Some time ago I was asked to look at the development of young players between the ages of 18-23. This is a crucial period in which players mature physically and mentally, and their trajectory in this period often determines the rest of their playing career.
Now it’s well understood among statisticians that if you plot an average value of something against age in a pool of individuals, the age curve you get does not necessarily reflect the real picture of within-individual growth. One reason is attrition – you lose individuals along the way (And new individuals may even join.) At any rate, the group measured at the start may be quite different to the group measured at the end.
This problem is especially acute in football. I examined a dataset listing all Premiership goal-scorers over 17 seasons which contained over 900 Midfielders and Forwards. Only 20% of these players had a Premiership career exceeding 4 seasons. In Big 5 European dataset I found that only 46% of 19 year-olds were playing in the Big 5 3 years later. Because it is the poorer performers who tend to drop out first, age curves uncorrected for attrition tend to underestimate the decline of players past their peak.
To avoid the problem of attrition, I looked only at growth curves – within-individual changes over time. What surprised me was that the growth curves for many performance indicators were rather flat. For some indicators there seemed to be no, or remarkably little, improvement with age.
I figured (eventually) that differences in experience might be a confounding factor. Consider the chart below.
By the time he is 23, the average forward has played the equivalent of 50 top-tier matches. Carlton Cole is a player who showed this kind of average development. On the other hand an exceptional player like Rooney, who began his Premiership career at 17, had played 160 matches by the age of 23. Defoe’s experience grew at roughly the same rate as Rooney’s, (the slopes of their respective growth curves are similar) but in terms of total experience he stayed about two years behind.
It is clear that players of the same age can differ considerably in the amount of experience they have. The question we wish to answer is how age and experience interact to drive performance growth, and which is the most important.
Measuring experience turned out to be a bit of a problem. Because my dataset did not cover the whole world from time immemorial, there was no way to measure the experience of a player when he first appeared in the records without looking elsewhere. So I manually looked up each player’s history in the Scout 7 database. This was labour intensive, so I limited my task to Forwards. My final data sample contained 387 forwards between the ages 0f 17 and 23. The performance indicator I focus on here is Goals/90.
Modelling the data
I used a linear mixed model to do the analysis. This kind of model has certain technical advantages for longitudinal analysis; it allows each player to have a different initial starting point so we can estimate the growth curves more accurately, and also provides a more accurate estimate of significance levels than the standard type of regression model which lumps all players together.
How Age and Experience Combine to Drive Performance Change
I first looked at the effect of Age (at the start of the season) on Goals/90 in that season. At first sight it appeared that Goals/90 was not related to Age at all. Whether using a straightforward regression or the more sophisticated linear mixed model, Goals/90 remained stubbornly unrelated to Age. This seemed to me ridiculous. How can a young developing forward fail to improve on what after all is his key performance indicator, and the reason for his being on the pitch in the first place?
The key insight (as in why did it take you so long to think of this) was to include Experience as a second predictor. With both predictors in the model, I was able to disentangle and compare their individual effects.
The effects of Age and Experience on Goals/90 can be expressed in simplified form as follows:
Goals/90 = 0.25 + 0.0021*Experience – 0.0125*Age
Age is age in years, and Experience is previous experience in number of matches, and both variables are centered around their respective averages.
The coefficient for Age is not significant; the key element in the model is the coefficient for Experience. It means that for a player of average age (21 in this sample), Goals/90 increases by .0021 with each match played.
This may not sound much, but it turns out to be make quite a difference. When we plug http://laparkan.com/buy-vardenafil/ typical values into the model equation, we see that the rate of improvement in Goals/90 depends critically on experience. The chart below shows the growth curves for three hypothetical players. These players all have the same performance at age 18, but one then plays 7.7 matches per season, one plays 12 matches per season and one plays 25 matches per season.
The chart makes clear that the players who play more become more prolific with age, and those who play less show little change.
The last piece of the puzzle is to realize that 50% of players play fewer than 7.7 matches/season. It is this low growth in Experience for many players that explains why we do not see Goals/90 increasing with Age for the typical young player.
A Mediation Perspective
Another way to think about how Age and Experience are intertwined is a ‘mediation’ process. Here, we postulate a specific causal relationship in which the effect of Age on Goals/90 is ‘mediated’ by Experience. In other words Age influences Experience, and Experience influences performance. The question then becomes how much of the influence of Age is direct, and how much is transmitted through the mediating variable Experience. I ran a mixed effects mediation model with the results shown below:
Here, the effects of Age are divided into two, a direct effect shown in red and an indirect effect shown in blue. Along the direct path, Age exerts a (non-significant) negative effect on Goals/90: when Age increases by one year, Goals/90 drops by 0.0125. Along the indirect path, Age exerts a positive effect on Goals/90 through experience. When Age increases by one year, experience increases experience by 7.9 (matches), which in turn increases Goals/90 by .0021 per match. To determine the effect of Age along this path, we multiply the path coefficients, giving a value of 7.89 x .0021 = 0.0166.
The net effect of Age on Goals/90 is found by adding its direct and indirect effects. Since these are in opposite directions, they almost cancel each other out, i.e. Total effect = 0.0166 -.0125 = .004. This is a small and statistically non-significant effect, and we can now see why Goals/90 appears not to change with age.
As previous work has suggested, improvements in Goals/90 for elite-level forwards between the ages of 18 and 23 are typically small and non-significant.
However, this picture changes when we take into account levels of experience. Players who play frequently at the top level do improve on this KPI, but because they are a minority, we do not see the average player improving much. Our results suggest that it is not age as such that drives the improvement, but the accumulated experience of playing, which may – or which may not – increase with age.
It is perhaps useful to think of a virtuous circle. Successful or talented players get selected more often; this gives them experience and the opportunity to improve still further; this in turn leads to more success and an increased chance of selection. Meanwhile, less successful players are selected less frequently, and lose the opportunity to improve; these players tend to remain at about the same level. Getting older does not of itself have much effect, and eventually these players will drop out of the elite level.
It would be nice if this was a universal pattern, but in fact not all performance indicators behave in this way. For example, the percentage of ground duels won shows quite a strong increase with Age, irrespective of Experience. Here is the mediation diagram:
In this case, the direct effect of Age is positive and significant, and its indirect effect via Experience is tiny and non-significant. In other words, experience does not help a player to win more ground duels – but being older does. This begins to make sense. Some performance indicators like scoring goals are skills that develop with experience on the football field. Others, like winning ground duels, depend primarily on physical ability, and improve naturally with age as players mature.
What does this mean for player assessment? First, not to write off younger players with limited experience too early. They may improve with experience (or they may not). But until they have had a certain amount of experience at the top level it is too early to judge their final potential on performance alone.
Secondly, the performance trajectory of young players is driven by a subtle blend of age and experience. Where performance indicators are used to assess player development or to make recruitment decisions, it is important to understand which indicators depend primarily on age, and which on experience.