Thursday, December 6, 2012

Age and the Inverted U: Player Age and Transfer Market Valuations

Timeless beauty?
Some things, like a good wine, get better with age. Footballers do, too, but unfortunately only up to a point. Even in the era of Giggs, Scholes, and Friedel, no matter where athletes do their work, they will eventually see a decline in performance. If that's true, and if we assume that a player's performance is linked to his market value, both should increase during the first half of a player's career and decline thereafter.

But is that really the case? And if it is, where exactly is that turning point – the time at which players become more and less valuable? One way to answer that question is examine their performance; another way is to see what the market says. It's the latter we focus on here. We wanted to know: what is the connection between a player’s age and the price he can command?

To answer these questions, we collected data from the respected Transfermarkt website for all players currently on Premier League squads and performed a variety of calculations on their transfer values (complete data were available for a total of 502 players; we collected these data in early October).*

As in our previous analyses, we estimated a set of of regression models with the aim of accurately predicting a player’s valuation based on a variety of factors, including things like position, nationality, club, contract length, experience in the league, and so on. But critically, we also included two variables to assess the influence of a player’s age on his valuation – the actual age, to capture any linear trend in age and age squared, to see if the connection between age and valuation is curvilinear.

Lo and behold, our results reveal that the conventional wisdom holds.** Players’ valuations look like an inverted U, rising for some years but then peaking and falling afterwards. While these regression results confirm conventional wisdom, they don't tell us the exact shape of that inverted U.

To pinpoint when exactly the market says players peak, we used the regression models to calculate the average player's values in different age groups (and plotted them in the graph below).

We were surprised. According to these results, the current Premier League market valuations tell us that players peak relatively early in their careers.

Data source: Transfermarkt.

(c) 2012

In fact, our calculations suggest that players' market valuations are highest at age 26, at a price of £7.24m. The data also show that 18 and 33 year-olds are valued roughly the same, with players beyond 33 continuing to decline significantly - a 35 year old is half as valuable as a 31 year old or the average 20 year old.

Of course, there is no such thing as the "average" player - it's a figment of our statistical imagination by controlling for things like positions or nationality. Moreover, these calculations don't tell us whether there are differences in age curves for different positions or nationalities or players with different sets of skills (we strongly suspect there are, as Mr. Friedel would probably point out). And admittedly, the data are from a single season and therefore it's impossible to say whether they are generalizable beyond this year or how they have evolved and will continue to evolve over time.

At the same time, the numbers do tell us something about the logic of the transfer market. Players' valuations peak in their mid-20s rather than the late 20s, as is commonly assumed by people in the know. By the way, that doesn't mean you should sell your stellar 26 year old midfielder - his performance probably is in line with his value. Instead, to find value in the market, see if there are great bargains to be had among players whose valuations haven't peaked or who the market thinks are past their prime. You don't need to field 11 of those kinds of players - one or two will probably do.

* To appreciate what these data are based on, it's worth knowing that players’ prices are valuations, not actual sums someone paid for the player. This means that they are akin to the value of your investment portfolio - based on what the stock market says it is worth, but not realized gains and losses when the time comes to cash out. If you speak German, you can find more detail here.

** Both age terms in our regression were statistically highly significant (with age positive and age squared negative).