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Nate’s Notes 26: Probability and Performance

By June 6, 2022June 8th, 2023No Comments

As a sophomore in high school, my baseball team traveled to the big city, Boise ID, to play the defending state champions. I was the starting shortstop and I was scared. Though I was confident in my ability to field grounders, I was not confident in my ability to throw to first base. And the Boise Braves figured that out quickly, as grounder after grounder rolled my way. First, I threw a couple balls in the dirt, right in front of the first baseman. Next, I tried to compensate but threw the ball so far over the 1st baseman’s head that it went over the fence and out of play. The next one I threw in the dirt again. After my 5th or 6th error, another ground ball was hit to me, and as the ball was rolling, I distinctly remember hearing the Boise crowed groan…they seemed to be embarrassed for me… even they didn’t want to see me make another error. I scooped up the ball, shuffled toward first, threw the ball, and almost hit the pitcher’s mound…dozens of feet in front of first base. I had lost all confidence.

This game haunted me for years to come. Why had I performed so poorly? And was it just my lack of confidence that got the better of me? Ultimately it would take me more than a decade to make sense of that day.

One of the most important clues came to me years later while preparing for the LSAT, the law school admission test. LSAT results are provided both as a score and a score band. If someone scores a 170, their score band would be 167-173, meaning that if they took the test again, they probably wouldn’t score lower than 167 or higher than 173.

The creators of the LSAT understand that test takers’ performance varies day to day… that performance exists on a continuum or within a range.

Daniel Kahneman, the Nobel Prize winning psychologist, also understood the importance of evaluating performance on a continuum. While working for the Israeli Air Force, he tried to convince the military leaders that rewards were more effective than punishment at improving performance. But the leaders weren’t convinced.

They told Kahneman, “When student pilots have a bad flight, we yell at them and the next day they do better. But when they have a good flight and we praise them, like you suggest, the next day they do worse.”

At first Kahneman was stumped. But then he had an insight: regression toward the mean. Kahneman knew that pilots, just like LSAT-test takers, have a performance band.

If a pilot performs at the top of their performance band, it’s likely that several things came together just right for that to happen. But odds are, all of those factors won’t go just right the next day, so the pilot would likely regress toward the middle of their performance band the next day, they’d regress toward their mean. And if a few days later the pilot performs especially bad, it’s probably because several bad things all happened at once to ruin their performance. Odds are all of those bad things won’t happen tomorrow, so their performance will likely improve the next day, again, regressing toward the mean.

Kahneman realized that it wasn’t the criticism that was causing the pilots to perform better the next day, nor was it the praise that was causing the pilots to perform worse…the pilots were simply regressing toward the middle of their performance band.

Regression toward the mean helps explain performance fluctuations in the military and in athletics. For example, football fans are keenly aware of the Madden curse. NFL players who have exceptional seasons end up on the cover of John Madden’s video game. But once on the cover, those players tend to not match their previous year’s performance. They tend to regress toward the middle of their performance band the following year.

I once heard an NFL executive boast how teams use regression toward to the mean to extract value from their players. For example, if a defensive lineman has an outstanding year and wants to restructure his contract, teams will restructure the deal such that the lineman has to repeat his exceptional performance to get a big bonus, but otherwise the lineman will have to accept even less money than from his previous contract. Teams know that regression to the mean is likely.

Thinking about performance as a range, rather than a point value, has a name…probabilistic thinking. Rather than thinking in binary terms…I’m either clutch or I’m not…probabilistic thinkers recognize that they have a performance band, and while they will most likely perform close to the middle of their band, they will sometimes perform at either extreme. So when they do perform at the bottom of their band, they probably don’t need to stress too much, because odds are, they’ll perform better next time.

Thinking in terms of probability can reduce stress when we’re trying to perform our best. But even still the value of probabilistic thinking can be difficult to appreciate, because we’re not great at understanding probabilities.

