Wondolowski, van Persie, Ronaldo, and Messi: How Rare Are Their Goal Scoring Totals?

If 2012 seemed like the year of the goal scorer, it was because records fell around the world.  In the United States, Chris Wondolowski equaled Roy Lassiter’s record 27 goal total in an MLS season that was set in the league’s founding year of 1996.  While he didn’t equal Andrew Cole’s 1994 and Alan Shearer’s 1996 totals of 34 goals each, Robin van Persie did tie for the fifth highest single season goal total in the history of the Premier League and a total which has only been bested by one other player in the last ten seasons (Cristiano Ronaldo).  Meanwhile, Lionel Messi and Cristiano Ronaldo had another epic battle in what has been a three-year back-and-forth for La Liga’s Pichichi, with Messi besting Ronaldo’s 46 goal total with 50 of his own in 2012.

Comparing these goal-scoring greats can be a bit problematic.  The leagues and confederations in which they play are very different, and the level of competition varies greatly between them.  There’s also the factor of the number of matches, and thus goal scoring opportunities, available to each player – MLS has varied between 28 and 34 matches over its seventeen seasons, while both the Premier League and La Liga compete in 38 match formats.  The incentives for using players can also be different between the leagues. MLS uses a playoff tournament to crown their champion, perhaps leading to an incentive to rest players along different schedules than may be found in Europe given their top-of-the-table league format.  Fatigue factors may also be playing a role.  Travel distances and schedules can be a bit difference between European and North American leagues, while national team duty and travel greatly varies as well. This means there are a number of caveats that come into play with any comparisons between the four players mentioned above, but there is a way to equalize this a bit and draw some general conclusions about just how rare their goal scoring tallies have been.  From that we may be able to make a bit of a qualitative statement about just how good the players are in respect to each other.

The data used for this analysis is a record of the goal-scoring total over a number of domestic league seasons for each player who has scored at least one goal in the seasons studied.  Data for the entire history of MLS is available via the league’s website.  Similar data for the Premier League and La Liga is a bit more difficult to find, but this site provides a good compilation for the last twelve Premier League seasons and eleven seasons of La Liga.  The data was then aggregated into a count of each goal total over the full data set from each league, with the resultant counts shown in the graph below.  An exponential regression analysis has been provided for each league’s data set, with the regression lines and equations color-coded to match the individual data point format shown in the graph’s legend.  This first graph presents the data without Ronaldo’s and Messi’s goal totals from the last few seasons.  This is done to provide analysis of the prior likelihood of such totals being realized, with the post-event likelihood being discussed later in this post.  This first graph’s x-axis has been set to the same scale as the later graph’s x-axis to provide for an ease of comparison.

The graph above shows that the exponential model fits all three leagues’ data very well, and demonstrates the greatly reduced frequency of higher single season goal totals.  The decreasing coefficients when moving from MLS to the Premier League and then into La Liga suggests that higher player goal totals are to be expected most frequently in Spain and least frequently in the United States.  This should be of little surprise given the known difference in player quality, playing style, and four fewer league games available to today’s MLS players versus those in the Premier League or La Liga, although La Liga’s lower coefficients suggest that the Spanish league has a higher proportion of its goals concentrated in fewer players than in the Premier League.  These trends also have important implications for interpreting just how frequently one could expect to see any one player’s goal total in any one of the three leagues.

The graph above must first be turned into a cumulative distribution function to analyze the projected frequency of the observed player totals, which is done via some relatively straightforward math.  This transformation allows for the calculation of the projected “frequency per 100 seasons” we’d expect to see a goal tally of equal or greater value to those already observed.  The table below summarizes this statistic for each of the four aforementioned players, while similar data for Alan Shearer and Andrew Cole has been added to the table to provide additional context to van Persie’s total from last season.  The table shows not only how rare or frequent such goal totals should be in the league’s in which they actually occurred  but also how frequently we could expect to see such goal totals of equal or higher value in the other leagues.  If one prefers an alternative view of the data, the second table plots it in terms of “average years between occurrences”.

