So, I’m finally home from the trip to San Francisco and Palo Alto. Experiencing the US culture was again quite intriguing. The differences are pretty notable in comparison to Finland: the expectation of sociability and extraversion, the lunch spots that only do takeaway, and the enthusiasm around baseball and football. I spent a few evenings watching college football matches – and I have to say that they were quite exciting! If it wasn’t for the ubiquitous commercial breaks, I’d say football is one of the most intense and captivating sports on TV. What also caught my eye, however, was the lack of statistical sophistication of the commentators.
During a match, a team might make two or three really awesome plays in a row. For example, in Ohio State vs. Minnesota, Ohio made a few awesome touchdowns with long passes and and an over 80 yard run. After this streak of successes, the game got more even, with Minnesota actually managing to even the score. What’s special about this is that the commentators spent a lot of time arguing about momentum. In their view, Minnesota managed to “get the momentum to their side” with one interception and a few hard tackles, like this one:
During a match, a team might make two or three really awesome plays in a row. For example, in Ohio State vs. Minnesota, Ohio made a few awesome touchdowns with long passes and and an over 80 yard run. After this streak of successes, the game got more even, with Minnesota actually managing to even the score. What’s special about this is that the commentators spent a lot of time arguing about momentum. In their view, Minnesota managed to “get the momentum to their side” with one interception and a few hard tackles, like this one:
Well, I’m not so sure.
My statistical gut instinct says that this is just regression to the mean. That means that after a few lucky successes (or a streak of bungles), what’s likely to happen is that the game returns to the mean. And in professional sports, the mean is that teams are pretty evenly matched. So instead of talking about momentum, the more likely explanation is that Ohio St just wasn’t so lucky anymore.
Regression to the mean is especially tricky since we tend to see patterns everywhere, including places where there are none. Kahneman describes the famous case, in which he was working for the Israeli air force. The air force trainers had a habit of dressing down cadets who made mistakes harshly. In their experience, this helped the cadets to get a grip and concentrate, so they wouldn’t make an error the next time. Kahneman decided to look into this intuition. At first, it looks like that was the case: a failed training flight that included harsh criticism was usually followed by a better flight. Isn’t this evidence that harsh negative feedback caused improvements?
Well, not necessarily. Basing that conclusion on the data would be a case of a fallacy called post hoc, ergo propter hoc, or what it’s more commonly called the post hoc fallacy. What the Latin name means is “after this, hence because of this”. It’s a conclusion of the form “since B came after A, B must have been cauded by A”. This is of course rarely true. My waking is followed by a sunrise – but that doesn’t say I’m causing the sunrise! Of course, this example is so ridiculous that we never think I would be causing the sunrise. But the same principle applies in other cases.
So what happened in Kahneman’s air force case? Well, they considered that the air force trainers might be falling for the post hoc fallacy. Instructors believed that improvement after a bad flight was due to the harsh feedback. In fact, it was simple regression to the mean. An average training flight is the most likely case, so that is usually going to follow a bad training flight. In fact, in being the average it usually follows any kind of training flight!
To take this back to sports, I think regression to the mean is often at play in the sports domain. Exceptional performances are followed by average performances, and the same is the case in moving from bad to average performance. Especially in sports that contain many sequences – like American football or tennis, for example – are likely to contain divergence from the mean, followed by regression to the mean. Someone might make a few awesome plays, but that’s unlikely to last long no matter what the other player or team does. Tactical changes do have some effect, depending on sports, but I think regression is much more important than we usually think. And regression is the reason why a Rookie of the Year is unlikely to perform as well the next year, or why an awful batting season tends to be followed by a better one. It all comes back towards the mean.
My statistical gut instinct says that this is just regression to the mean. That means that after a few lucky successes (or a streak of bungles), what’s likely to happen is that the game returns to the mean. And in professional sports, the mean is that teams are pretty evenly matched. So instead of talking about momentum, the more likely explanation is that Ohio St just wasn’t so lucky anymore.
Regression to the mean is especially tricky since we tend to see patterns everywhere, including places where there are none. Kahneman describes the famous case, in which he was working for the Israeli air force. The air force trainers had a habit of dressing down cadets who made mistakes harshly. In their experience, this helped the cadets to get a grip and concentrate, so they wouldn’t make an error the next time. Kahneman decided to look into this intuition. At first, it looks like that was the case: a failed training flight that included harsh criticism was usually followed by a better flight. Isn’t this evidence that harsh negative feedback caused improvements?
Well, not necessarily. Basing that conclusion on the data would be a case of a fallacy called post hoc, ergo propter hoc, or what it’s more commonly called the post hoc fallacy. What the Latin name means is “after this, hence because of this”. It’s a conclusion of the form “since B came after A, B must have been cauded by A”. This is of course rarely true. My waking is followed by a sunrise – but that doesn’t say I’m causing the sunrise! Of course, this example is so ridiculous that we never think I would be causing the sunrise. But the same principle applies in other cases.
So what happened in Kahneman’s air force case? Well, they considered that the air force trainers might be falling for the post hoc fallacy. Instructors believed that improvement after a bad flight was due to the harsh feedback. In fact, it was simple regression to the mean. An average training flight is the most likely case, so that is usually going to follow a bad training flight. In fact, in being the average it usually follows any kind of training flight!
To take this back to sports, I think regression to the mean is often at play in the sports domain. Exceptional performances are followed by average performances, and the same is the case in moving from bad to average performance. Especially in sports that contain many sequences – like American football or tennis, for example – are likely to contain divergence from the mean, followed by regression to the mean. Someone might make a few awesome plays, but that’s unlikely to last long no matter what the other player or team does. Tactical changes do have some effect, depending on sports, but I think regression is much more important than we usually think. And regression is the reason why a Rookie of the Year is unlikely to perform as well the next year, or why an awful batting season tends to be followed by a better one. It all comes back towards the mean.
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