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On skepticism of defensive statistics in football

The job of a defense is to prevent goals, and you do that by preventing high quality chances. A bunch of other defensive stats we have are interesting, but they don't correlate with the underlying job of a defense.

Stu Forster

Can you identify a good defensive player statistically? With good attacking players, we can usually point to things like shots, shots on target, expected goals, goals, assists, and key passes. This is in no way a sufficient method of identifying good players, but it will usually give you some reasonably useful lists. And the great thing is, we know the stats we're talking about are broadly meaningful. At the club level, shots and shots on target (and obviously goals) correlate really well to team quality. So the players who contribute good shots, they contribute to overall team stats. The parts add up to the whole.

This isn't true of individual defensive statistics. At the team level, we can look at total shots allowed or expected goals allowed. But individual defensive players don't have a "shots prevented" statistic equivalent to "shots" for attacking players. Shots prevented by definition don't show up in the statistical record because they didn't happen.

What we have instead are statistics that seem to tell us about good things that defensive players have done. These numbers are usefully descriptive, and it can tell you a lot about a player if he has a lot of tackles, for instance. If I wanted to describe what kind of player Étienne Capoue is, I could do worse than by telling you about his interception rate. But does that interception rate mean that he's good? Do players who get more interceptions prevent more goals?

Simply put, I don't know. The fundamental problem is that these defensive statistics don't add up, at the team level, to a useful measure of team defense. The parts do not add up to the whole.

As a demonstration, the following table contains team tackle and interception totals for the 2013-2014 EPL season. The "+" columns express the team totals in terms of percentage above or below league average. So Spurs' 110 Int+ means that Spurs have 10% more interceptions than the average club this season.

Club Tackles Tack+ Int's Int+ Tackle/Int TI+
Crystal Palace 495 118 356 120 851 119
Hull City 433 103 346 116 779 109
Newcastle United 427 102 344 116 771 107
Manchester United 383 91 383 129 766 107
Southampton 469 112 292 98 761 106
Tottenham Hotspur 431 103 327 110 758 106
Stoke 460 110 296 99 756 105
Arsenal 433 103 310 104 743 104
Liverpool 469 112 272 91 741 103
Everton 420 100 285 96 705 98
Aston Villa 449 107 252 85 701 98
Swansea City 365 87 334 112 699 97
Norwich City 385 92 311 105 696 97
Manchester City 425 101 268 90 693 97
West Bromwich Albion 387 92 295 99 682 95
Fulham 376 90 298 100 674 94
Chelsea 444 106 212 71 656 91
West Ham United 383 91 266 89 649 90
Sunderland 422 100 222 75 644 90
Cardiff City 345 82 282 95 627 87

This table tells you very little about which clubs are good or bad defensively.

There is some interesting information in there. José Mourinho has clearly set up his defense to avoid taking chances in the passing lanes, leading to a league low 71 Int+. David Moyes by contrast has his players keying on intercepting passes. I might have expected both Liverpool and Swansea to focus more on interceptions than tackles defensively, but instead you see a divergence between the EPL's two possession sides in how they prefer to break up play. So, these are useful descriptive statistics. Which is great.

What this means is that individual player defensive statistics stand on shaky ground.

But it's not information about who is good and who is bad at football defense. Fulham have clearly the worst defense in the Premier League, but they've got more tackles and interceptions than Chelsea. The big clubs highest on this list, Manchester United and Tottenham, have both been mediocre as defensive units.

The problem here is not that it doesn't take skill to either win a tackle or intercept a pass. Obviously it does, generally speaking. The problem is that tackles and interceptions, at the team level, are influenced by too many other factors to be useful measures of the defensive skill that is required to win a tackle or intercept a pass. (One theory might be that tackles and interceptions correlate inversely to possession, but at least so far this year that is not true. The R-Square for T+I and possession in .0002. So you can't just adjust those numbers for possession to get something useful.)

And what this means is that individual player defensive statistics stand on shaky ground. If a player has a good number of interceptions or tackles, does that means he's good at defense? Or does it mean that within his team's tactics, interceptions and tackles within his area of the pitch are going to happen more often for reasons that don't reflect either his own skill or the club's? Right now, I don't think we can distinguish.

Since the parts don't add up to the whole, we can't conclude from a player's individual tackle or interception numbers that he has contributed to quality team defensive play. This is my main argument here. I'd like to conclude with some speculation about what these stats are measuring, if it isn't team defense or possession.

Rank Speculation

I think this is the first fundamental problem in the numbers. Tackles and interceptions are not the only two ways to break up opposition possession. Good defense doesn't only lead to a tackle or an interception. It can also lead to misplaced passes going out for a throw, to low-expectation shots leading to goal kicks, or to backpasses to the keeper which produce 50/50 clearances into midfield, and so on. Those quality defensive performances aren't going to be attributed to a single player, and they aren't even clearly tracked by Opta.

A good defense will maximize opposition possessions spoiled. Opposition possessions spoiled will include tackles and interceptions. But if a team for whatever reason maximizes other kinds of spoiling of possession, we will not be able to track that play in the stats we have. And if a player is good at other kinds of defending, we won't see that in the stats.

Further, there is the problem of opportunity. If a club's tactics maximize other kinds of spoiling possession, then players on that club will have relative low tackle and interception numbers not because they lack skill, but because they're contributing defensively in other ways. And more than that, tackling and intercepting are both risky plays. To win a tackle or intercept a pass, you have to commit to winning the ball. If you fail, you will often be out of position and find that you have created a good opportunity for the opposition.

The risk involved in tackling implies, from a game theoretical perspective, it is a better idea to attempt a tackle or interception in either high or low-leverage situations. In high-leverage, against an opposition break-away, diving in for a tackle that might end up being a foul instead makes sense. In low-leverage, with your defense set behind you, you can take the risk of stepping into a passing lane looking for a turnover because you know that if you fail, it's unlikely to lead to a bad outcome. Any number of factors can contribute to there being more opportunities to make a tackle or an interception in a certain area of the pitch. It is difficult, at this point, to distinguish between players who make valuable contributions with their tackles and interceptions, and players whose tackle and interception statistics reflect other factors and not their own quality.

And that is why I am skeptical of defensive statistics for football.