Soccer is indifferent to statistical justice

Does the playoff race inspire lame appeals to justice?

Take, for example, Clarence Goodson of the San Jose Earthquakes, commenting on Saturday's draw with Seattle:

I'm a toe from hitting it, Oba gets a foot on it and it's just under the bar. It's unlucky. I think we deserved to win the game. We should have won it, but we didn't.

Or, take Greg Vanney of Toronto FC, last week:

I thought the guys played great and laid it all out there on the field. I thought we deserved something out of the match, but ultimately, these games come down to a play here or a play there.

Or Caleb Porter, lamenting the lot of the Portland Timbers:

I thought Seattle was fortunate, but that happens in football. They feel good, they get the points, we feel bad, we don't, but I thought we deserved more out of the game.

This language is not, of course, exclusive to Seattle matches. Consider Houston's Tyler Deric, commenting on a draw against New York:

This one's tough. I think nine out of 10 times we should win this game... We're disappointed to come away with just a point considering as many chances as we had. I thought we deserved more than one point.

Or Dan Kennedy's remarks on Dallas' loss to the LA Galaxy:

It's definitely a hard loss to take, but it should motivate us because I think we deserve more... I think the Galaxy feel like they stole one tonight.

Greg Vanney, again:

I thought it was one of the best performances that we've had all year, but sometimes the ball doesn't go in... We missed the target too much: nine times. We hit people seven times.... We dominated in every statistical category that there was, except for the one on the scoreboard, which is the one that counts.

For three weeks in a row Sounders opponents have claimed they earned a better result than they received. Each have been wrong for different reasons. Goodson's complaint, in particular, is easy to dismiss without any elaborate discussion - an opponent forced into 2 injury substitutions at the half and a third injury substitution by the 60th minute cannot be considered "lucky" - but we can set his ingratitude before the football gods aside for the moment. This is a great opportunity to discuss what constitutes a "deserved" result, via histogram...

Out of the first 268 games of Major League Soccer's 2015 season, 171 (63.8%) have been decided by 1 goal or less (GD in the bins above is measured as home team - away team performance). If you look instead at a game-by-game expected goals model (newly available, courtesy AmericanSoccerAnalysis.com), the location and situation of shots taken converts into expected goal margins between -1.5 and 1.5 91.4% of the time (41.4% of games fall between -0.5 and 0.5). No MLS team runs up a massive differential in dangerous shots in a tied game - in an even game state, all but 4 games (98.5%) have a margin between -1.5 and 1.5. The xGD numbers haven't yet been processed for Seattle an San Jose, but will undoubtedly fall solidly in the center bar. The competitive disparity in MLS is insufficient for building up lopsided statistic, and Saturday's quite even game is no exception.

The cruelest sport encourages cynicism. Every single team in the league has, on occasion, adjusted tactics to limit overall chances, hoping to grab a goal on the counter and sacrificing players upfield. I'm tolerant of bemoaning results affected by unambiguously bad officiating on scoring plays - goals change games, and misapplication of the rules of the game should never influence a result - but rather intolerant of the full measure of Goodson's complaint. Most goals rely on minute successes. If your appeal to fortune relies on a single bounce not falling within range (and a half chance at best) of Obafemi Martins in the box, you didn't earn anything.

I called out the relatively small disparity in scoring results (GD) and good scoring chances (xGD) in the chart above, but there are several other features worthy of mention. The traditional advantage of home teams is clear in all three histograms. More notably, xGD models almost never build up the margins corresponding to blowout games. Many observers will (and probably should) consider this a part of the natural shortcomings of expected goals metrics, and one shouldn't fully attribute the difference between GD and xGD to luck (as I've come dangerously close to doing here; take a look, for example, at Jared Young's recent post at ASA concerning luck, using the same dataset in a very different manner). However. most games exhibit a reasonable correlation between xGD and GD, even if the numbers don't translate directly.

In fact, if one looks at games in which GD and xGD differ by more than 0.5 (excluding draws) GD and xGD pick the opposite favored team (say, for example, a positive xGD and negative GD) only 52 times, marked in red squares for the right hand plot (about 1 out of 5 games, or 1 out of 4 non-draws). Many of those are explained in part by game state, with the winning team having an xGD advantage while tied but disadvantage over the full game, defending a lead (this includes, incidentally, Seattle's recent win over Portland). Only 19 games have a disagreement between GD and both xGD measures, reminding us that - for all the perceived randomness of the game, a consistent advantage in dangerous shooting chances typically brings reward.