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Posts tagged ‘Randomness’

Fooled By Randomness

In my last post I discussed the myth of the SI jinx. Here is a brief recap. Athletes and teams are usually on the cover of SI for extraordinary performances. Almost always, an extraordinary performance is followed by an ordinary performance. So the SI jinx is easily explained by athletes and teams that have regressed back to their normal performance level. Contrary to popular belief, therefore, Sport Illustrated is not actually causing an athlete or team to play worse. However, people have a difficult time understanding this, and this is largely due to their inability to perceive and understand randomness. In this post, I want to build off of this point by illustrating just how bad we are with randomness. Let’s start with ipods.

When Apple first sold the ipod shuffle, users complained that it was not random enough. Though the engineers at Apple had programmed the ipod shuffles to be random, people were convinced that they were not. The problem was that “the randomness didn’t appear random, since some songs were occasionally repeated.” I took to the Apple blogosphere to see if this was true and on the Google’s first hit I found the following two posts:

User 1: There are 2800 songs in my ipod, I found that the Shuffle Songs function is not random enough, it always picks up the songs which I had played in the last one or two days.

User 2: It is random, which is why it’s not paying attention to whether or not you’ve played the songs lately.

User 2 is right, the ipod shuffle is random, making it entirely possible for a song to be played two days in a row, or two times in a row for that matter. The mistake made by User 1, is that people perceive streaks and patterns as indications that sequences are not random, even though random sequences inherently contain streaks and patterns.

Our tendency to misinterpret randomness is exemplified by the gambler’s fallacy, which describes our intuition’s habit of believing that the odds of something with a fixed probability are influenced by recent occurrences. For example, we think that the more times a coin lands on heads the more chances it has of landing on tails. In reality though, if a coin landed on heads one hundred times in a row it would still have a 50/50 chance of landing on heads the 101st time.

We make the same mistake when we watch sports. In 1985 Cornell psychologist Thomas Gilovich published a paper that “investigated the origin and the validity of common beliefs regarding the ‘hot hand’ and ‘streak shooting’ in the game of basketball.” His study was motivated by the common belief shared by fans, coaches, and players that a player’s chance of hitting a shot are greater following a hit as opposed to a miss. To see if basketball players actually “heat up,” Gilovich collected shooting stats from the Philadelphia 76ers 1980-81 season. He found that the chance a basketball player has of making a shot is actually unrelated to the outcome of his previous shot. In his words:

Contrary to the expectations expressed by our sample of fans, players were not more likely to make a shot after making their last one, two, or three shots than after missing their last one, two, or three shots. In fact, there was a slight tendency for players to shoot better after missing their last shot… the data flatly contradicts the notion that “success breeds success” in basketball and that hits tend to follow hits and misses tend to follow misses (1991, p. 12).

Gilovich’s conclusion comes as a surprise to most people. For some reason, our intuition tells us that a basketball player’s field goal percentage is influenced by his previous shots. This is why we want a player who is shooting well to continue to shoot, and vice versa.

Similar results have been found with baseball players and baseball teams. Michigan State University psychologist Gordon Wood demonstrated that the probability of an MLB team winning after a win, or losing after a loss, was fifty percent after analyzing the outcomes of all 1988 Major League Baseball games (26 teams & 160 games). Likewise, Indiana University statistician Christian Albright found the same with batters. He states that, “The behavior of all players examined… does not differ significantly from what would be expected under a model of randomness.” Like the outcome of a basketball shot, an MLB game and at bat were unaffected by past performance

None of these studies are denying that streaks exist; but they are saying that our intuition does a poor job of understanding and perceiving randomness – we mistakenly “see” patterns amongst randomness.

There are powers and perils to this cognitive bias. If you bet your life savings on a falsely perceived streak in the stock market, you could easily lose a life’s savings. Likewise in gambling, if you have gotten lucky on a slot machine you will want to keep going thinking that you have found a “hot” slot (in the end, of course, you will most likely have less than you started). On the other hand, our tendency to see order amongst random-chance events is an incredibly useful survival technique. Think what it would be like if you perceived the world as a series of random events; imagine that headache. With this in mind (not the headache), it seems awfully useful that we can “see” patterns that aren’t actually there.

  • Thanks Nassim Taleb for the title of the post.
  • The ipod shuffle discussion can be found here.

The Myth of the SI Jinx

When the 2003 regular season ended, things were looking good for the Chicago Cubs. They had won the National League Central – edging out the Houston Astros by one game – and were lined up to play the Atlanta Braves in the first round of the playoffs. They also had two of the best pitchers in the game, Kerry Wood, who had recorded a career-high 266 strikeouts, and Mark Prior, who went 18-6 with a 2.43 ERA. Earlier in the season, Sports Illustrated dubbed them “Chicago Heat,” and they indeed appeared unbeatable. On top of that, the Cubs had a solid line up that consisted of power hitters Sammy Sosa and Moises Alou, speedster veteran Kenny Lofton, and recently acquired young star Aramis Ramirez. Needless to say, Cubs fans were thinking that this was finally their year.

