Ruthless Math of WoT.

Just a copy paste from my thread on the Offical forums.


Alright, before I begin, I want to credit Zinegata for making this absolutely wonderful guide. I looked everywhere for it here, and EVERYONE needs to see this, plus, I don't want to be a jerk, so, thanks again Zinegata. forum.worldoftanks.com/index.php?/topic/227903-the-ruthless-math-of-wot-and-why-every-tank-matters/
For the original.

The Ruthless Math of World of Tanks

One of the major "debates" that rage in the forums is the ability of a single player to affect the entire course of the match. In general, the concensus is that a single tank can in fact affect the course of an entire match (often termed as a "carry").

However, the problem with this "debate" is that it invariably boils down to what I call "win-rate makes me right" argument. We have some players who play solo and yet have very high win rates. Ergo, it is possible to "carry" a team all by yourself because the high win rates cannot simply be explained by "luck".

The problem with this approach is that it does very little to actually explain how such "carries" are actually possible. Often, we just get some pretty vague (and often bordering on mythical) explanations, usually centering around "skill".

This thread attempts to answer the "how". It will not be a discussion about skill or tactics (although it will reveal why some tactics are so vital). It will instead simply show the unbending gaming principles behind how WoT battles actually work - the "ruthless math" of the game, if you will.

The Key Concept: The Hitpoint Mechanic and Critical Existence Failure

To begin to understand the "math" of the game however, one crucial concept needs to be understood by the reader: "Critical Existence Failure" (henceforth abbreviated as "CEF"). And yes, I'm using the TV Tropes terminology; because it's more fun this way.

Basically, CEF is the model used by most games that use the hitpoint mechanic. Under this model, a unit can function at same level regardless if it was at full hitpoints, or if it was down to just 1 hitpoint. In WoT, it means a Sherman tank at 1 HP will still deal as much damage as a Sherman at full health. (And yes, I'm ignoring the module damage factor for now. See the side bar below)

What this means is that a 1 HP Sherman tank can potentially remain as effective as a Sherman with full HP. In fact, if the Sherman at full HP is an utterly bad player (whose shots keep missing or keep hitting spots that will just bounce the shell) it is entirely possible for a 1 HP Sherman to utterly demolish one at full health. I'm sure that most good players have done this one time or another, and it should already serve as an indication of how superior player knowledge ("skill") can lead to a decisive difference on the field.


Spoiler
Show


The Myth of 15 vs 15

However, in reality, most matches are not won by a 1 HP Sherman duelling a full HP Sherman to death. Many will in fact point out that matches involve 15 tanks on both sides. Cue boohooing about how one tank can't carry 14 others.

But in reality, matches are not actually grand battles of 15 vs 15. Instead, most matches are actually a series of smaller (sometimes inter-related) fights - which I will term as "skirmishes", with often just two to four tanks of either side fighting for a particular section of the map.

As an example, take your average Lakefield battle. Let's assume there's two arty per side, and relatively competent players on both sides. Each team will probably send 2-4 tanks into the valley, 1-2 tanks into the mid, and the remainder (7-10) going into town.

But even in the case of the town, that big group often actually gets divided into a bunch of smaller skirmishes - with some tanks going to the lake shore, the others going to the church, and some hugging the map edge - none of which necessarilt interact with each other.

In fact, it is actually quite rare to see an outright slugging match involving more than 5 tanks from each side. Hence, the old excuse that "I'm just one tank out of fifteen" rings very hollow. You almost never actually fight 15 enemy tanks at a time at the point of contact. You will, in general, be fighting 2-4 enemy tanks, and you'll have about as many allies with you too.

And really, what tends to happen in a match is that the 15-man team will win some of these skirmishes, and then lose a couple of others. Your lake-shore team might overwhelm their counterparts, but your map-edge team might have similarly folded. Afterwards, the survivors of their respective skirmishes will make contact with each other into a series of new skirmishes; and the process is repeated until one team is wiped out.

Spoiler
Sidebar: One of the "skills" lacking in many players - yet few people seem to be able to articulate - is their inability to recognize that these small, localized skirmishes are actually happening. Most players will understand the Valley-Mid-Town dynamic of Lakeville for instance, but they don't further subdivide and understand that the town actually has multiple different areas of conflict. In part, I blame the minimap for this, which tends to be rather bad at representing how these skirmishes are actually seperated by buildings.

The Anatomy of a Skirmish, as Dictated by CEF

When people think of a 4 vs 4 match, they tend to think that it should result in a "fair" fight, wherein both sides essentially wiped each other out. And indeed, this is what sometimes happens - with only 1 or 2 badly damaged survivors emerging from the furball of 8 tanks.

But the reality of most skirmishes is actually different, especially if it involves players of different skills levels.

