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Filtering by Tag: goals

Power Laws and Goal Scoring

Ford Bohrmann

Is there a normal number of goals scored in a season for a striker? To answer this, one may be tempted to just take the mean of the goals scored of every player in a season. If we do this for last season, the mean is 1.83. Of course, this is misleading. There isn't really such thing as a "normal" number of goals scored in a season. The reason for this is that goals scored does not have a standard distribution, the bell curve we are used to. For example, if you looked at the distribution of heights in a population, you would see a nice bell curve. Most people are right around the average height, and as you go towards the extremes either way (really short or really tall) you find fewer and fewer people. Therefore, the mean of heights in the population is instructive because it gives us the "normal" or "typical" height. The problem is, goals scored in a season does not follow a standard distribution. Instead, most players score no goals at all. The next most common number of goals scored last season? Just one goal, of course. This distribution continues, and it follows a power law distribution.
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Answer to my Question via Twitter Posted Earlier

Ford Bohrmann

The question I asked earlier today via my twitter @SoccerStatistic was, "Which statistic correlates best with a team's point total?" The options were goals against, corners, goals for, and shots on target. The answer is extremely surprising to say the least.

Another way to ask the question is "Given the goals against, corner, goals for, or shots on targets total for a team in the EPL, which variable would allow you to best predict the point total of the team?" Turns out the answer is not goals for, goals against, or even shots on target. Yep, its the corner total. This means the amount of corners a team accumulates during the season is a better indicator of the team's standing than the other variables. To me, this is mind-boggling. The point of the game is to score more goals than your opponent, yet the amount of corners predict point totals the best.

The way to figure this out is with linear regressions between points and the 4 statistics in questions using season totals for EPL teams. A linear regression tells us how strong the linear relationship between two variables are with a number called the correlation coefficient. A value of 0 would mean there is absolutely no relationship, and a value of 1 would mean a perfect linear relationship. Below is a chart of the 4 variables and their correlation coefficient value. The absolute value of the correlation coefficients are given below, as goals against obviously has a negative relationship with.

Corners just edge out goals for and goals against as the strongest relationship. There is only really one explanation I can think of to explain this: Corners result from pressure on the goal, and more corners would mean more pressure on the goal which corresponds with more wins and a higher point total. Still, the fact that the relationship is stronger than the relationships between points and goals for and points and goals against really amazes me.

A few things to point out: First, the best way to really predict a team's success is with their goal differentials. However, it is still interesting that corners have the strongest relationship of the 4 variables above. Second, the relationship between corners and points shouldn't be read in to too much. This doesn't mean that if a team goes out trying to get more corners they will be more likely to win the game; instead it means that better teams tend to earn more corners based on the way they are playing.

This also leads in to something else I will be working on in the near future which relates somewhat. Are the amount of goals scored by a player a good indication of the quality of the player? Forwards are the highest paid players in soccer, but what if goal scorers are significantly overvalued? Is it right when we say "Player x is a better player than player y because he scored more goals this season"? I think there are a number of ways to test these questions, so check back in the coming week for some results and analysis.