RIVALRIES in football can come and go, but there is no surer bet for a high-stakes club match than the biannual Clásico between Real Madrid and FC Barcelona, the two titans of Spain’s La Liga.
On March 22nd Barça pulled out a spirited 2-1 victory, increasing their margin in the standings over second-place Real Madrid from one to four points.
Meanwhile, in the league’s parallel and almost as closely watched scoring race, Cristiano Ronaldo (pictured, at left), Los Blancos’ biggest star, slipped home his 31st goal of the season in the 31st minute, bringing him within one of the 32 scored so far by Barcelona’s Lionel Messi (right).
Ever since Mr Ronaldo was transferred to Real Madrid in 2009 for a then-record fee of £80m ($130m at the time), setting the stage for him and Mr Messi to square off at least twice a year, they have been regarded by common consent as the two best players in the sport.
Their ranking relative to each other, however, has flip-flopped. Mr Messi won the annual Ballon d’Or award issued by FIFA, football’s international governing body, to the top performer of the year for four straight years from 2009-12.
During the past two campaigns, however, Mr Ronaldo has captured the prize.
There is little mystery as to the cause of this changing of the guard: in a sport whose currency is goals, Mr Ronaldo was money more often than Mr Messi in both 2013 and 2014.
However, not all goals are created equal: their value depends entirely on the context in which they occur. Some land in the 90th minute of a 1-1 tie and secure a win all by themselves; others are tacked on at the same point in a match once a team is already up 3-1.
And while the assumption that goals should be distributed more or less normally between high- and low-leverage situations certainly holds over large sample sizes, it often breaks down at the level of specific players.
A proper measure of individual scoring output would consider when shots find the net as well as how often. And upon further scrutiny, it turns out that the Ballon d’Or voters—or at least those who based their decision on scoring—appear to have erred.
Even during Mr Messi’s two “down” years, Barcelona and Argentina benefited more from his comparatively modest 86 goals than Real Madrid and Portugal did from Mr Ronaldo’s prolific 105.
The statistic that weights goals according to their context is called Expected Points Added (EPA), an application of the Win Probability Added framework originally developed for baseball.
By extrapolating from over 4,000 English Premier League matches played from 2001-13, the analytical website SoccerStatistically.com offers an applet that lists the odds of a team’s win, draw or loss at any point in a match given the venue, time remaining and goal margin.
Comparing these probabilities immediately before and after a goal shows how much each score changes the expected outcome.
For example, take the two situations mentioned above. With the score tied in the 90th minute, a team playing at home has an 11% chance to win, 82% to draw and 8% to lose.
Multiplying by three points in the standings for a win, one for a draw and zero for a loss, its expected points (EP) are 1.13. With a one-goal lead, in contrast, its win probability shoots up to 95% and its draw odds fall to 5%, which equates to 2.89 EP.
The gap between them of 1.76 points is the EPA associated with such a critical goal. In the alternate situation, with a two-goal lead in the 90th minute, the home team already has a 99.7% chance to win and 0.3% to draw.
Adding on a final goal as an exclamation point is worth just 0.007 of EPA—250 times less than the tie-breaker.
The only necessary adjustment to this simple calculation comes on penalty kicks. As soon as one team commits a foul, their opponents’ expected points increase by the EPA of a goal multiplied by the league’s average spot-kick conversion rate, which in La Liga has been 78% since 2009-10.
If the designated kicker nails it, he is then credited with the remainder, while if he flubs it, his account is debited 78% of the goal’s value for the missed opportunity.
As an illustration, take Real Madrid’s home match on March 1st. It remained scoreless in the 52nd minute, giving Los Blancos1.60 EP. When Villarreal was called for a foul, the home team gained a 78% chance to score a goal that would improve their EP to 2.46, a difference of 0.86 points.
Mr Ronaldo duly netted his spot kick, adding 0.19 points of EPA (the remaining 22% of 0.86) to his ledger.
Conversely, in a match on February 24th Barcelona led Manchester City 2-1 four minutes into added time, for an EP of 2.90. City fouled in the penalty area, raising Barcelona’s EP to 2.98 by giving them 78% odds of scoring a goal worth 0.10 of EPA. But Mr Messi missed, dropping his team’s EP back down to its previous level, and thus reducing his EPA total by 0.08.
So what happens when this analysis is applied to every single goal scored by the game’s two leading lights in La Liga, the pan-European Champions League and the World Cup during 2013 and 2014? Mr Ronaldo’s edge all but vanishes.
The pride of Portugal’s 105 goals contributed 41.6 EP to Real Madrid and his national squad, an average of 0.40 EPA per goal.
