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Like you, I am interested in the winning percentages of sports prognosticators such as Norman Chad (Cheap Seats, “Free to Bet,” 9/17). But perhaps not for the reasons you are. One would think that the statistics of these choices would be well understood by the people writing about it, but that’s not true. I don’t agree with you that being better than 50 percent correct nine years in a row is a 1-in-512 accomplishment. I will try to explain below.
But Chad keeps boasting, “I am the man,” for just getting over 50 percent each year. That is no meaningful accomplishment. Obviously, each year, just flipping a coin on games with a (correct) point spread, anyone has a 50-50 chance of getting half the games right.
Statisticians (I am not a statistician; I am a scientist who uses statistics in my work) make a criterion of 1 in 20 that a finding better than expected is due to skill, not luck. In a given 13-game weekend, this takes a record of 10 and 3 or better. While 8 and 5 is better than 50 percent, it is not necessarily better than flipping a coin would do. Coins don’t always flip 50-50 in a small number of tosses. Over a 16-game season with 208 games, Chad would have to do 124 and 84 or better to get a significant result.
Over nine years, the criterion is not 2 to the 9th power, but the statistical distribution of 9 times 208, or 1,872 games. A year of 208 games with a slight positive bias cannot be scored like the 100 percent certainty that the coin came up heads just one time. These numbers are getting a little hard for me to do quickly, but I calculate that the cutoff for significance is about at 1,000 wins and 872 losses. So, if Chad has done this well over all nine years, there is just a 1 in 20 probability that such a record was achieved by chance and a 95 percent chance that it arose from skill. As his margin falls from this winning percentage, the accidental occurrence probability increases and the lucky coin-tosser becomes more probable.
Anyway, I do enjoy the column. You provide a good alternative view of the sporting scene.