In The Drunkard’s Walk: How Randomness Rules Our Lives, Leonard Mlodinow writes that “mathematical analysis of firings in all major sports, however, have shown that those firings had, on average, no effect on team performance” (p. x). In fact, in today’s era of quick hires and fires, some of the greats of the coaching profession likely never would have achieved greatness: John Wooden and Coach K likely would have been fired far before either won his first national championship due to the impatience of the administration and fan base.
Despite this analysis, the public believes strongly in the importance of coaching changes, even though nobody has created a good way to analyze a coach’s performance beyond wins and losses. Mlodinow writes “the human mind is built to identify for each event a definite cause and can therefore have a hard time accepting the influence of unrelated or random factors” (p. xi). If a team does well, the coach is regarded highly; if the team does not do well, the coach is regarded poorly.
Mlodinow introduces the law of large numbers, which essentially states that one needs a large number of observations to be confident in the accuracy of the observations. For instance, this is how Gallup decides how many people to poll to be confident that the results are within 5% of the population as a whole. He also introduces the (untrue) law of small numbers, which is applied in day to day life with inaccurate or biased results.
The (untrue) law of small numbers is obvious in a small sample of shooting. For instance, how many half-court shots does a player take in a season? One, maybe two. What if a player makes one of those two attempts? One could argue that because the player shoots 50% from half-court, he should attempt more shots from half-court. Is that a reasonable argument? If he took 100 or 1000 shots from half-court, how many shots would he be expected to make? With 100 or 1000 attempts, we would get a more accurate picture of his shooting ability from half-court. Of course, that does not mean that if he attempts only one shot from half-court this season, that he will miss it.
In terms of coaching, does one game or one season give an accurate account of one’s coaching? It depends on how one arrives at the conclusion. As I have argued previously, to evaluate a coach, we need to evaluate more than years of experience or won-loss record.
“It is more reliable to judge people by analyzing their abilities than by glancing at the scoreboard. Or as Bernoulli put it, ‘One should not appraise human action on the basis of results.’
Going against the law of small numbers requires character. For while anyone can sit back and point to the bottom line as justification, assessing instead a person’s actual knowledge and actual ability takes confidence, thought, good judgement, and, well, guts” (Mlodinow, 2008; p. 100).
As Ayn Rand wrote in The Fountainhead:
It takes two to make a great career: the man who is great, and the man – almost rarer – who is great enough to see greatness and say so” (p. 512).
How can we judge a coach by his or her abilities? What should a fan, the media, or an athletic director seek from a coach? If you eliminate the won-loss record, how can you evaluate a coach and his or her performance? How much does randomness affect our perceptions of coaches? How can we eliminate the effect of randomness in an effort to evaluate coaches without bias?