Plus or Minus Gareth Bale: Stats for Week 34

We are still a long way from a reasonable statistical measure of football player value. There is some interesting work done on fantasy football, and it seems like we can make some non-crazy estimates of expected player goals and assists, but that hardly begins to describe actual player value. I say this because I want to have something to say about how Tottenham Hotspur might play without Gareth Bale, based on the numbers, and I do not have a lot.

So, I figured I'd try something out. I've long thought that some sort of adjusted plus-minus is the most promising statistical model for football player value. You compare how a team does with a player to how they do without him. Rather than trying to estimate the value of passes and tackles and shots on target, you just add up the team-level outcomes. I compared Spurs with Bale to Spurs without Bale, looking at expected goals scored and expected goals allowed.

The big problem here is sample size, as we're only looking at five missed Bale games. I'm concerned that I've captured a lot more noise than signal, as Nate Silver might say. Here's a table with the plus-minus data:

Spurs' attack has been just as effective without Bale, but the defense has become suddenly porous. That certainly isn't intuitive, but I can perhaps squint and make some of the numbers make some sense. Gareth Bale doesn't defend all that much himself, but he forces the other club to dedicate significant resources to defending him—resources which otherwise could be pushed forward. Likewise without Bale, more attacking responsibilities are shunted the fullbacks to provide width and to the deeper-lying midfielders to provide attacking runs. So, at least in theory, Bale's effect on the game might show up as an effect on team defense. Bale could "improve" the defense by forcing the opposition to only use a portion of their attacking strength and enabling his teammates to take more defensive roles.

On the other hand, it's just five games. It includes the Chelsea game where Spurs (also lacking Dembele and Lloris) were ripped apart at will by Juan Mata, Eden Hazard and Oscar. Spurs also put up mediocre defensive performances overall in their games against Everton and Reading without Bale, but the extent of the effect is definitely skewed. And come on, Bale must have some greater effect on the attack. A big hunk of this has to be assumed to be randomness.

I would want to do a full adjusted plus-minus like they use for basketball stats, but once you start adjusting for other players in and out of the lineup, the samples get even smaller.

This is something I want to keep playing around with, but the sample size issues are going to be significantly confounding.

Projections of Week 34

This week is huge for Chelsea. The underlying stats love Liverpool and project dropped points for the Blues. If Chelsea can get a win, if Liverpool perhaps aren't as good as the stats say, Chelsea will be in extremely good shape for the Champions League.

Arsenal once again are facing a mid-table side in a game that they could easily lose. But it sure seems like they won't lose any of these games. I've included here three Tottenham projections, first their average projection, then the projections based on the plus-minus analysis.

As you can see, Spurs have played most of their games with Bale in the squad, and so the "Tottenham w Bale" numbers are effectively identical to the overall numbers. Based on the plus-minus numbers, without Bale the goals allowed jump way up, with expected effects on the loss column.

Since all of these games project to be relatively close, the effects of a win, especially for Spurs or Chelsea, would be a major improvement in the winning club's top four hopes. These are chances of making top four for each club, depending on the outcome of their games this weekend:

Every week it gets closer. Chelsea have an opportunity to turn this into a two team race for one spot. So far both Spurs and Chelsea have blown recent opportunities to pull away, but that doesn't mean the Blues will screw it up a second time.