# How many league points do 10 Goalimpact add?

/#### The case of highly competitive league

Let's first look at a league like Bundesliga in which all 18 teams are equally good. We would expect all teams to earn the same number of points (46). Preseason, we would have no clue whatsoever who is going to be champion as everybody is equally good.Some insight we gain by the first line in the table. It shows the expected points conditional to a team ending on the respective rank. We thus expect the winner of this league of equally good teams to earn 59 points while the last ranked team only earns 33. Notice that this is pure random variation. While we expect the winner to have 59 points, we have no idea of who this is going to be.

At the end of the season probably the winner will have positive media coverage and can sell newly made star players at a premium whilst the last team saw its trainer replaced two times during the season. Humans tend to act of random outcomes, but that is not path to success. They are just fooled by randomness.

To overcome this, teams need quality measures that are not based on the actual random league position. Statistics is a way of achieving this. You could evaluate your team using TSR, EXPGRatio or other team quality measures, but this works best only during or after the season. Preseason, you'd need to use player based quality ratings such as Goalimpact.

#### Sticking out

Now imagine, one team in this very competitive league is 10 Goalimpact points better than the others. It did some investments in better players and gained an advantage. How does this affect the expected league outcome?We picked Werder Bremen as the lucky team. They increased their expected points by 6 to 52 taking an equal share of the other teams. The chances are more than 50% that they will end Top4 at the end of the season. Odds to relegate dropped significantly, though in a freak season it could still happen.

The conditional points that the league winner holds hardly changed. Although we shifted the odds significantly, we couldn't tell that Werder Bremen is a better team just by looking at the final standings. They'd probably have something like 60 points and we couldn't tell if they were better than the others or just lucky unless we use analytics.

If we increase the team quality further to have 20 points more than others in the league, The team is expected to dominate the league and win with a chance of more than 60%.

The winner is expected to end the season with 62.7 points and the runner-up with 57.1. This is five points different and chances are that the winner will be Werder Bremen and it will have won the title before the last match day. But there is still a 40% chance that one of the other team will win the title or at least be close to it with a chance of winning on the last match day. Again, just looking at the final standings, may not give conclusive insight on the team quality.

#### Points per Goalimpact

To be able to plan, how many extra points does my team earn for 10 extra Goalimpact? From the tables above, we can see that Werder Bremen added 6.2 points by increasing the Goalimpact from 100 to 110. Increasing it from 110 to 120 added another 7.9 and hence more than first increase. If we calculate this for a number of Goalimpact values, we come up with such a distribution of points added per 10 Goalimpact.As a rule of thumb, a team gains over a season 6 extra points gained by extra 10 Goalimpact. That said, depending on the actual distribution of skill in the league this can be a bit higher. There are two peaks in the chart when moving from a Goalimpact of 80 to 90 an when moving from 110 to 120. If you have a lot of opponents at a distance of 10 Goalimpact points, increase you team's quality further may hence be extra efficient.