Quantitative Market Valuation Model of Top European Strikers in Football: Rooney Is Vastly Over-valued

By: Megan C.

September 10 2013

Abstract:

The European football transfer market seems to be quite inefficient, evidenced by large disparities between player performances and wages. The transfer saga this past summer with Rooney brought to mind Rooney’s performance and compensation, which, compared at face value with those of other players like Van Persie, seem out of proportions. Given this, I chose ten of the top strikers in Europe, dividing their careers into two age brackets (20-23 and 24-27), and attempted to quantify their true value – relative to other players of similar pedigree; whether a striker, compared to another with similar goal out put and efficiency, is over or under-valued by its club. Similar to the stock market valuation method of Price to Earnings ratio (PE), I developed two quantitative measurements called Goal Efficiency (GE) and Price Per Goal (PPG). I compared these values using statistical analysis, and came to the following conclusions: Rooney is the most over-valued player of the top 10 European club strikers I analysed; Messi is more efficient than Ronaldo; Roberto Soldado is the most under-valued player of the 10 I analysed. It should be noted, however, that this PPG model does not take into account other factors such as marketing value, league competitiveness, club ranking, etc. For Phase II and III of my research, in addition to increasing my sample size, I plan to incorporate those other factors into a more comprehensive valuation model, fitted specifically to each player.  

Introduction:

The transfer saga with Rooney to Chelsea this past summer got me to thinking about whether Rooney’s price tag is justified or not based on goal output. He posted respectable numbers last season with 21 goals in all competitions, but is valued at a hefty 67 million euros. Compare him to Van Persie, whose goal output was 35 and is valued at 58 million euros, and Rooney seems a bit overpriced to me. Of course there’s the whole “he’s playing in the #10 position now” or “Van Persie’s stealing his thunder”, but regardless of whether or not those things are true, the fact remains that Van Persie is starting and playing in his favoured position because he’s better at it than Rooney is. Yet his pay is less, even taking into account marketing value, which is worth a couple million euros. Which leads me to wonder that the transfer market appears to be quite inefficient and inconsistent. As stated in the abstract, based on this hunch, I attempt to quantify the relative value of each striker’s goal per 90 minutes played, comparing the PPG average and GE using statistical analysis methods (mean/median, Standard deviation, z-score).

The method I use is similar to one used to value stocks. Here is my methodology and steps/calculations (all done in Microsoft Excel):

1. Collect data for player’s age, goals scored, minutes played, and market value (euro)
2. Split up into following age brackets: 20-23 yrs, 24-27 yrs, 28-31 yrs, as those are the rough transition stages of the striker’s career (ignore last one for now)
3. Normalize the minutes played and goals scored in each season to number of goal per 90 minutes played, called Goal Efficiency (GE). GE measures each player from the same base in regardless the minutes played due to many factors. GE is similar to Earnings Per Share used by any for profit corporation
4. Use the market value of each player and divided it by his GE, let’s call this Price Per Goal ratio (PPG). A higher PPG means that the club is paying more for every goal this player score per 90 minutes played.
5. To smooth out possible 1 year abnormal performance with each age group, I average the PPG for each player over the age brackets I defined earlier (i.e. PPG average for Rooney aged 20 –23, aged 24-27)
6. Another useful number here is to average the Goal Per 90 Minutes – Goal Efficiency (GE); the higher, the more goals scored given the same amount of minutes played

The next step is to compare the PPG average of each player in each age bracket to the mean and/or median of all the players across all age brackets:

7. Find the mean and median PPG Average for each age bracket
1. The mean and median for age 20-23 is quite different; mean is 39 and median is 28; this is because the data is skewed towards the larger numbers due to outliers, thereby inflating the mean
2. The mean and median for age 24-27 is much more similar, and therefore more reliable; mean is 57 and median is 56.9; this is because the data is almost symmetric with few outliers
8. Find the standard deviation of the PPG averages for each age bracket; it ends up being 20-23 is 29.2 SD’s, and 24-27 10.6 SD’s
9. Find the z-score of each player at each age bracket using the mean and standard deviation we just calculated; the z-score measures the number of standard deviations the data value is from the mean; if the z-score = 0, it’s the same as the mean (meaning no deviation); if the z-score is 1 or –1, the data value is either one standard deviation above or below the mean…etc.?

