“Hot hand” is a word which comes from basketball. It refers to a player who is in good form, who is said to have hot hands. According to perceived wisdom, this player is more likely to be successful with a shot if his previous attempts were successful.
What does this have to do with sports betting, we hear you cry? Well, quite a lot, actually: there is a belief among some that a bettor who has been successful previously has a better chance of replicating that success in the future.
Juemin Xu and Nigel Harvey of University College London examined this purported phenomenon in detail, analysing the history of over 700 bettors to ascertain whether there was any scientific evidence for hot hands in the betting world.
The duo first noted down a list of winning streaks in betting, some of which were rather short and others which were relatively long. They then sought to work out whether there were any patterns depending on the lengths of the streaks. Did a longer run of success affect the probability of a given bet being a winner?
In the first random sample, the probability of victory was 0.48 – just less than half. Of those who triumphed in that selection, the probability of victory in their next bet was 0.49. Conversely, the probability of victory for those who lost the first bet was 0.47.
Xu and Harvey continued to record their findings as the study progressed, and the results were remarkable. The group who had been successful with the first two bets had a probability score of 0.57 of winning the third, significantly higher than the 0.45 who did not have the benefit of a winning streak.
The trend continued thereafter. The bettors who had triumphed three times in a row suddenly had a probability of 0.67 for a fourth consecutive victory. The probability of those who had not been winning, meanwhile, was just 0.45. The next step was 0.72 for those with four successes, with the rest of the sample still stuck at 0.45. After that, the figures rose to 0.75 and 0.46 respectively.
Finally, the small group who had won six bets on the bounce again saw their probability nudge up, this time to 0.76. This compared favourably to the probability of 0.47 of those without a run of victories under their belts.
Xu and Harvey then turned their attention towards losing streaks. In the random sample, those who lost their first bet had a 0.47 chance of winning their second. Those who lost their first two bets had a 0.4 chance of winning the third. Those who lost their first three bets had a 0.32 chance of winning their fourth. Those who lost their first four bets had a 0.27 chance of winning their fifth. Those who lost their first five bets had a 0.25 chance of winning their sixth. And finally, those who lost their six three bets had a 0.23 chance of winning their seventh.
The data appears unequivocal at first glance, seemingly backing up the suspicion that the hot-hand phenomenon is not a fallacy. However, is there another explanation for Xu and Harvey’s findings?
Anyone with even a rudimentary understanding of statistics knows that each outcome is independent and is utterly unaffected by previous results. We would therefore not expect the above trends to appear, which is why the study’s findings are initially surprising.
However, there is a logical explanation to the results. Xu and Harvey looked at how the outcome of a bet influenced the selection punters made next time around. At first, the mean level of odds of all participants was 7.72. However, this dropped to 3.6 for the winners and continued to fall the longer the streak went on.
The opposite was true of those who suffered an initial loss. The mean level of odds after six successive defeats was a mammoth 17.07. Meanwhile, those who had won on each of the previous six occasions opted for mean odds of just 0.85, showing that they were primarily looking to avoid risk to keep the run going – and perhaps believing that they were bound to run out of luck soon and should therefore keep things safe.
What about when we look at the key measure: profitability? On this count the results were virtually the same. Those bettors with a six-bet winning streak had an average loss of £1.0078 per £1. Those without the winning run had an average loss of £1.0077 per £1 – a negligible difference.
So, when it comes to sports betting, ignore the outcome of your previous bets and simply focus on the one that lies ahead.