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Basketball Study #1

June 1, 2011
15 people like this post.

Let me tell you about a classic psychological study that I found online and has important insight for us as traders and investors.

In the early 1980s, two psychologists Amos Tversky and Thomas Gilovich began sifting through years of statistics from the Philadelphia 76ers – a US basketball team. (Amos Tversky is well known for his ground breaking research with Daniel Kahneman on making judgments in uncertain environments based on heuristics and biases which has lead to a whole new field in finance called ‘behavioural finance’.) The psychologists looked at every single shot taken by every single player, and recorded whether or not that shot had been preceded by a string of hits or misses. All told, they analyzed thousands upon thousands of field goal attempts.

Tversky and Gilovich were interested in testing the “hot hand” phenomenon, which occurs when NBA players are convinced that they’re ‘hot’, on a ‘roll’ or, in ‘the zone’. While players, coaches and spectators were convinced the hot hand was real, the psychologists knew that humans are notoriously bad at detecting “streaks”. After all, we’re the same species that gets convinced we’re playing a “hot” poker machine or enjoying a ‘purple patch’ on a roulette wheel.

After analyzing all the shots of the 76ers, the psychologists discovered that there was absolutely no evidence of “the hot hand.” A player’s chance of making a shot was not affected by whether or not their previous shots had gone in; each field goal attempt was its own independent event. The short runs (of goals or missed attempts) experienced by the 76ers were no different than the short runs that naturally emerge from any random process. Bagging a goal was just like flipping a coin. The streaks were a figment of our imagination, and each event is random in its outcome, and completely unrelated to all previous outcomes.

The 76ers were shocked by the evidence. Andrew Toney, the shooting guard, was particularly hard to convince: he was sure that he was a “streaky” shooter, and went through distinct “hot” and “cold” periods. But the statistics told a different story. During the regular season, Toney made 46 percent of all of his shots. After hitting three shots in a row – a sure sign that he was now “in the zone” – Toney’s field goal percentage dropped to 34 percent. When Toney thought he was “hot,” he was actually freezing cold. And when he thought he was cold, he was just getting warmed up: after missing three shots in a row, Toney made 52 percent of his shots, which was significantly higher than his normal average.

But maybe the 76ers were a statistical outlier. After all, according to a survey conducted by the scientists, 91 percent of serious NBA fans believed in “the hot hand”. They just knew that players were streaky. So Tversky and Gilovich decided to analyze another basketball team: the Boston Celtics. This time, they looked at free throw attempts, and not just field goals. Once again, they found absolutely no evidence of hot hands. Larry Bird ( a Celtics player) was just like Andrew Toney: After making several free throws in a row, his free throw percentage actually declined. The study also indicated that after a string of goals Bird got complacent, and started missing shots he should have made!!

Why, then, do we believe in the hot hand? Confirmation bias is to blame. Once a player makes two shots in a row – an utterly unremarkable event – we start thinking about the possibility of a streak. Maybe he’s hot? Why isn’t he getting the ball? It’s at this point that our faulty reasoning mechanisms kick in, as we start ignoring the misses and focusing on the makes. In other words, we seek out evidence that confirms our suspicions of streakiness. The end result is that a mental fiction dominates our perception of the game.

All of this evidence has important points for us as traders. Often when we are convinced we are on a winning streak, people will do random things like increasing position sizing and taking higher risks, only to find that a losing streak occurs that does hefty damage to their account and their psychological state. It also highlights the fact that the outcome of each and every trade is random and completely separate from any other trade that has preceded it and any that will follow.

Next week, we will delve a little further into this psychological study and examine further aspects of confirmation bias and the random outcome of events, and the impact these can have on our trading results if they are not fully understood and managed.

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15 people like this post.

Comments

  • Annie Burnaby says:

    …on a similar theme, The Gambler’s Fallacy…
    guess we need to understand the difference between wishin’ and hoping’, and evidenced patterns such as EW.

    New to Share Wealth Systems but enjoy your writings,

    Annie

  • BG says:

    Hi Gary,
    I’m a bit confused as to how does a trading system have a positive edge if the outcome of every trade is random? Doesn’t a positive edge mean that over a number of trades there will be a high probability that there will be an overall profit, which implies that trades are only entered that have a high probability of making a profit, which implies that every trade outcome is not random, otherwise we might as well pick trades randomly?

    Regards,
    BG.

    • Gary Stone says:

      Response to Comment by BG:

      Great question! The randomness occurs within a set of probabilities and then in the distribution of outcomes.

      If an edge has a probablity of winning in 20% of events (trades or spins) and each win, on average, is twice the size of each loss, there will be a random distribution of winners and losers in this edge that will gravitate towards the winners numbering 20% over a large sample, but overall the edge has a negative expectation (-0.4).

      Using this edge, over a large sample of trades in a single equity curve and over a large sample of different equity curves, each with a different random distribution of winners and losers, but with winners averaging 20% at a ratio of 2:1 to losers, nearly all the equity curves will track downwards and lose money. However, it would be possible, due to randomness and hitting a positive streak of winners (out of the 20%), that a very small number of equity curves could be positive.

      Using another edge where the win rate is 45% and the average winner is 2.8 x larger than the average loser (positive expectation of +0.71), the distribution of outcomes would also be random but over a large sample the probability is that the winners would number 45% rather than 20% and would be 2.8x larger.

      With the second edge the probablity of a long losing streak and of ruin is much lower and the probability of any of the equity curves being negative over a large sample is much lower, however, not non existent, because anything can happen.

      It all comes down to probabilities…… and then how much risk is taken on each event (trade) once the probabilities are known. But that’s another story which is covered by risk and money management.

      Regards
      Gary

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