At Sounder at Heart, there is a long and storied tradition of attempting to weaponize math to explain a phenomenon long thought to be completely indecipherable to the rational mind: the behavior of referees. With Chris Penso’s recent outing against Seattle resulting in his fourth red card in nine games on the pitch with the Seattle Sounders, we attempted to take a closer look at what the numbers have to tell us and to see if there are any basis to a fan’s deepest fear — that the man in the middle is, in fact, out to get you.
A preliminary disclaimer on this article: it has been some time since I have engaged in a meaningful way with the mathematical world of statistics. Like most sportswriters, I can decipher a box score, but it has been years since I have had to attempt to compile a chart (which, to my chagrin, I discovered that Excel has done away with the completely logical Chart Wizard in place of allegedly user-friendly nonsense).
With that in mind, let’s set some ground rules. Some referees have only ref’d one or two Sounders matches. To that end, I’ve excluded every referee that hasn’t worked at least five Sounders matches in the interest of this site’s primary user base.
Let’s meet today’s contestants and see how many Sounders matches they have been in charge of:
Baldomero Toledo - 20 matches
Jair Marrufo - 14 matches
Hilario Grajeda - 14 matches
Kevin Stott - 14 matches
Mark Geiger - 14 matches
Ismail Elfath - 14 matches
Alan Kelly - 13 matches
Ricardo Salazar - 12 matches
Silviu Petrescu - 10 matches
Chris Penso - 9 matches
Allen Chapman - 8 matches
Drew Fischer - 8 matches
Armando Villareal - 7 matches
Juan Guzman Jr. - 6 matches
Jose Carlos Rivero - 5 matches
What are we trying to prove?
Obviously, the projections of this study are going to be messed up somewhat by the small sample size. Even in Toledo’s case, 20 data points is a small number to try and draw reliable observations.
So, what if we bump up our sample size to include every MLS match a ref has ever worked? If we do that, then we’re given a much better data sample. Guzman Jr. has worked the fewest matches with 61, and the venerable Toledo tops out the range with 110 appearances. Most other referees are in the mid-80s range.
By tallying up the number of yellows and reds shown by a given referee, divided by his total number of appearances, we can determine who gives out the most yellow and red cards in a given match, on average.
Here’s the list:
WhoScored doesn’t seem to make an obvious distinction between red cards given for a second yellow and straight red cards, so bear in mind that the right-hand column is probably better termed “dismissals per game.”
As you can see, Penso tops the list, which suggests that he doesn’t particularly dislike Seattle, he’s just card-happy. Credit to Toledo, too, who has sent off 45 players in his 14-year MLS career, most recently Graham Zusi and Christian Bolanos in a hotly-contested SKC-Whitecaps match last October.
Interestingly, the color scale in the second column doesn’t follow along as neatly as one might think. This suggests that a referee’s willingness to dismiss a player doesn’t seem to correlate to his willingness to caution one.
Let’s chart that:
As we can see, certain referees, like Toledo and Penso, are far more likely to send a player packing than their counterparts. Others, like Marrufo, seem distinctly interested in letting a match finish with 22 men on the field. In fact, in Marrufo’s case, he barely hands out cards at all. The 40-year-old has dismissed just seven players in the 85 matches he has governed, five fewer than the next lowest figure in this data set.
Penso, then, doesn’t seem to have it in for Seattle as much as he’s just very willing to send someone off. Sure, Clint Dempsey and Obafemi Martins may have both twice felt the sting of a Penso dismissal, but so have 29 other players in the referee’s 89 non-Sounders matches. Granted, Penso has now issued a red card in 44 percent of his Sounders games, but again, the limited size of the data set makes it impossible to draw any meaningful conclusions.
So what? Maybe Toledo and Penso happen to get handed all the bloodbaths? Right?
Let’s take a look at the average number of fouls given by each referee over the course of their career, and then chart that against average number of cautions given to see what we can shake out:
Note the high discrepancy in cards issued across such a relatively short spectrum of fouls-called per match. This seems to confirm what the data was already suggesting: some referees are more inclined to give out yellows despite calling a similar number of fouls as their counterparts.
As a final look into the relationship between fouls and punishment, take a look at the graph of dismissals against fouls-given:
As expected, Toledo and Penso remain at the top, but the grouping of the main body of referees may actually be reason to take heart with most MLS refs. The tendency to dismiss a player does not seem to increase with referees who tend to call more fouls, suggesting that for the most part referees only tend to dismiss players in egregious situations.
Certainly, Toledo and Penso are two of the harshest refs in MLS. They’re certainly the most avid bookkeepers in our data set. This of course, sparks the eternal debate of whether harsh referees are good ones, but I’ll let that one play out in the comments.
It hardly comes as a revelation that different referees call the game differently. It is interesting, though, to attempt to chart these tendencies from a mathematical standpoint and display them for further consideration.
Obviously, there are issues presented with the data here. First, this study makes no attempt to determine how many of these cards were given justly or were the result of referee error. What is more, looking at a referee’s entire body of work will only the show net average of the referee that he has been, not necessarily what he is or will be (like players, referees go through periods of good and bad form).
Still, this data shows that the Sounders can expect very different things out of a match depending on who is in the center of all the action. Brian Schmetzer doesn’t seem like the sort of coach to tailor his tactics to a referee’s tendencies, but the club may want to start giving players a heads up if the ref has been handing out a lot of business cards lately.
And if you’re ever looking to two-foot the guy who took the last hotdog at the barbecue, hold out for a Marrufo match.