With a secondary title as naturally contrarian as ‘Why everything you know about football is wrong’, The Numbers Game, written by football statistician Chris Anderson and behavioural economist David Sally and published earlier this year, was always likely to appeal to us here on The Value Perspective – and so it has proved.
Take the parallels with value investing contained within the authors’ argument that, perhaps counter-intuitively, it is of greater value to prevent a goal in football rather than score one. As such, although clubs are inclined to spend heavily on strikers – what we might call the high P/E stocks of their sport – defenders, statistically speaking, add more value in the long run.
Elsewhere in The Numbers Game, Anderson and Sally discuss an academic paper from 1985, in which three US psychologists considered whether the so-called ‘hot hand’ – the widely-held belief in basketball that a player who has just scored a basket is more likely to score from their next shot than someone who has just missed – has any statistical basis.
In ‘The hot hand in basketball: on the misperception of random sequences’, Thomas Gilovich, Robert Vallone and Amos Tverskey analysed the 3,800 ‘attempts on basket’ that occurred during the Philadelphia 76ers’ 48 home games over the 1980/81 season. They found great players would score a basket from about 70% of their attempts while all the professionals averaged a 52% success rate.
Scoring a basket is obviously a more complex act than tossing a coin but the distribution of outcomes is very similar – heads they score, as it were, tails they miss. As it happens, it is mathematically possible to calculate how many times you might expect to see a run of heads if you tossed a coin a particular number of times.
Say you tossed a coin 16 times, how often might you expect to see a sequence of three heads in a row? Well, the maths says you can expect to seeat least one run of three heads 60% of the time. You’ll see a run of five heads around 20% of the time. Likewise, in basketball, scoring three shots in a row is as random as three heads in a row – it is just that people attribute a greater psychological value to the baskets.
To prove the point, Gilovich, Vallone and Tverskey’s analysis of those 3,800 attempts on basket showed the probability of a player scoring a basket after scoring from the previous shot was 51%, essentially the same as the long-run average; in reality, the ‘hot hand’ denotes nothing more than the way the human brain instinctively misunderstands short sequences.
Meanwhile, the probability of a player scoring a basket having missed their previous shot was 54% – so actually it was the opposite of what people thought about the ‘hot hand’, even if the difference is so small as to be completely meaningless. And – perhaps unfortunately for investors – there is no ‘hot hand’ equivalent in investment either.
People may think of fund managers having good and bad runs and look to invest with those enjoying the former but, again, the reality is a lot more random. Even great fund managers are likely to suffer a bad run of performance at some stage – as can be seen from the following chart from US investment firm Davis Advisors.
The chart shows that 70% of the top-performing large-company equity fund managers over the 10 years to 31 December 2010 saw their performance fall into the bottom quarter of their peers for at least one three-year period. When the spread of underperformance is widened to the bottom half of their peers, that figure rises to 95%.
Whether one is looking at basketball or fund management, performance is more random than most people believe ' and is not always a reliable indicator of future performance. As such, investors need to guard against mistaking short-run underperformance or outperformance for a change in a long-term trend.