Wednesday, December 14, 2011

Apophenia. Or As It's Also Known: "Tebow-Mania"

A personal note before starting this post: I know that you're thinking, "Why are we talking about Tim Tebow on a college basketball blog"? And, honestly, we're not really talking about Tim Tebow here. I'm not going to analyze his play or talk about how good I think he is. Rather, I want to talk about misconceptions about clutch play, since that's been such a hot topic in the comments on this blog the past couple of weeks, and I can't think of a better example of human irrationality on clutch play than Tebow-Mania.

So let's get into this:

Stare at the picture right above these words. What is it? What does it look like?

The answer, I'm sure you're saying to yourself, is that it's a human face. But why? All that's really been drawn are two circles and a straight line inside a larger circle. Why is it so natural to think that's a face?

I'll get back to that.

One of my favorite places is Las Vegas. I love the sports books. I can sit there all day watching sports and betting on games. But I will sometimes do other gambling, even though I know I'm going to lose. It's a social event and it's fun, and on rare occasions I'll get lucky and I'll win. Of the "pure chance" games, I enjoy roulette the most. Even if you've never been to Vegas, you've presumably seen a roulette wheel, either at a Native American casino, or wherever else.

To review quickly, a roulette wheel has the numbers 1-through-36, half of which are red and half of which are black. They also have a "0" and "00" space so that the casino can make money. You have a 1-in-38 chance of hitting on any random number, and the payout is 36-to-1. Or you can bet red spaces at 1-to-1, or black, or whatever. Just for the sake of making the math easier, let's pretend that we are at a casino that had no intent of making any money and which took out the "0" and "00" spaces. Hitting on red is a 50-50 proposition, and you get paid 1-to-1. If you bet $10 on red and hit it, you'll get $20 back.

Now, what do you see next to every casino roulette wheel? An electronic scorecard that tells you the result of the past 20 spins. It will look something like this:

Let's say you're at a roulette table that's been hitting black a lot lately. Let's say six straight. It'll draw attention. What would you think? Would you think black is "hot" and you should keep riding it? Would you think red is "due", and so you should bet on red? You'll find people who believe both theories. If the colors are alternating - red, black, red, black, red, black, red - most people will think a black will be "due" next.

Of course, we're all fooling ourselves. The odds of hitting a black next are exactly the same as hitting a red next - 50% (again, assuming we've ripped out the "0" and "00" to make the math easier). We think there's a pattern, but there isn't. Each spin is completely independent of the previous spin. Any streaks or patterns are random noise.

Why do we fool ourselves into thinking there's a pattern at a roulette wheel? It's the same reason we think that two circles and a straight line drawn inside a larger circle are a face. The human brain is wired to find patterns, even when they are tenuous or don't exist at all. It's called Apophenia.

Apophenia isn't a disease or disorder. You can't beat it. We all have it - we all find patterns in places that they don't exist.

In our early ancestors, it was Apophenia that drove their superstitious beliefs. Why did the sun come up every day? They didn't know, but they needed a reason. They had to convince themselves of something. Had to be a Sun God! The idea of just accepting that they didn't understand physics and not assuming that it had to be a God was anathema to human psychology. It bothers us to not have a reason for why things are the way they are. We rationalize. We force things to make sense to us. We find patterns.

And this pattern-searching is with us today. Just watch any post-game sports analysis and that's what you'll see. A team won? They made the right decisions, their players "willed themselves to win", they were more motivated. A team lost? Dumb decisions, not enough leadership, outworked.

And that brings me to this guy:

You know the talking points by now. He's awful for three quarters and great in the fourth quarter. In his eight starts this season, despite his team only outscoring its opponents by a grand total of two points, he's 7-1.

Now I'm not going to get into football here - you don't read this blog to see me break down football. Is Tebow better in the fourth quarter because power rushing teams wear down opponents? Because a scrambling quarterback is more effective against the type of zone prevent defenses opponents tend to run when they're winning late? Doesn't matter for the sake of this post.

No, the real question is: did Tebow "will" his team to 7-1? Is there some reason why his team keeps pulling out these close wins, instead of constantly falling short with close losses? Is it all just a random series of luck? The truth is that it's almost certainly the latter.

We can go through each game one by one to note all of the breaks that happened that had nothing to do with Tim Tebow. This past week it was Marion Barber running out of bounds, then fumbling in overtime, and Denver's kicker hitting a clutch 59 yard field goal as time expired in regulation. The week before it was Christian Ponder throwing an interception deep in his own territory with around 1:30 remaining. The week before it was San Diego's kicker missing a 53 yard field goal attempt in overtime.

