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HATTRICK - A Study on Cards

Hattristics' page http://www.hattristics.org/pub/statCards.php contain a set of data not easy to understand immediately. I try to tweak it to find some information on the dynamics of the cards.
We start by eliminating from the table some little important data and highlighting what are the eventkeys we consider:

The table distinguishes players for their level of
  • Aggressiveness: Tranquil, Calm, Balanced, Temperamental, Fiery
  • Honesty: Righteous, Upright, Honest, Dishonest, Infamous
we expect aggressive players to commit more fouls, while the dishonest will receive more cards for misconduct.
The table shows the data by type of player, the number of players with that type ("players") and the number of games played by those players ("Played"). The values are the occurrences of events, marked with "#" and their frequency "mpbc (Match Played Between cards) that is in how many games we can expect a card for that type of player

to simplify we consider the individual classes of players regardless of the secondary characteristic, that is eg. analyzing the behavior of all tranquil, regardless of their honesty, or all infamous regardless of their level of aggressiveness.

Let's start with classes of players according to their aggressiveness

is obvious that the foul number is related to aggressiveness: just see the yellow columns for fouls, in which tranquil players gest a yellow card every 315 games (only 1 in a Hattrick career) up to one every 60 games for the calm ones, one out of 24 for balanced, one on 13 for a temperamental and one on 8 for fiery ones.
Similar developments in the column of the 2nd yellow for a foul and in the column of direct red.

In addition to these, aggressiveness seems to affect the second and fourth column, those of the misconduct too (the figure of the second column for the balanced is contingent on the value of balanced / virtuous which bust theaverage).

We continue considering the HONESTY

Here again, we considered the average of all players with a certain level of honesty, regardless of their aggressiveness. In fact, the first column suggests that the yellow for a foul are independent of the honesty of the player, they are all coming to a value of one every 80 games. As for the other columns the effect of honesty is a bit more uncertain and it is difficult to draw firm conclusions, except that the direct reds seem independent of honesty.

In conclusion it seems possible to say that there is a clear relationship between aggression and cards, while the honesty seems to be detached (or with an uncertain effect) to disciplinary
consequences .

Consequences of fouls .
Hattristics also analyzes the consequences of the fouls, noting how often an injury follows a cards, trying to see if players more aggressive or dishonest cause more injuries than others.

it can be seen immediately, but also reorganizing, that

injuries inflicted on the opponent seems to be absolutely independent from aggressiveness and the honesty of those who do the foul, always reaching values close to 8.5% of bruises and 16% of injuries.

A final note: the classes of players have the same frequency: reorganizing the data in fact shows that they are distributed according a normal (Gaussian) probability distribution, just look at the details of this table:

look at the four values at the sides (righteous/tranquil, righteous/fiery, infamous/tranquil and infamous/fiery): 933/862/863/815 everyone is equal to 0.25% of total players.
Similarly for values more and more inside: 2889/2773/2614/2591, 4256/4039 others, the four 6589/6153/6506/6208 and so on.

or if you want a graphical representation:

The curve that is formed is not symmetrical, however: there were noticed seeing that values honest/tranquil and honest/fiery were higher than
righteous/balanced and infamous/balanced.
This is because the distributions of aggression and moral conduct are similar, but with different variance. The curve of honesty has a much smaller varianc, so honest players are 6 times the sum of righteous and infamous, while the balanced are just over two times the sum of tranquil and fiery.

Andreac (team ID 1730726 in Hattrick)

This opera by Andrea Candio is licensed under a Creative Commons Attribuzione-Non commerciale 3.0 Unported License.