I am interested in the probability that any NFL player will win the Super Bowl.
If a player is randomly drafted onto one of the 32 teams, his probability of winning the Super Bowl in any given season is 1 - (31/32) = 3%. If he plays two seasons his probability is 1 - (31/32)^2 = 6%. Continuing this exercise, we get these probabilities.
So if a player manages to have a full 12-season career, he still only has a 32% chance of winning at least one Super Bowl.
As the chart below demonstrates, even if you played 100 seasons, there would still be a 4% chance of not winning a Super Bowl.
George Blanda, a quarterback and kicker for five different teams, had the record for the longest career of 26 seasons (1949-1975). If he played in modern times with 32 teams, even he would only have a 56% chance of winning at least one Super Bowl. Blanda never won one (although the Super Bowl did not begin until 1967, his 18th season).
According to the NFLPA, the average NFL athlete plays only 3.5 seasons, resulting in an 11% probability that an NFL player will ever win a Super Bowl.
From the chart below, the probability that a high school football player will go on to win a Super Bowl is roughly 1 in 8,090. (Better than I would have expected.)
(Hat tip: Barking Up the Wrong Tree)
