And on the seventh day, Bob Sunesson created the Chance Distribution…

Let’s face it, no one can deny that Chance Distribution is the most discussed feature in the Hattrick World. Whether it is seen as too random or too predictable, not a week goes by without this algorithm be brought to trial in the forums. So what was Bob thinking in his office when he designed it? Let’s find out. We will start by taking a step back and look at how chances work in general.

First, we will break it down a little. As you may well know, chances come in three categories.

1) Normal Chances
2) Special Events chances
3) … and all the others 😃

The Normal Chances are really the foundation in the game engine. They are either created in a specific sector (right, left or middle) or they appear as a set piece chance (a free kick or penalty). Since normal chances are responsible for the vast majority of chances in Hattrick, we will focus on them this time and leave the other categories for another blog post. Let’s peek into the Match Engine now and see how this works.

We have 15 normal chances, in every match, to divide between the two teams in the regular 90’ time. Five of these chances are “open”, in the sense that they can be awarded to either of the two teams. Each of these open chances the teams will “fight” using their midfield ratings, and if your team loses this battle, the other team will snatch up the chance and use it. In addition to the open chances, there are also another five chances per team which are earmarked for that particular team, making it another 10 chances in total. These chances the teams will also fight over, but if Team A loses one of “their” chances, it will not be snatched up by Team B, instead it will just fizzle out into nothing.

To sum this up, every team has to fight the other team to create any chances, and there is a limit to ten normal chances per team and game.

Statistics time!

To understand and explain the outcomes of this system better, we decided to dig down deep in our database.

We gathered 10.000 matches for each of six different ball possession scenarios: The 50/50% standoff, followed by matches where one opponent has the upper hand by either 55%, 60%, 65%, 70% or 75% ball possession. We excluded all the matches that used some sort of tactical choice by either opponent and we also excluded also all matches that had variations in ball possession that was greater than one percentage point between the first and the second halves. We did to ensure we had as clear cut matches as possible to compare.

In our first graph we show the distribution plot for each case, where you can see how many times a team get a specific number of chances in the 10 000 match sample. (For better accuracy, you should check the last graph on this page which has far bigger sample)

NumberOfHomeChancesDistributions

As you can see, with 50% ball possession, the most likely to happen is to that you five chances. As the ball possession increases, you are also more likely to get more chances. Nothing unexpected here, but what about the minimum and maximum number of chances in our matches? There is an old joke in stats says that if you put your head in an oven and your feet in ice, your average temperature is just fine. And this is exactly the reason we cannot see how the boundaries act in each case when we have only the average. So we added another graph called “box plot” which will provide some deeper insight.

A box plot (or, as some prefer, a box and whisker diagram) is a standardized way of displaying the distribution of data based on the five number summary: minimum, first quartile, median, third quartile, and maximum.

Starting from the bottom, the first horizontal line is the minimum value on the dataset, the box starts on the lower quartile (25% of data less than this value), the horizontal line inside the box is the median, the box ends to the upper quartile (25% of data greater than this value) and the last horizontal line on the top is the maximum. Enough with the definitions. To our case now.

NumberOfChancesBoxplot

Let’s see the Green Box Plot with 55% of ball possession. How can we translate the above in the Hattrick World? The box limits are from 6 to 8 in vertical axe and from the definition of the box plot, it means that half of the matches with 55% ball possession will have 6, 7 or 8 normal chances. One in four matches will have less than 6 chances and one in four more than 8 chances.

Ok Bob, but what are those little dots under the limit of 3 chances? We have seen matches with similar ball possession and 1 or 2 chances. Those are called outliers (bad things happen!). They are isolated cases that are not common enough in the data to considered as minimum and maximum number of chances. Most of the times, less than 1% of the data are marked as outliers in a normal distribution. Last week, we had about 1 200 000 matches in Hattrick World. What that means? More or less 12 000 matches that could be an outlier. If you were one of the teams on the receiving end of such a case, you could safely call yourself unlucky… – or very lucky indeed!

Do you want to stop here? Nope. We will not. What about the rest of the cases? What will happen in a match with 53% or with 85% ball possession? It wasn’t easy to find comparable data for every case. So, we run a simulation of 1 000 000 times for each ball possession between 50% and 99% and calculated the average number of normal chances that a team will get and had the data drawn up as a distribution plot. Here are the graphs with the results:

AverageChancesInSimulation

Can you see it? Up to 65% the trend seems linear. Every single percentage point could make the difference and give you an extra normal chance in the match. What do you think about ball possession above 65-70%? Is it worth the effort? It’s up to you to decide it!!!

And at last, we can see in scale how the first graph of the post behaviour in every single ball possession of a team. What do you think Bob? – “I could say, the more the merrier.”

SimulationDistributions

Did you enjoy it? Do you want more blog posts like this one? We plan to publish one blog post every month and once or twice per month a simple graph that could be about users demographic, economy, match engine, forums or whatever you feel it would be great! Send us your feedback and tell us what exactly you want to do for the next time.