Most everybody acknowledges these breaks, but applies a caveat about Tebow somehow having some cause. Tebow is inspiring his defense to make plays. He's motivated his kicker to do better. Or even worse, that it's some "divine" intervention. That's what Tebow's pastor claims, apparently. Even people who don't buy the divine intervention stuff still give Tebow the credit. He's a great locker room guy, he's incredibly clutch, whatever.

Sorry, but you're committing Apophenia.

Think about how boring Sportscenter would be if sportscasters told the truth, if they admitted that the above XKCD cartoon was true. The reality is that the dominant factor in a close game is... luck. If your team wins four straight games in overtime you might be clutch, but more than that you were lucky.

It's not that clutch play doesn't exist, it's that it's overrated. Vastly overrated. To use the baseball example I like using, Alex Rodriguez is the least clutch elite player in baseball, and Derek Jeter is a clutch player. But in the clutch, over their careers, Rodriguez has been better than Jeter. That's because the difference between being "horrible in the clutch" and "just fine in the clutch" just isn't that big. In "high leverage situations" A-Rod has a .969 OPS, compared to .826 for Jeter. In "late & close" situations A-Rod has a .900 OPS, compared to .796 for Jeter. We remember the times Derek Jeter got a big hit, and we snark every time A-Rod strikes out with the bases loaded, but we're just committing confirmation bias. Over the long run, if you objectively look at the stats, A-Rod has better clutch stats than Jeter.

The classic example I always talk about here is "guts vs stomps". Let's say you have two teams that have played common schedules and similar records. One team has gutted out a bunch of close wins against quality teams and weak teams alike. The other team has blown out every weak team they've played, but has suffered losses in almost every close game against elite opponents. Which team is better? Almost every casual sports fan would say it's the former team. It's actually the latter. And this has been studied many, many times by sports statisticians. The great guys at Football Outsiders did the analysis here. Basketball-Reference did the same analysis on basketball here.

If you spin a roulette wheel a bunch of times, you're bound to hit a bunch of reds in a row, or a bunch of blacks in a row. It doesn't mean that the wheel suddenly became biased. It's because of luck. Sometimes you just hit a bunch of reds. Sometimes you just hit a bunch of blacks. Sometimes your team wins a bunch of close games in a row. Sometimes they lose a bunch of close games in a row.

We all try to explain random noise by finding patterns and then explaining them. When teams win close games we create a narrative. You could "see it in their eyes", they "just wanted the win more". The players were motivated by press clippings, or a great halftime speech. They just "found a way to win". All of these are codewords for "We're trying to explain random statistical noise, and don't want to admit that there was just a bunch of luck involved".

Is Tim Tebow clutch? Sure he is. The stats say he is. But he could just as easily been equally clutch and ended up 1-7 instead of 7-1.

A lot has been made of the fact that Tebow's six fourth quarter comeback victories in his first 11 career starts are an NFL record. And yes, they are. But three quarterbacks are just behind him with five comeback victories in their first 11 starts? Who are these legendary comeback specialists? Montana? Elway? Marino? Manning? Brady? Nope. Scott Brunner, Marc Wilson and Jake Delhomme. Three quarterbacks with more career interceptions (257) than touchdowns (240) and a career 100-86 record. Why? Because over such a small sample size, fourth quarter comebacks are just luck. It's random noise.

I talk about this all the time with college basketball teams. Yes, in college basketball your resume is your resume. On Selection Sunday you get credit for who you beat and who you lost to - it doesn't matter how you got there. But if we want to project how teams are going to do in the future, and whether they are going to finish the season as well as they've started, or whether they're due to over-perform or under-perform in the NCAA Tournament, the reality is that you should bet against the teams that have won a disproportionate number of close games, and bet on the teams that have lost a disproportionate number of close games.

Yes, teams can be clutch, but if you think that the most clutch team on earth is going to win more than around 55% of overtime games over a large enough sample size then you're not any different from the guy who sees a bunch of reds hit in a row at the roulette table and thinks reds are due. You're not analyzing sports - you're committing Apophenia. It doesn't make you stupid, it makes you human.


Anonymous said...

Hi Jeff, why you never want to predict some games of each day? Many sites, put his predictions. Maybe you can predict one or two games against the spread and check your record. It could be interesting to see your predictions against the spread.

Jeff said...

I do that for the NCAA Tournament each year and have a good record against the spread (around 65%). I'm not sure I really want to do that each week - I don't want this to become a gambling website. I'll see... depends if enough people ask.

Anonymous said...

Excellent Jeff, thanks for the answer.