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EchelonIII

EchIII Import #1: Artillery and Variance Theory

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I'm working on importing most of my threads from the main forum to be posted over here as a form of pre-emptive strike on the bads which will trickle in.

 

This article is now outdated as of patch 8.6, but I think it's still worth a read

Arty is bad because it enables players to win games they do NOT deserve to win

My hypothesis is that artillery in its current state negatively affects better players more than it affects bad players, I shall aim to prove this through quantifying player skill through the creation of an arbitrary variance constant.

The fun part is that while I'm attacking artillery, I've also simultaneously checkmated the "low game" argument of win rate deniers.

Part 1: The Player Skill Model

I will aim to quantify the probability distribution of a player's ability in one game through the usage of a normal distribution P1 = N~(X,Y), where P1 is the player in question, N designates a normal distribution about mean X, where X is the mean player skill, and Y is the variance in the player's skill distribution, for the ease of readers, please note that standard deviation is NOT the same as variance, however, for the purposes of this experiment, please note that this is not relevant, and that I will be using the two terms interchangably as we are only exploring the relative impact of the magnitude of a higher and lower standard deviation (effectively, the effect of amplified RNG), not the actual probabilities.

For the record, the standard deviation is the square root of variance. In terms of a normal distribution, about 66% (specifically, it's 68%) of results fall within 1SD, 95% of results within 2SD, and 99% of results within 3SD (refer to diagram below for reference)

A player with a higher mean skill (i.e. higher X) is a more skilled player than a player with a lower mean skill. The best way to think of the "mean skill" is as "base skill".

The term "variance" is my way of simulating the RNG, for the purposes of this experiment, it does not need to simulate the RNG precisely, only act as a sufficiently similar analog, basically, the higher the variance, the higher the impact of RNG on the player or player group.

For example, if I have an average player P1 with an E75, who is a fairly consistent player, with an average skill of 50, and a standard deviation of 5, it means that...
1. About two-thirds of the time, he will have an impact of 45-55

2a. Approximately every 1 in eight times, he will have an impact of either 40-45
2b. Likewise, 1 in every eight battles, he will have an impact of 55-60

3a. Once every fifty battles on average, he will play really badly and have a team impact of 35-40
3b. On the flipside, about ONCE in every fifty battles, he will have a great game and play with a team impact of 60-65

Part 2: The Fun Begins

There is a very interesting thing about these normal distribution models, which is in fact the reason I chose these models, we can use them to simulate interactions between players.

Part 2A: Curbstomp Land
For example, let's say that luck and the RNG plays absolutely ZERO role in a single instance, in which case the variance will be zero, the SD will be zero, and the means between players will be what determine what happens.

So let's have a few players, a unicum (mean skill 60), an elite (mean skill 55), a good player (mean skill 53), an average player (mean skill 48), a bad player (mean skill 45), and a pubbie (mean skill 40). Note that this is a VERY COMPRESSED skill curve, in reality, the skill curve would be logarithmic, it would take more than two average players to overcome a unicum, and certainly more than two bad players to overcome an elite.
In the land of curbstomp where the RNG is zero, the player's skill distribution probabilities look like this
P1= Unicum ~ (60, 0)
P2= Elite ~ (55, 0)
P3= Good ~ (50, 0)
P4= Average ~ (48, 0)
P5= Bad ~ (45, 0)
P6= ARMED player ~ (40, 0)

In this land, Unicum always beats elite, elite always beats good, good always beats average, average always beats bad, and so on down the totem pole.

We can compare player's chances against each other in a few ways, I will use both a simple explanation and a technical one.

The Simple Explanation
The way we can compare a player's chances of beating another player's is through the simple act of subtracting one's normal distribution from the other. If the first player is better, then the resulting distribution should be positive, if the second player is better, then it should be negative.

For example, take a Unicum with a distribution of (60, 0), and subtract a Bad (45,0), the resulting distribution would be one of (15,0), which results in a 100% win rate for a unicum)

The Technical Explanation
What we're essentially doing here, is finding the probability of a unicum beating a bad via the function P (for probability) of (P1 > P5), which is 100%. It seems simple now, but it'll get much, much more complicated later on.

Part 2B: Enter Randomness
Let's add in some randomness into the battles.

For the ease of all of us, we can assume, if all players play the same tank, that the variance on each tank will be the same, for the purposes, we'll assume each player is playing in an E75, and that the natural variance of luck on an E75 is 5.