The most memorable probability demonstration I saw was during a law school stats class. Professor Daniel Ho called two students to the front of the room and said, “I want one of you to flip a coin a 100 times and write down the outcome of each flip on the board. I want the other person to try to simulate what a 100 coin flips would look like, and write down your simulated results on the board.”

“I’m going to leave the room while you each write your results. But when I come back, I’m going to look at your results and tell you which results are from the real coin flips.”

Professor Ho left the room, and after 10 or so minutes returned, once both students had finished writing their results. Professor Ho looked at the board for about 5 seconds and then correctly chose the results that were real.

The trick he said, was to look for the longest string of consecutive runs. When something has a 50% probability of happening, we expect it to follow a somewhat predictable pattern like, heads, tails, heads, tails, heads, heads, tails, tails, heads, tails. But in reality, when you flip a coin a 100 times, you tend to see runs of six, seven, or even eight in a row. So, all Professor Ho had to do was look at the 2 results on the board and find the one that had the longest consecutive runs.

One application of this demonstration is that a 50% basketball shooter will often miss 6, 7, or even 8 shots in a row. In that moment they’ll be tempted to quit shooting due to a lack of confidence. But if they think in terms of probability, they’ll keep shooting, because they know that they’re just performing in their score band, and will soon regress toward their mean and start making shots again.

Another application of this is that a shortstop who is only accurate with his throws 50% of the time, would be expected, at some point during each season, to make six, seven, or even eight bad throws in a row.

For both the basketball shooter and the shortstop, performance bands and probability are probably more important than confidence. Justin Su’a, the renowned sports psychologist who has worked for the Boston Red Sox, Cleveland Browns, and Tampa Bay Rays, frequently reminds athletes that confident players can perform poorly, and unconfident players can perform well. What matters more than confidence, he says, is the athlete’s competence…their performance band…how high their band is and how narrow the range is. Instead of chasing confidence, athletes should chase competence.

Eight years after my nightmare in Boise, I found myself thinking about that day again. I was named starting wide receiver for the BYU football team, and I was scared again. We were playing Boston College, and I wondered if I would crumble like I did as a sophomore in Boise.

On the second play of the game, in my first Division I football game, in my first game as a starting wide receiver, I ran a swing pass to the right. Our quarterback dropped back, threw me the ball, and I easily caught it. It was as simple as riding a bike. I ran for 7 yards before I was tackled by the all-American Mathias Kiwuanaka.

I’m sure Kiwanuka thought nothing of the play & has forgotten it all these years later. But for me, it was unforgettable. I had mentally moved past that day in Boise.

I also learned an important lesson…that it wasn’t my confidence that made the difference. It was my competence. In high school, I never showed up early or stayed late to work on my throws to first base, and my throws to first were just as wild during practice as they were during games. I didn’t have confidence because I wasn’t competent. However, the summer before that football game against Boston College, I caught hundreds of balls each day, tens of thousands of balls over the summer. When I played that first football game for BYU, my performance band was high and narrow.

But so what. Why does this matter?

As a college professor, I have students tell me every semester that they’re not confident test takers. And every time I hear them say that I think back to my high school self. I then tell the students that if they read each chapter twice, memorize all the vocabulary words, create 30 practice questions from each chapter, and then learn the answer to each of their practice questions, they don’t have to worry about their confidence.

Albert Bandura, the psychologist who coined the term self-efficacy would agree. Self efficacy is the confidence someone has in themself to perform well. And Bandura argued that one of the best ways to improve self-efficacy was to improve competence.

Because ultimately, competence beats confidence.

So kids, when you find yourself nervous about a test, a free throw, a penalty kick, a throw to first base, or a performance on stage, remember that you will perform somewhere in your performance band…likely close to the mean. So relax.

And if your performance band is lower than you want it to be, make it higher and narrower. In other words, seek competence over confidence.

It’s a simple idea. Please take it seriously.

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