In 1985, Amos Tversky and Thomas Gilovich conducted a study into whether players are more likely to score successful shots based on previous success rates. Titled the “Hot Hand Fallacy: On the Misperception of Random Sequences” [PDF], the two scientists discovered there was no relationship between previous successful shots and future success rates, and that correcting for the basic underlying skill of professional basketball players able to hit 50% of their shots, the success rate of shots reflects a random sequence. In layman’s terms, “streaks” in basketball are just statistical noise, not signal.

Determining whether there is truly a “hot hand” in basketball is relatively easy. As the study authors indicate, despite the relative difficulty of a shot depending on where on the court it’s taken and the strength of the opposition, the free throw data provides a sample free from those “contaminating effects.”

These effects are a little harder to isolate in football, beyond penalty kicks of course. But the basic parameters of Tversky and Gilovich’s work is still reproducible in a football setting (although it would arguably need a larger sample of games): is a player who scores in several games in a row statistically more likely to score on subsequent chances, at a rate exceeding 50%?

This question came up on Twitter yesterday involving Robin van Persie. The Manchester United star forward failed to score against Chelsea. This was, we discovered, the ninth game in a row for Man United in which the Dutch player failed to score (he did score for Holland during the last international break, including a brace against Romania saw him break Johann Cruyff’s national scoring record).

Almost immediately, theories emerged about some sort of player slump. Robin van Persie was clearly losing confidence.

This is quite an empirical leap. For one, drawing this conclusion would require a lot of statistical ground work. Has Robin van Persie had the same number of chances to score from the same advantageous areas of the pitch since he last scored on Everton in February? What was the quality of competition among Man United’s opponents in those games? Was van Persie able to get into good positions to score based on United’s formation? Or the opposition’s formation? Did scoring effects distort the persistence of Man United’s attack?

Once we’ve isolated for individual game effects, we then have to move into probable causes for Robin van Persie’s alleged “slump.” Is van Persie recovering from an injury? Has he lost a measure of pace? Have his teammates lost confidence in him and are passing to him less?

After dismissing those possibilities, we’d have to do some work on establishing a real relationship between personal confidence and shooting accuracy and chance creation. Do we know for a fact that Robin van Persie’s failure to score has had an effect on his personal mood? Is there a demonstrable correlation between personal confidence and scoring that would have an effect over a relatively small number of matches?

This is not to discount the possible effect of psychology on athlete performance. But the burden of proof rests on those who would blithely state that Robin van Persie’s “goal drought” is somehow a crisis of confidence and not a random sequence possibly augmented by a series of opponents that included Real Madrid twice and Chelsea twice, and four games in which he did not play more than 70 minutes.

In any case, we do know a little of Robin Van Persie’s overall historical performance record in the Premier League over the past four seasons (the EPL is a good source too, with its spread of competition and number of games). This season his shooting percentage is currently 17%. Last season it was 17%. The season before it was 19%, although he played fewer matches. Moreover, he has maintained a shot-on-target rate of 21% in the last three seasons. This is not the most ideal indicator of underlying performance, but it is at least consistent. This would suggest it’s not completely out of the realm of possibility that both Robin van Persie’s “streak” and his “slump” were random events (I’ll leave it to a more dedicated analytics guru to perform a study similar to the one done in basketball in 1985).

Why does this matter? Well, it’s important to be skeptical of the notion that, if a good striker stops scoring after a few games, it’s an indication “his mind’s not right.” First, it does a disservice to the real work and importance in the mental health of athletes. Second, it currently drives a cottage industry of “sports psychologists” ready to give their assessment of Fernando Torres’ confidence problems to a willing media despite not having directly spoken to the player, or having done any research into whether there might be other factors at play. Third, it diverts attention away from other, perhaps less obvious indicators, some of which may not have anything to do with the player himself.

We can’t say with total confidence that the hot hand fallacy definitely applies to soccer, but finding out with clinical accuracy is a far easier task than simply blaming “confidence” when a good player doesn’t score after an arbitrary sample of games.

Comments (12)

  1. Does this mean that Fernando Torres could drop 55 goals at any minute?

  2. I’m a big fan of what you guys do, but what is the point of a comment section if I dont say what I feel so here goes. This focus on analytics that seems to be prevalent in every other article is really a drag for me. Articles like this are filled with fluff and what ifs but with very little substance. After all that’s said and done nothing substantial has been stated here. Yes there are other factors besides confidence involved, it doesn’t take 500 words to say that. Again I love what you guys do, but perhaps if the focus is going to be analytics, hold off until something with any weight can be written about, not just that a strikers from rests on more then confidence, we already know that without watching a single game. Don’t mean to rant and hopefully others will reply and say whether I am alone in feeling this way or not. Stay classy.

    • Strikers form* not from

    • I don’t mean this facetiously at all, but I tend to “circle off” my analytics posts on Tuesdays, in this column called the State of Analytics. Sometimes I will dedicate a shorter post on some small aspect, but I think one column a week on a set day with a set title makes it easier for you or others who don’t like it to skip it.

      As for your criticism that this is ‘obvious,’ I would agree except for the fact the notion that slumps and streaks are related to confidence/lack of confidence is still prevalent at all levels of media coverage. So that’s why this kind of thing needs to be done from time to time.

      Again, the easiest thing to avoid being annoyed by these is to just not read them on Tuesdays.

      • Cheers thanks for the response. And I agree 100% that media outlets generalize these so called ‘slumps’ as coming down to confidence when the obvious such as an injury isn’t involved. As per RVP specifically, I wonder how much the way their season has played out affects him. Specifically that the BPL title has been theirs for a while now, no CL, now out of cups. Their league games are mostly going through the motions for a team of that quality and with the lead they have. Perhaps his desire to give 100% isn’t always there. He has certainly done his part in winning the league title already. Just a thought, cheers.

    • I agree. I think this makes a complete meal of the issue. It takes the analytical approach way too far, to the point where it doesn’t seem as valid. As much as football can genuinely be anti-scentific, the flow of the game means it does require a certain amount of ‘intuition’ to ‘get’. Anyone who’s played has been in RVP’s situation. It isn’t even a matter of ‘confidence’, so think Richard is actually taking the wrong angle here. It’s just, sometimes you’re doing it without thinking. That inevitably stops and then you dwell a little more. It’s happened to all of us.

      • I have no idea what you’re saying here. Sorry.

        • RVP has realistically played 2-3 meaningful games in the last couple months (excluding WCQ). Perhaps his desire to score and give 100% isn’t there at this point in the season with nothing really to play for on a team that can easily win domestic games without his goals.

  3. The problem with these analytics pieces is not necessarily their frequency, it’s the repetitiveness of your argumentation (i.e. chastizing ‘the media’ for their overly simplistic analysis by referencing the same underlying empirical factors) and the lack of positive conclusions or theories drawn from the discussion. Put simply: too much humbugging and not enough in depth analysis.

    • I disagree. I’ve looked at things far beyond a simple angle of “the media’s got it wrong.” Check the backlog and you’ll see. Posts on everything analytics related under the sun.

  4. The problem is that statistics is a very complex space in which to work and even more difficult to explain. There are many angles to approach a subject and even more people to explain how their angle is right. Some may make sense and some may not. That said one shouldn’t shit upon another for trying to play out an angle. If there was a holy grail of soccer statistical analysis, I haven’t seen it. If you don’t like his view or angle, move on to the next blog.

  5. Of course it applies, as does regression to the mean.

    It’s just that those are terribly boring stories for the (mostly) UK media to spin. I’ve never understood the obsession over individual player “form” and team form tables and “enjoying your football” and all the other idiotic cliches spouted from the British press.

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