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GE and chance-distribution

Автор Cuomos

My aim with this article is to introduce managers that perhaps do not know much about Game Engine (GE) yet too how it works. I believe as this is a game of probability, one would get to know this game better if introduced to the core. I have made a spreadsheet where I simulate 1575 matches to reveal the chance-distribution (ChD).

First of all what is chance-distribution?
Chance-distribution (ChD) is how the Game Engine (GE) distributes the 10 normal chances that a team, as a maximum, can receive in a match, without taking chances from tactics and SE’s into account. What decides who gets the chance is ball possession (BP): the higher BP, the more chances. Up until around ~70% BP advantage is worth going for as you by then are having a statistically probability of having 9,X chances per match and therefore would benefit from strengthening your team in other zones than midfield.

How do I get a chance?
Getting a chance is a battle between midfields. To find your BP-ratio you need your midfield rating and your opponents in this formula:

{ BP = Team A/(Team A + Team B) }

Let’s have an example of 2 midfield ratings to show the procedure where you are Team A and your opponent is Team B:

Team A has a midfield rating of 32 hatstats
Team B has a midfield rating of 28 hatstats

Team A 32/( Team A 32 + Team B 28) = 53,33 BP

So now we know that you (Team A) have the upperhand with a 53,33% BP, but how many chances will that give you in a match?

A match contains 3x5 normal chances:

● 5 chances exclusively for your team and received if you win the midfield battle

● 5 chances exclusively for your opponent and received if he/she win the midfield battle

● 5 mutual chances where the midfield battle decides who wins it

That leaves us at a total of max 10 normal chances per team per match. How many chances you get is calculated by this formula, using the teams BP rating:

{ Probability to get chance = Team A^3/(Team A^3 + TeamB^3) }

Using the formula we could calculate the probability for you to get a chance whenever a chance of either your exclusive chances or the mutual chances are called from GE in the match (you can use either your midfield ratings or BP ratios):

Team A 32^3/(Team A 32^3+Team B 28^3)= 0,5987338839 ~ 0,599

That means you will have 59,9% probability of getting the chance and as a match contains 10 normal chances for your team to battle for you would have; 0,599*10= 5,99 chances with a 53,33% BP.
The chance distribution probability for the match would look like this (calculated from a test of 1575 matches):

Chances	Probability
0	0,06%
1	0,51%
2	1,27%
3	4,76%
4	9,90%
5	20,32%
6	24,00%
7	22,10%
8	11,81%
9	4,57%
10	0,70%

As you can see there’s a 24% chance that you will get 6 chances (called mean as that percentage is the highest), but there’s a 76% chance that you will not! There’s ~66% chance that you will get from 5-7 chances in the match and only ~34% that you will not, ect.

How many goals would I score?
To simplify things a bit I’m setting set-piece chances to the same scoring probability as for a regular chance. If every other ratings in Team A and Team B were equal except for the BP, we could easily calculate the scoring probability as for even strength it’s ~0,46. That means the score for the match would be:

Team A Score = 5,99*0,46= 2,7554 goals
Team B Score = 4,01*0,46= 1,8446 goals

The goal probability for Team A, with 53,33% BP, based on 1575 test matches, is shown in a table below:

Goals	Frequency	Probaility
0	66	4,19%
1	224	14,22%
2	388	24,63%
3	407	25,84%
4	279	17,71%
5	139	8,83%
6	58	3,68%
7	11	0,70%
8	3	0,19%
9	0	0,00%
10	0	0,00%
	1.575,00	100,00%

As you can see every then for ~5,4 matches you would end up scoring only between 0-1 goal, but in almost just as many matches you would also have the probability to score 4 goals. However the mean says you probably score around 3 goals.

That’s all from me. I hope you got a bit more interested in GE and how it works in other ways too. If you want to know more about this specific subject then check out hattricks own DEVBLOG (here: (https://devblog.hattrick.org/2016/02/and-on-the-seventh-day-bob-sunesson-created-the-chance-distribution/). Another great place to get to know more about this and the game in general, is the global forum thread called The Unwritten Manual (you can find it hear: (17372624.1))

Best of luck and may the probabilities be with you ;)

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