To demonstrate, let's construct a thought exercise. Let's assume we have two teams of four tanks apiece. Each tank has 450 HP and inflicts 120 damage with each shot (so 4 shots to kill an enemy tank). Let's assume both sides hit and penetrate 100% of the time (a bit unrealistic, but bear with me).

However, let's give Team A a small but crucial advantage. Let's assume that Team A knows how to focus-fire, while Team B does not. Team B's tanks will only shoot their opposite-numbered tank, until that tank is destroyed.

Given this setup, the following will happen:

* At Start:
Team A Tank 1: 450 HP
Team A Tank 2: 450 HP
Team A Tank 3: 450 HP
Team A Tank 4: 450 HP

Team B Tank 1: 450 HP
Team B Tank 2: 450 HP
Team B Tank 3: 450 HP
Team B Tank 4: 450 HP

* After First Volley:
Team A Tank 1: 330 HP
Team A Tank 2: 330 HP
Team A Tank 3: 330 HP
Team A Tank 4: 330 HP
Total Damage Done: 450

Team B Tank 1: DESTROYED
Team B Tank 2: 450 HP
Team B Tank 3: 450 HP
Team B Tank 4: 450 HP
Total Damage Done: 480

* After Second Volley:
Team A Tank 1: 330 HP
Team A Tank 2: 210 HP
Team A Tank 3: 210 HP
Team A Tank 4: 210 HP
Total Damage Done: 900

Team B Tank 1: DESTROYED
Team B Tank 2: DESTROYED
Team B Tank 3: 450 HP
Team B Tank 4: 450 HP
Total Damage Done: 840

* After Third Volley:
Team A Tank 1: 330 HP
Team A Tank 2: 210 HP
Team A Tank 3: 90 HP
Team A Tank 4: 90 HP
Total Damage Done: 1350

Team B Tank 1: DESTROYED
Team B Tank 2: DESTROYED
Team B Tank 3: DESTROYED
Team B Tank 4: 450 HP
Total Damage Done: 1080

* After Fourth Volley:
Team A Tank 1: 330 HP
Team A Tank 2: 210 HP
Team A Tank 3: 90 HP
Team A Tank 4: DESTROYED
Total Damage Done: 1800

Team B Tank 1: DESTROYED
Team B Tank 2: DESTROYED
Team B Tank 3: DESTROYED
Team B Tank 4: DESTROYED
Total Damage Done: 1170

Rather different from the expectation of mutual annihilation, isn't it?

Indeed, by simply focus-firing, Team A was able to inflict 50% more damage than Team B, while preserving the life of 3 tanks which can now be redeployed elsewhere for decisive effect! How did this happen?

Well, I promised the math, and here it is. What we're witnessing is what is called the "snowball effect" - wherein something of seemingly minor importance suddenly balloons into something more dangerous and disastrous.

In this case, the disaster began when Team B lost its first tank during the first volley. Because of CEF, Team B lost 25% of its firepower at this moment - firepower that could have inflicted another 360 points of damage had Tank 1 survived to fire for the remaining 3 volleys. That's actually enough damage to destroy two of Team A's remaining tanks! (Tank 2 & 3 have only 300 HP remaining in total)

Thus, the loss of just one tank was the difference between Team A winning with 3 surviving tanks instead of just 1 surviving tank. It was, in all likelihood, also difference in winning the whole match overall.

And really, if you actually take a while to look at how skirmishes develop, you'll notice this pattern often when your team is winning: After your team destroys one tank, the second kill comes faster, and the third even faster, until the enemy team seemingly collapses like a house of cards. It's all because each and every gun matters in these skirmishes - once the enemy team has fewer tanks your team is now much more able to focus-fire and bring down enemy tanks in rapidity, while the enemy has much less firepower to throw back at you.

So when people stress the importance of focus-fire and target prioritization, listen. Because the snowball effect of losing just one tank can cascade to victory or defeat for a specific skirmish, which in turn can win or lose an entire match.

That being said, it must be noted that focus-fire situations are actually pretty rare. Most players are now smart enough not to just expose themselves and let themselves be shot at by multiple players at a time. With peak-a-boo tactics, even skirmishes of 4 vs 4 tanks may in reality turn into 1 vs 1 engagements.

Hence, the need to create situations where you can rapidly kill an enemy tank - a technique which I call the "isolation".

Spoiler
Sidebar: The above math should also demonstrate to people the utter folly of camping at the base cap. Yes, it is okay to camp at a good firing position as long you're actually firing and dealing damage to the enemy; thus helping win some of the skirmishes. No, it is totally NOT okay to camp at the cap circle where you will not be shooting at anything 90% of the time, and the remaining 10% you're just shooting at scouts when it's already too damn late. Burn this reality into your brains: Every tank matters. Deserters will be shot!