There are a number of conclusions that can be drawn from the table:

• While Chris Wondolowski’s 27 goals in an MLS season is quite impressive, it’s within the expected frequency of occurence.  A 27 goal total or better should be expected 15 times per 100 MLS seasons, or once every 7 years.  The fact that this has occurred twice in 17 years is bit less frequent than expected, but still not a statistically significant under occurrence.
• Robin van Persie’s total demonstrates the extremely non-linear reduction in frequency for a minimal increase in goals scored.  Staying in the MLS column, we see that an 11% increase in goals (Wondolowski’s 27 to van Persie’s 30) results in a projected 53% reduction in projected frequency of the goal total.  Looking across the van Persie row, the EPL column shows the expected frequency of  a 30 goal total happening 24 times per 100 seasons versus an MLS frequency of 7 per 100 seasons.  This suggests such a goal total would happen nearly 3.5 times as frequently in the EPL as MLS.  There have been eight Premier League players with 30 or more goals in the league’s 20 year history for a rate of forty occurrences per 100 years, although five out of the eight occurrences were in the league’s first eight years.  Again, the difference between the actual and predicted frequencies is not statistically significant.
• The models suggest that we should see 34 goals or more from a single player 10 seasons out of every 100 in the Premier League, and the league is holding that pace given Andrew Cole and Alan Shearer scored as many in two of the first three years the league’s existence.
• The tables demonstrate just how much a set of outliers Ronaldo and Messi have been the last three years.  Prior to the 2011/12 La Liga season, Ronaldo’s 46 goal total was to be expected once every 61 years.  Even more rare was Messi’s 50 goal total last season.  Based upon the last ten years of history, we would have expected such a performance once every 135 years.  Messi appears to literally be a once-in-a-century player when it comes to goal scoring totals!

The way Ronaldo and Messi have pushed each other has not only been great for both players and the fans that watch the sport, but they’ve also shattered records along the way.  In any other year Ronaldo’s 46 goals in 2011/12 wouldn’t have just secured him the highest overall goal total in Spanish first division history (a record he held with his 40 goals in 2010/11), but it would have also earned him the top overall spot in history for European club football.  That spot instead goes to Messi and his fifty goals, a feat he may already beat as he has 25 goals in 16 games this season putting him on pace for 59 come next May.

Returning to the earlier graphs helps our understanding of just how much a set of outliers Messi and Ronaldo have been.  The graph below is very similar to the first one presented earlier in this post, but Ronaldo’s and Messi’s goal totals have been added to the data set.  The effect on the regression equation is quite large, with those three additional goal totals reducing the amount of variation in goal totals explained by the model by 10%.

The effects of this new model are translated to updated projected frequency numbers in the table below.  The updated numbers suggest we would expect to see goal totals of 46 or more about once every ten La Liga seasons, while the previously untouchable total of 50 goals would be expected about once every twenty years.  The statistics, both from the regression equation’s R² term and the resultant projected increased frequency of goal totals in the table below, are heavily biased due to the outlier impacts of Ronaldo and Messi.  The fact that Messi is on pace for another 50+ goal season suggests such an event is far more likely to occur than once every 135 years per the original model, but it’s also fair to say that it’s unlikely to happen as frequently as once every 17 years as the updated model suggests.  The true frequency lies somewhere in between, with it likely being closer to a once every fifty- to seventy-five-year occurrence.

While no one should discount the work required to make an MLS, Premier League, or La Liga squad let alone score a single goal in any three of the leagues, players like Chris Wondolowski, Robin van Persie, Cristiano Ronaldo, and Lionel Messi are in a club of goal scorers all of their own.  Even across the spectrum of great goal scorers in 2012 there were huge capability gaps, no matter how small the difference between the goal tallies.  The small differences in goal totals translate to large differences in expected frequency of such tallies.  Robin van Persie’s total is projected to happen half as frequently as Wondolowski’s, and Alan Shearer’s/Andrew Cole's half as frequently as van Persie’s.  Ronaldo’s and Messi’s totals are literally an order of magnitude better than Shearer’s and Cole's judging by the projected frequencies of such goal totals.  Stories will be told of Ronaldo’s and Messi’s goal scoring feats to later generations.  They’re once a half-century or longer kind of players.  What we witnessed last year and may be seeing again this year is likely not to happen again until the later half of this century.  Enjoy it while it lasts, because you're unlikely to see it again in your lifetime.