Saturday, February 13, 2010

Do you think that's air you're breathing?

One of my favorite themes in bowling is causality and perception. We see changes in our bowling performance from day to day and week to week. We want to believe that we are responsible. When we bowl really well, we feel a sense of pride. When we bowl poorly, we feel like we had a temporary lapse of ability and have let our team down. It's like the hitter in baseball who goes hitless for 10 straight games. They are in a slump. Something isn't working. There is a hitch in the swing. Slumps feel real, painfully real, but are they? One of the major conclusions of those who study sports statistics and performance is that streaks and slumps are an expected outcome of the operation of chance, and only very rarely can they be demonstrated to differ from what we would expect given the operation of the rules of probability.

Here's a nice description of the problem. This is from a paper titled "Twenty years of “hot hand” research: Review and critique" by Michael Bar-Eli, Simcha Avugos, and Markus Raab, published in the journal Psychology of Sport and Exercise (2006, Vol. 7, p. 536):

"No one doubts that streaks do occur in sports. Obviously, every now and then a professional basketball player may hit a string of nine or ten shots. The key issue in the debate, however, is whether the observed superior (or inferior) performance really deviates from what could occur by chance. Clearly, even random processes such as coin flipping could occasionally result in long streaks of heads or tails. So, an ‘‘unusual’’ performance by an athlete or a team may represent pure statistical probability, or it could be related to a real ‘‘streakiness’’ mood. Supporters of the hot hand strongly believe that even if one accepts the notion that in the world things are often random, there are still some moments in time when athletes act well above or below their norm (i.e., their base rate)."

What brings this to mind is my own recent performance. I started this bowling season on a tear. Consider this. Over the entire course of the prior season, a total of 36 weeks, I had in sum three 500 series, including the first of my bowling career. This season, I had 10 during the first 16 weeks. I was bowling like somebody who was starting to understand what the hell he was doing. Yet, over the last month, I feel like I can't get even close to 500. That's my perception, anyway. In reality, my last four series have been in a narrow range, from 442 to 460. The point is that my perception is that my bowling ability has eroded, but has it really? If you have read any of my prior statements on similar topics, you should be able to anticipate the answer.

There are some simple statistical methods that can be used to determine if there is some trend underlying a time series. A time series represents the collection of data over a period of time, such as hourly measurements of temperatures, daily stock values, or weekly measurements of bowling ability. If there is some underlying trend, like I am getting progressively worse at bowling, then I should be able to predict next week's performance based on this week's performance. In fact, I might be able to predict to some extent how I will bowl three weeks from now. If there is no underlying trend, prediction falls apart, and the data tell us that either no trend exists, or that it exists over much longer time scales.

One simple way of examining this problem is a technique called "serial correlation". It's pretty simple. Put all of your bowling series in a list in one column sorted by date. Put the same data in the next column over, but shift the values down by one row, as shown in the picture to the left. Now, make a scatter plot of those data. What we're doing is comparing last week's score to this week's score. If there is some underlying trend, we should see some kind of relationship between the two. If not, there is no trend. Here are two hypothetical examples:

On the left, the bowling series show a smooth rise and then a gradual drop. If we compare the previous to the subsequent week's bowling scores, there is a clear correlation. What this means in the simplest sense is that if I bowled well last week, I will also bowl well this week. If I bowled poorly last week, I will also bowl poorly this week. In other words, the system is to some degree predictable, and we can use past performance to predict future performance. For the time series on the right, scores seem to fluctuate wildly. When we do the serial correlation, there is no relationship between scores from week to week. This means that the system is totally unpredictable and that there is no underlying trend. Something else is driving these ups and downs, something like chance. I should note that you can shift the values down again to see how well your performance from two weeks ago predicted this week's performance. The more you shift the values down, the greater the time depth of prediction you are examining.

How does the real world compare? Here are the time series and serial correlations for four Bowl Movements for this season (Sorry K-Terk, I don't have enough data for you):
In brief, this system appears to be totally unpredictable at this time scale. Various degrees of correlation are present with the greatest being that for JD, but none of these correlations are greater than would be expected by chance. Interestingly, most of the correlations are negative. This means that if you bowl well one week, you are actually more likely to bowl poorly the next and vice versa, but we should not read too much into that as these are not meaningful patterns.

So... going back to my recent slump, it does not appear to be real. It feels real. It feels like I can't get more than 10 strikes in a series anymore. It feels like picking up spares is much more difficult than it used to be, but these ups and downs are simply to be expected. If I was bowling in the Matrix with Morpheus right now, he would be asking me, "Do you think those are bowling shoes you're wearing right now?"


  1. This comment has been removed by the author.

  2. I think I must have offended your bowling god before last week's games. Whenever you wax statistical, you have to consider any x-factors. And, perhaps, the inexplicable, like my bowling this season-- as you may recall me lamenting about it early on, I dropped 11 pins in average in the first three weeks. My goal (among many this year-- I gave myself goals because I thought my bowling was improving) was to come into league on a tear, lift my 160 to a 170 early and then attempt to stay there. What happened, instead, was a psychological earthquake and plenty of aftershocks since Week 1.

    I, too, have only had 3 500+ series. I am so disappointed in my inability to get up and stay up for more than a good practice or one good week of league play. (And I felt like I knew what I was doing two weeks ago-- really! Then last week it didn't feel good all, because I knew I wasn't bowling right, but I couldn't help myself.)

    My total pins differential over the last three weeks is truly remarkable: 347 to a 547 (+200 pins) back down to a 395 (-152 pins). I'm a bowling freak of nature. Who knows what will happen on Tuesday night? 175 pins maybe. But in which direction?!

    I should be bowling 500+ series the majority of the time; yes, there are going to be bad days, but that's how it should be. Currently I live in the opposite, where there are going to be good days...

    My goal now is to just get out of this season. And to bowl well next week, because, as the team doctor says, "there's always next week."

    And, by golly, he's right.

    [And, if nothing else, I'm a good blog illustration...]

  3. You are simply inconsistent, but i have no idea why. You are right that there must be psychological factors. In fact, I am planning a pyschological post or two based on some published research.

  4. I should free-lance as a case study. :)


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