worse than it actually was vs some units (most notably units above 640 HP).

I obviously recommend redownloading the data files if you want to work with Firefly data.