Then, just as the stars were aligning, everything collapsed. With a 3-0 lead in the 8th inning of the 6th game of the National League Championship Series versus the Florida Marlins, Mark Prior surrendered five straight runs (three earned) and was replaced by reliever Kyle Farnsworth, who gave up three more runs; in the blink of an eye, the Cubs went from a 3-0 lead to a 8-3 loss – Wrigley was speechless. Fortunately, it was a best-of-seven series and there was still one more game to play. Kerry Wood was starting, and he and Prior hadn’t loss back-to-back games the whole season. However, in typical Cubs fashion, Wood pitched poorly, the offensive didn’t score enough runs, and they lost.

Next came the finger pointing, and it seemed like the actual performance of the Cubs was last on the list. On the top, there was the curse of the Billy Goat, Steve Bartman, and of course, the classic SI jinx. For those that don’t know, the SI jinx is an urban legend that states that a team or player’s performance is made worse by being on the cover of Sports Illustrated. Below is a clip from the ESPN show “Mike & Mike In The Morning,” which illustrates the SI jinx debate. Listen closely to Mike Greenberg (the one on the left with the blue collard shirt) explain why he thinks it is a real thing (Begins around 1:00).

I hope that you are smart enough to realize that Greenberg’s pseudo psychological story is completely wrong; the classic “I read a book” example just doesn’t cut it. But I want to tell you why he is wrong, and for that we need to rethink what it means for something to be random.

Leonard Mlodinow’s The Drunkard’s Walk tells the story of how psychologist Daniel Kahneman was first motivated to understand the cognitive biases behind people’s tendency to misunderstand randomness. According to Mlodinow, Kahneman, then a junior psychology professor at Hebrew University, was lecturing to a group of Israeli air force flight instructors on the importance of rewarding positive behavior and not punishing mistakes (a well established finding in psychology). During the lecture, however, Kahneman was met with sharp objections. Many instructors believed that their praises were almost always followed by worse performances and vice versa. But Kahneman knew that in any series of random events, an extraordinary event is most likely to be followed, due purely to chance, by a more ordinary one.

Any especially good or especially poor performance was… mostly a matter of luck. So if a pilot made an exceptionally good landing – one far above his normal level of performance – then the odds would be good that he would perform closer to his norm – that is, worse – the next day. And if his instructor had praised him, it would appear that the praise had done no good. But if a pilot made an exceptionally bad landing – running the plane off the end of the runway and into the vat of corn chowder in the base cafeteria – then the odds would be good that the next day he would perform closer to his norm – that is, better. And if his instructor had a habit of screaming “you clumsy ape” when a student performed poorly, it would appear that his criticism did some good. In this way an apparent pattern would emerge: student performs well, praise does no good; student performs poorly, instructor compares student to lower primate at high volume, student improves. The instructors in Kahneman’s class had concluded from such experiences that their screaming was a powerful educational tool. In reality it made no difference at all (2008, p. 7-9).

This explains why the instructors are wrong, and illustrates what psychologists call the regression fallacy. The regression fallacy refers to the tendency for people to “fail to recognize statistical regression when it occurs, and instead explain the observed phenomena with superfluous and often complicated causal theories.”

As you may have guessed, the SI jinx is a prime example of the regression fallacy. Though people like Mike Greenberg tend to think that SI actually causes a poor performance i.e., “everyone talking about the curse gets in your head and you start squeezing the bat tighter,” the regression fallacy illustrates his mistake. The reality is that athletes are usually on the cover of SI for an extraordinary performance. And like a superb landing by the pilots, an extraordinary performance by an athlete is usually followed by an ordinary performance. So it is not that athletes do worse because they were on the cover of SI, it is that their performance regresses back to its norm. This also explains why Michael Jordan and Wayne Gretzky, two athletes who have been on the cover of SI many times, are not affected by “the jinx.” Relative to most athletes, their ordinary performances are extraordinary.

Returning to the Cubs. Prior and Wood were never the same after the 2003 season. From 2004 to 2006, they went 30-32 and combined for an ERA over 4.00. Prior didn’t play in the majors after 2006, and Wood, who is still active, has only seen moderate success since. This suggests they were average pitchers with one great season, not great pitchers with a handful of average seasons. As they say, “You can have a lucky day, sure, but you can’t have a lucky career.”

So we can safely conclude that the SI jinx is in fact a myth. In addition, we can also understand why it exists in the first place – the regression fallacy. So the next time you see your favorite player or team on the cover of SI, relax, take a deep breath, and realize that SI isn’t actually causing anything.

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