Analysis:

1. Messi is a clear outlier; this is evident by both looking at his raw PPG Average and his z-score
2. Rooney (as per my earlier hunch) is the most over-valued striker of all ten that I analysed; in fact, Manchester United forks out more money per goal (96 when he was 20-23 yrs and 101 from 24-27 yrs) than Barcelona do for Messi, arguably the most prolific striker (and player) in the world. His z-score of 1.95 (20-23 yrs) and 1.44 (24-27 yrs) are the two largest in the entire set, more so than Messi’s 1.04 and 1.40; this means that for every goal he scores per 90 minutes, he is currently being paid 1.44 times the standard deviation from the mean (the scary thing is that his is actually less than what he was paid as a teenager)
3. Other over-valued players are Hulk and Ezequiel Lavezzi. After Messi and Ronaldo (their high valuation is justified due to huge marketing potential), Hulk and Lavezzi have 3^rd and 4^th highest PPGs, 74 and 67, respectively. In addition, Lavezzi has a GE of 0.3, the current lowest of all 10 strikers.
4. Roberto Soldado of Tottenham is the most under-valued player out of the 10. He’s currently being paid a measly 28 million euros for every goal he scores per 90 minutes (all relative of course), but his goal efficiency (average of minutes per goal played) is 0.6, which is the median of all players; it also happens to be the same as Rooney’s, yet Rooney is being paid about 4 times the amount Soldado is for the same goal efficiency (If you want to compare goals alone regardless of minutes played, Soldado scored on average 28 goals in each of the last 3 seasons compared to Rooney’s 25 goals)
5. At first glance, Cristiano Ronaldo’s and Messi’s stats are actually quite similar over the past few years, with Ronaldo scoring an average of 59.7 goals in each of the last three seasons and Messi scoring 62. In recent years, their PPG Average has been very similar: Messi is 87 and Ronaldo is 89; for the same reason, their z-scores are similar at 1.0 (Messi) and 1.04 (Ronaldo). However, Messi has a higher GE, 1.3, to Ronaldo’s 1.0. Messi’s GE z-score is 2.1 while Ronaldo’s is just 1.1; Messi’s GE is two standard deviations away from the mean GE while Ronaldo’s is only 1 – this suggests that Messi is more efficient in front of goal than Ronaldo

**An important note in interpreting the numbers is the fact that they do not take into account other factors, such as marketing value, league competitiveness, club ranking, position at club (starter/bench), exact striker position (#10 or #9), willingness of club/owner to pay (i.e. Tottenham v Real Madrid), club financial health/spending power, general economic condition, injuries, playing style, contribution to club…etc. PPG and GE are designed to be used as guidelines relative to other players, not definitive markers.

**Only games played with club are counted (not international).

**Raw data from transfermarkt.co.uk

Conclusion:

The goal of this study was to quantify the value of strikers to determine whether they are over or under-valued. This was done by creating the PPG (Price Per Goal) average and GE (Goal Efficiency), using mean/median, standard deviation, and Z-score to compare players relative to each other. Analysis showed that Messi is more efficient than Ronaldo, Rooney is the most over-valued player on the list, and Soldado is the most under-valued. In the next phase, Phase II, I am planning to expand my sample of strikers. I will also attempt to find if there’s a historical “normal” or “average” path of PPG and GE for a striker, and if so, use this path to project future PPG for young players aged 20-23 years.

Planned Phase 2 and Phase 3 Research:

·         Expand stats to include more samples size/players

·         Collect and analyze stats by age to find out if there was historical normal/average path of PPG for a striker

·         Use financial concept of “Price to Future Earnings” valuation method, develop methodology to apply and calculate PPG based on future Goal per 90 Minutes - GE

·         Project future PPG for any given players incorporating all other considerations: stats (quantitative and qualitative)

·         Develop fair market value model to measure each player