P1= Unicum ~ (60, 5)
P2= Elite ~ (55, 5)
P3= Good ~ (50, 5)
P4= Average ~ (48, 5)
P5= Bad ~ (45, 5)
P6= Pubtard~ (40, 5)

Suddenly, things have changed, the Elite player has a chance of beating a unicum if he catches the unicum on a bad match... let's take a closer look.

Now, there is a very funny thing when we subtract distributions from each other, while the function we apply to the mean is the same as denoted by the positive or negative sign, the variances are always added

The odds of unicum beaying elite; P ~ (P1>P2) is no longer zero, but rather the odds that [N~5,10)]<0, which is 0.69, an elite player has about a 1 in three chance of beating a unicum, it's still heavily weighted in favor of the unicum, but a strong player has a good shot (if you can call a 30% chance "good)

The odds of elite beating good; P ~ (P2>P3), have similarly dropped to .69, a good player at 50% can beat an elite a third of the time.

The odds of Unicum beating average; P ~ (P1>P4) in this model are 0.88, all of a sudden, an average player can suddenly beat a unicum about one in eight fights.

Interestingly, the odds of a pubtard beating a unicum are about 2.2%, of course, this just shows that this is just a model.

The Catch

The catch we have here, is that not all tanks have the same variance. Tanks with low accuracy, for example, tend to have high variance, guns such as those found on artillery, specifically, have a much, much higher variance than on a tank like a heavy.

Due to the fact that the RNG for damage is -/+ 25%, tanks with a higher base damage will introduce higher variances at that instant as their RNG range will be higher

Part 3: Suddenly, arty
Artillery having such a high variance compared to standard tanks can change the game

Using the system, let's add an artillery player to each side, for fairness, we are going to add the SAME PLAYER to both sides.

Arty = Control Player ~ (50, 20)
P1= Unicum ~ (60, 5)
P2= Elite ~ (55, 5)
P3= Good ~ (50, 5)
P4= Average ~ (48, 5)
P5= Bad ~ (45, 5)
P6= IOC~ (40, 5)

Suddently, unicum and arty has become (110, 25), elite and arty has become (105, 25) and Pubtard with arty has become (90, 25).

The odds of P ~ ([Arty+P1] > [Arty+P6]) can be simplified to P ~ [(20,50) > 0] are now 0.6

The odds of a Unicum with artillery support beating a pubtard with artillery support has suddenly dropped from a 97% chance to a mere 60% chance.
A pubtard with artillery support stands a 40% chance of beating a unicum with artillery support.

An average player alone stands a .12 chance of beating a unicum
With both sides having arty, that has increased to 45%

For reference, an elite player stands a 30% chance of beating a unicum alone.
With arty on both sides, an elite stands a 49% chance of beating a unicum.

You will notice something in the odds of all the players in beating a unicum
Pubtard went from 2% to 40%
Average went from 12% to a solid 45%
Elite went from 30% to 49%.
Notice how the pubtard benefitted a LOT more from the arty player than the added variance than the elite did?

Part 4: Why this is so
Let's face it, when a good player takes on a bad player, he wants minimal interference.

From the good player's position, he can follow what is known as a "match" strategy, the good player can do anything a bad player can, and more, all he has to do is play horse with the bad player, matching his every move, and then taking advantage of an inferior move.

For the bad player to improve his chances, he must try to introduce more randomness into a fight to shake up the variances.

In short, a welcome dice roll to a bad player to shake up the odds (i.e. artillery) is an unnecessary gamble for a unicum.

A bad player has NOTHING to lose from artillery being added

A good player has EVERYTHING to lose from artillery being added.

Q.E.D. Baddehs.

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This is good to have here. I threatened to reference it on the WoWP boards in response to people thinking that wings randomly being blown off was a good idea. Fortunately it never got to the point where I'd have to brave the WoT forum search function.

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Fundamentally, artillery just does too much damage, regardless of how good you are. A bad player can still deal massive damage in artillery because the mechanic is basically point, click and hope RNG is favorable. It takes a great deal of difficulty to skillfully play a fragile medium tank and deal massive damage with a DPS gun that is reliant on you staying alive for a prolonged period of time. It takes very little skill to sit in the rear and get a favorable RNG role, killing said good player because he got lit despite his best effort, or had to take a calculated risk. Obviously arty factors into said risk (e.g. chance of getting nuked while moving into a new position), but due to the randomness of artillery (which Ech did a great job of explaining through complicated maths), it's difficult to access how likely you are of getting killed. When my enemy has bad artillery players I tend to play a little bit more aggressively if necessary, whereas I would have been more conservative had the enemy had good artillery players. Generally that formula pays off, but you still run into those situations where out of nowhere you find that half your HP is gone due to an ARMED GW Tiger.