Although he assured himself a second straight Ballon d’Or with three goals in the semi-final and final of last year’s Champions League, all of them were mere pile-ons. In the return leg against Bayern Munich, he scored when Los Blancos already led 3-0 and 4-0 in the aggregate, for a combined EPA of just 0.29. And in the final, his score was a penalty kick in extra time when Real Madrid already enjoyed a 3-1 lead, yielding a trivial 0.004 of EPA.
In contrast, the supposedly slumping Mr Messi squeezed 40.3 EPA from his 86 goals, an average of 0.47 each. He showed a remarkable knack for scoring when it counted: on five different occasions in 2013 and 2014, he netted a tie-breaking goal in the final 20 minutes of a contest. In other words, the Argentine’s 20% deficit in raw goals relative to Mr Ronaldo was almost entirely offset by a 20% advantage in the importance of the goals he did score.
Moreover, even this metric fails to do full justice to the superior timing of Mr Messi’s scoring. Just as important as when a player’s goals occur within a match is which matches they occur in.
And Mr Messi’s goals—particularly his match-winners—have been heavily concentrated in his teams’ most crucial contests.
There is no straightforward way to assign weights to different matches. Only the most die-hard club supporter would consider a La Liga championship to matter as much as a World Cup title—but who’s to say precisely how much more the Cup is worth? One potential measure is television viewership.
Using readily available statistics from Britain, and adjusting for whether England was playing and whether the match was broadcast over the free airwaves or only via satellite, Champions League matches ranged from having an equivalent audience to a domestic-league contest (in the group stages) up to three times as much for the final. And interest in the World Cup never fell below a multiplier of 4.7, soaring up to 15.2 for the championship game.
Finally, using a different methodology, Clásicos are often said to be worth twice as much as other La Liga matches, since the victors of these Barcelona-Real Madrid contests both secure three points for themselves and deny three points to their chief rival.
Only when this element of context is taken into account does Mr Messi’s superior performance fully reveal itself. After factoring in the importance of a match, Mr Messi pulls away with a 59.5 weighted EPA in 2013 and 2014 (an average of 0.69 per goal), compared with 50.4 for the Ballon d’Or winner (an average of 0.48).
By EPA alone, Mr Messi’s most valuable goal during the past two years was a 91st-minute winner on neutral turf. But he delivered this coup de grace not to a lowly opponent in La Liga, but rather to Iran in the group stage of the World Cup, a match that attracts 4.7 times more interest.
He also scored twice, breaking a tie both times, in Argentina’s match against Nigeria four days later. In contrast, Mr Ronaldo only found the net once during the Cup, against Ghana. And even that goal had a marginal impact: although it was the deciding score in the match, Portugal needed a four-goal swing relative to the United States to advance out of its group.
As a result, Mr Ronaldo’s yeoman effort did nothing to prevent his countrymen from heading home early. If that match were treated as reducing a four-goal deficit to three, Mr Ronaldo’s EPA for the two years would collapse to 43.6, 27% lower than Mr Messi’s.
Fans of Mr Messi should be careful not to overinterpret this analysis. First, goal scoring is just one part of football. Half the game is defence, which is excluded entirely from this calculation. And even on offence, playmaking ability—consisting both of passing skill, and of the ability to draw defenders’ attention and open space for teammates—can matter as much or more as the final act of slipping the ball past the keeper.
Moreover, even when it comes to goals alone, none of this means that Mr Messi has more ability to score when it counts than Mr Ronaldo does. In general, evidence across sports is scant that “clutch” ability, or its opposite “choking”—meaning a tendency to improve or decline in the most important situations—are repeatable skills or deficiencies.
In a sufficiently large sample, players’ performance in critical moments usually resembles their contributions overall. Some will always happen to do better than their averages with the game or season on the line and others worse, but these deviations rarely exceed the amount of variance one would expect from chance alone.
The best predictor of how Mr Messi and Mr Ronaldo are likely to do in a high-stakes match like a Clásico, or in the final minutes of a must-win contest, is their average output over all matches during the past few years, adjusted for their health and the quality of their opponents—not merely their performance in the subset of past Clásicos or other important matches.
Nonetheless, as a purely backwards-looking, descriptive measure, observers who point to Mr Messi’s return to the top of the goal leaderboard as evidence that he has at lastrediscovered his form after a pair of disappointing-by-his-standards campaigns are mistaken.
Mr Messi has indeed been the world’s most valuable goal scorer this year. He was also the world’s most valuable goal scorer in 2014, and in 2013, and (as is well-known) during the four years before that. The Ballon d’Or voters may have suffered from “Messi fatigue” for their past two selections. Supporters of Barcelona and Argentina, however, most surely have not.