A lot of people complain about "always doing minimum damage, all the time!". Parallel to that I felt, that the T34 does way too often 300 or 500 damage. Because of that I decided to take a closer look at the damage distribution.

What do we know or what do we think we know?

According to the WoT-Wiki the damage ist distrbuted according to the normal distribution. There are two values in this distribution worth looking at: µ and sigma. The expectation or mean value (µ) defines the center of the curve (highest value), the standard deviation (sigma) defines its width. Two examples:

What we see here:

- Minimum and maximum damage: Black dashed line

- Blue curve: Between minimum and maximum damage are 2 sigma (sigma = µ / 8). Therefor nearly 95,45% of all shots are between minimum and maximum damage.

- Red curve: Between minimum and maximum damage are 3 sigma (sigma = µ / 12). Therefor nearly 99,73% of all shots are between minimum and maximum damage.

Worth mentioning: I chose 2 und 3 sigma because these values are relevant at accuracy, too, according to the Wiki

Until now it was pure theory, now to the real thin with two question:

**1. How is the damage really distributed?**

2. What happens to the shots that fall theoretically below or above the minimum or maximum damage?

2. What happens to the shots that fall theoretically below or above the minimum or maximum damage?

Question 1: How is the damage really distributed?

Because of the nice average of 400 (minimum 300, maximum 500) the T34 is a really nice test vehicle for this. Unfortunately the RoF is very low, so it takes a lot of time to get enough shots (and it's very expensive!). Therefor I took the QF 6 pdr, mounted on the M7/T21 which fires every 1.96 s. Thats fast enough to get enough shots to do a statistical analysis.

- Mean damage: 75

- Minimum damage: 56

- Maximum damage: 94

The diagramm now looks like this:

Still it's not clear, which diagramm is the correct one.

Therefor, here are the measured values (701 shots, blow ups and kills ignored):

Lets put both curves (2 sigma and 3 sigma) into this diagramm:

If one calculates the error between the measurement data and the two curves (3 Sigma: 0,44%, 2 Sigma: 0,16%, sum of errors^2),

**it's obvious, that the 2 sigma curve has a lower error and is most probably the correct aproximation**.

One thing attracts our attention now:

Why are minimum and maximum damage so frequently, compared to other values?

With this in mind, lets come back to the second question:

2. What happens to the shots that fall theoretically below or above the minimum or maximum damage?

We now know, that the damage ist distributed by 2 sigma. This means that about 95.45% of all shots are between minimum and maximum damage. The rest of it, about 4.55%, has to be outside of minimum and maximum damage. Because of the symetryof the distribution, one half of the 4.55% shots, about 2.28%, has to be above maximum damage, the other half (also 2.28%) has to be be below the mimimum damage.

If you looks closely at the minimum damage, you can see that it should appear only in 0,55% of all shots. According to the measurements it happends a lot more frequently, about 2,5%. This is aproximately 2% higher than expected. Theses 2% are the 2.28% of all shots that do lower than mimimum damage. Apparently

**WoT is pushing all shots, which would do damage below mimimum, up to the mimimum damage**. The same happpends with the maximum damage,

**all shots with above maximum damage are reduced to the maxmimum damage**.

This portion is quite high and can not be ignored. Just to show you how frequent this ist:

**Maximum and minimum damage combined are more frequent than the medium damage**. Usually feelings are not a good indicator for statistics, but

**this time the feelings were right, a lot of shots have minimum or maximum damage.**

One question automatically comes to my mind:

What happends at the penetration calculation? Do we have the same phenomenon there? At least the distribution is similar ...

Solution:

All values below minimum or above maximum damage should be rejected and recalculated. Because of the calculation methode, one automatically gains two random numbers, so the number laying inside the boundaries should be chosen. If both values are invalid, a new damage value has to be calculated.

Link to the German thread: http://forum.worldof...chte-messwerte/

Edit: Syntax checked