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My problem with artillery is that it's far too easy to ruin someone's day, whereas it actually takes skill to completely ruin someones day in a tank.

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I didn't understand most of this considering I'm an arty player and have reduced this game to left-clicking the red pixels and hoping to win. So if you could give a better explanation on why arty should be removed from the game that would be great.

I'm glad the Garbad apologists have finally arrived.

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I didn't understand most of this considering I'm an arty player and have reduced this game to left-clicking the red pixels and hoping to win. So if you could give a better explanation on why arty should be removed from the game that would be great.

I'm glad the Garbad apologists have finally arrived.

 

My role is to give an expert opinion in maths, not an expert opinion in tanks, not to be an apologist for Garbad (I don't even like the guy all that much).

 

While we're at it, at no point did I say arty needed to be removed, all I said was that in its current state, it favors low-skill players.

 

 

Further note that this thread is now OUTDATED as of 8.6

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Seems like a lot of math/effort to prove something that pretty much everybody agreed was true anyways?

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Seems like a lot of math/effort to prove something that pretty much everybody agreed was true anyways?

 

Its always good to have things backed up by maths. Anything you can't prove with maths is probably wrong.

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In short, a welcome dice roll to a bad player to shake up the odds (i.e. artillery) is an unnecessary gamble for a unicum.

A bad player has NOTHING to lose from artillery being added

A good player has EVERYTHING to lose from artillery being added.

Q.E.D. Baddehs.

I think it's important to point out that this is a very simplified model -- and only really valid for one-on-one from-full-health battles, which rarely happen in the game.

 

Often you will see a good player facing 2 or more players of varying skill level (often because the good player is the one left standing after the lower skill players are eliminated), in which case it's not true to say a good player has nothing to gain and everything to lose from arty being added.

 

As a personal anecdote, I recall a match I played as arty on Erlenberg, north spawn, where my team only sent a single TD to the north side. While our giant blob of mostly uselessness was flailing around in the south, myself and the other arty supported the TD, keeping their team from overwhelming him and allowing us to hold the north and win the game. The TD player wasn't a unicum, but was at least good, and was very grateful for the support--even a unicum would have had a lot of trouble holding that side against 5+ reasonably competent enemy tanks. Those kinds of situations absolutely do arise in real games, and there are times you simply can't play horse with a single enemy because you're not actually facing a single enemy -- and in those cases, you need support, whether from arty or from some other source.

 

 

Using this model to say "arty is a pure negative for good players and a pure positive for bad ones" doesn't hold up to the actual complexity of the game, in other words. (I'm not sure that Echelon was actually saying that -- I just don't want anyone else to take that conclusion either.)

 

Whether arty is the best way to solve that need I won't get into (I think it's very arguable that it's not ;) ) but it's also not a pure negative in the game as actually experienced.

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I think it's important to point out that this is a very simplified model -- and only really valid for one-on-one from-full-health battles, which rarely happen in the game.

 

Often you will see a good player facing 2 or more players of varying skill level (often because the good player is the one left standing after the lower skill players are eliminated), in which case it's not true to say a good player has nothing to gain and everything to lose from arty being added.

 

As a personal anecdote, I recall a match I played as arty on Erlenberg, north spawn, where my team only sent a single TD to the north side. While our giant blob of mostly uselessness was flailing around in the south, myself and the other arty supported the TD, keeping their team from overwhelming him and allowing us to hold the north and win the game. The TD player wasn't a unicum, but was at least good, and was very grateful for the support--even a unicum would have had a lot of trouble holding that side against 5+ reasonably competent enemy tanks. Those kinds of situations absolutely do arise in real games, and there are times you simply can't play horse with a single enemy because you're not actually facing a single enemy -- and in those cases, you need support, whether from arty or from some other source.

 

 

Using this model to say "arty is a pure negative for good players and a pure positive for bad ones" doesn't hold up to the actual complexity of the game, in other words. (I'm not sure that Echelon was actually saying that -- I just don't want anyone else to take that conclusion either.)

 

Whether arty is the best way to solve that need I won't get into (I think it's very arguable that it's not ;) ) but it's also not a pure negative in the game as actually experienced.

 

 

I had to make a compromise specificity to make it simple enough for the average reader without any knowledge of maths jargon to understand.

 

If I had my way this would have gone into game theory, but let's not even go there.

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