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A Game of Isolations

"Isolation" is the art of bringing as much firepower to bear on an enemy tank - with the intent of rapidly destroying it - while at the same time preventing your own forces from being exposed to lethal fire from the enemy.

As I already noted before, most players don't sit out in the open anymore shooting at each other. They'll often use cover and try to at least make themselves a harder target for the enemy. The 4vs4 example I showed above should not literally play out that way in real matches (hence why it's a thought exercise).
What instead happens is that good players are constantly moving and maneuvering, looking for a way to create a situation wherein they can quickly gang up on an enemy tank without suffering much return fire - preferrably only from the target tank.

In fact, a well-played isolation is how "skunks" (matches wherein one team loses no tanks, while the enemy is wiped out) actually happen. Again, let's do the thought exercise thing, but this time with Team A doing isolations instead of focus fire...

*At Start:
Team A Tank 1: 450 HP
Team A Tank 2: 450 HP
Team A Tank 3: 450 HP
Team A Tank 4: 450 HP

Team B Tank 1: 450 HP
Team B Tank 2: 450 HP
Team B Tank 3: 450 HP
Team B Tank 4: 450 HP

After First Volley:
Team A Tank 1: 330 HP
Team A Tank 2: 450 HP
Team A Tank 3: 450 HP
Team A Tank 4: 450 HP
Total Damage Done: 450

Team B Tank 1: ISOLATED, DESTROYED
Team B Tank 2: 450 HP
Team B Tank 3: 450 HP
Team B Tank 4: 450 HP
Total Damage Done: 120

After Second Volley:
Team A Tank 1: 330 HP
Team A Tank 2: 330 HP
Team A Tank 3: 450 HP
Team A Tank 4: 450 HP
Total Damage Done: 900

Team B Tank 1: ISOLATED, DESTROYED
Team B Tank 2: ISOLATED, DESTROYED
Team B Tank 3: 450 HP
Team B Tank 4: 450 HP
Total Damage Done: 240

After Third Volley:
Team A Tank 1: 330 HP
Team A Tank 2: 330 HP
Team A Tank 3: 330 HP
Team A Tank 4: 450 HP
Total Damage Done: 1350

Team B Tank 1: ISOLATED, DESTROYED
Team B Tank 2: ISOLATED, DESTROYED
Team B Tank 3: ISOLATED, DESTROYED
Team B Tank 4: 450 HP
Total Damage Done: 360

After Fourth Volley:
Team A Tank 1: 330 HP
Team A Tank 2: 330 HP
Team A Tank 3: 330 HP
Team A Tank 4: 330 HP
Total Damage Done: 1800

Team B Tank 1: DESTROYED
Team B Tank 2: DESTROYED
Team B Tank 3: DESTROYED
Team B Tank 4: DESTROYED
Total Damage Done: 480

In this case, not only did Team A come out without losing a single tank, but they not inflicted more than 3x the damage of the enemy team!

And really, this is how the "unicums" actually achieve most of their wins. It is not about some mythical "skill" requiring better gunnery or whatnot. Instead, it revolves around the ability to pick out vulnerable (but important) enemy tanks in the pack, rapidly destroy them, which starts a snowball effect wherein the missing damage from the destroyed tanks rapidly adds up to their team's advantage.

More importantly, this can be achieved outside of platooning, so long as you remain constantly aware of how the game revolves around isolation. As a final thought experiment, let's do our Team A vs Team B thing again... only this time let's assume that Tank 1 of Team A is a skilled player who knows how to focus-fire...

At Start:
Team A Tank 1: 450 HP
Team A Tank 2: 450 HP
Team A Tank 3: 450 HP
Team A Tank 4: 450 HP

Team B Tank 1: 450 HP
Team B Tank 2: 450 HP (Focus-Fire Target)
Team B Tank 3: 450 HP
Team B Tank 4: 450 HP

After First Volley:
Team A Tank 1: 330 HP
Team A Tank 2: 330 HP
Team A Tank 3: 330 HP
Team A Tank 4: 330 HP
Total Damage Done: 480

Team B Tank 1: 450 HP
Team B Tank 2: 210 HP (Focus-Fire Target)
Team B Tank 3: 330 HP
Team B Tank 4: 330 HP
Total Damage Done: 480

After Second Volley:
Team A Tank 1: 210 HP
Team A Tank 2: 210 HP
Team A Tank 3: 210 HP
Team A Tank 4: 210 HP
Total Damage Done: 930

Team B Tank 1: 450 HP
Team B Tank 2: DESTROYED (Old Focus-Fire Target)
Team B Tank 3: 210 HP
Team B Tank 4: 210 HP (New Target for our unicum, who assumes Tank 2 will target tank 3)
Total Damage Done: 960

After Third Volley:
Team A Tank 1: 90 HP
Team A Tank 2: 210 HP
Team A Tank 3: 90 HP
Team A Tank 4: 90 HP
Total Damage Done: 1320

Team B Tank 1: 450 HP (Last target, everyone is going after him now!)
Team B Tank 2: DESTROYED
Team B Tank 3: DESTROYED
Team B Tank 4: DESTROYED
Total Damage Done: 1080

After Fourth Volley:
Team A Tank 1: DESTROYED
Team A Tank 2: 210 HP
Team A Tank 3: 90 HP
Team A Tank 4: 90 HP
Total Damage Done: 1800

Team B Tank 1: DESTROYED
Team B Tank 2: DESTROYED
Team B Tank 3: DESTROYED
Team B Tank 4: DESTROYED
Total Damage Done: 1410

So despite Team B doing a little more damage than in the pure focus-fire example, and our unicum being the only casualty on Team A, his focus-fire efforts was actually enough to make his team still do 50% more damage overall, while leaving 3 of the 4 tanks intact. Heck, if Team A's Tank 2 had shielded our unicum, they would all have survived.

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My own thoughts:

In addition to the above, you can also add in spotting damage to the mix, by having one tank go out and spot, and if said spotter is unseen, you effectively gain free damage without receiving enemy fire as well. This is a HUGE part as to why an unseen TD and a good spotter can utterly destroy a flank, and should be your go-to plan in part of playing well. (Not camping, but doing damage without getting damage in return.)

So in summary, the "ruthless math" of the game, thanks to CEF and its snowball effect, revolves around the rapid destruction of enemy tanks to reduce the opposing team's firepower; while preserving your own team's damage-dealing ability. Keep even your 1 HP teammates alive because they can pump out damage that is the difference between victory and defeat. Just one tank out of four knowing how to focus-fire can lead to huge swings in a match.

Of course, real WoT matches involve much more than just the thought experiment highlighted above. It doesn't take into consideration things like tier mismatches (e.g. a Tier 6 skirmishing two Tier 5s), nor does it account for more random things like bounces, no-damage hits, or misses. The number of volleys to kill enemy tanks also isn't as neat in the game, with different tiers and different kinds of guns.

But what it does show is that if everyone is playing consistently, then each tank does matter. It's time to give up on the notion that you're just one tank out of fifteen.

Thanks for reading this guys, and I hoped it helped. Once again, cannot credit Zinegata enough here.

GestapoFish's bit:

Wish I hadn't figured this out, but here it goes:

Assuming there is an even chance of winning any given match (p = .5) here are the 95% confidence intervals for various numbers of battles based on the formula p +/- tinv(alpha, n-1) * sqrt(p*(p-1)/n).
p = probability of a win,
n = number of trials (battles)
tinv() is the inverse student's t-distribution
alpha = confidence level


Battles Lower Upper
10 14% 86%
15 22% 78%
25 29% 71%
50 36% 64%
100 40% 60%
250 44% 56%
1000 47% 53%
2000 48% 52%
5000 49% 51%

The confidence interval represents values of the parameter for which the value of sample statistic is not statistically significant at the 05% confidence level. Treating your win rate as a sample of your actual skill, if your win rate after n many battles is within the given range, then it is likely due to chance. [edit: said another way, if your win rate is outside this range it is likely reflective of your skill level in that vehicle.] This is somewhat imprecise, but if taken with a grain of salt this should give you an idea of whether you are lucky or good/bad.

If you want to get more specific, you can use the above formula with the WN8 or noobmeter value for expected win percentage for a specific tank as (p).

Example: The expWinRate for the Covenanter is 56.72%, the t-score after 20 battles is tinv(.05, 20-1) * sqrt (.5671*(.5671-1)/20) = .2319.

.5672 +/- .2319 = {.3353, .7991} My win rate in the Convenanter after 20 battles is 80%, which could be due to skill, or could be due to luck. Honestly, as imprecise as the meaning of confidence interval can be, I wouldn't worry about getting this precise with any given tank. Getting +/- .001 more precision within a +/- .05 tolerance is kinda silly.

[edit: It was luck. After 88 battles, my win rate is now 48%. Still within the confidence interval, but my DC/DR and K/D also fell.]

Anyway, just another tool in the belt. Knowing that after 100 battles a win rate of 50% +/- 10% is well within random chance might keep you from giving up on a tank, or keep you from thinking you're awesome in a tank when you're not. This helped me realize that my 60% win rate in my VK 30.01 (H) was just luck and when it plummeted to 44% percent it was probably due to me thinking I was more awesome in that tank than I really was.

Let's hope I don't have to necro it here either.