Super Bowl - What are the odds?
So the Steelers won yesterday - their 5th title in the 40 year history of the Super Bowl. Two other teams (the 49ers and the Cowboys) have also won 5 times in that 40 year span. That means that 3 teams, out of the 32 in the NFL, account for 15/40 (37.5%) of all Super Bowl victories.
That seemed very unlikely to occur by random chance and is likely to represent strong evidence of football ‘dynasties’ furthered by outstanding management at the teams in question (the Steelers have had one owner and only two coaches in the last 37 years). Being a numbers geek and a programmer, it was easy to whip up a function to check if this was just statistical fluke.
I ran a simulation 1 million times, randomly picking a ‘Super Bowl’ winner from among the number of teams in the league for each year (26 back in 1967, 32 nowadays).
Simulation results?
The top 3 teams won 15 or more games collectively less than 1% of the time (0.97% to be exact). So the odds that such a small handful of teams could collect so many trophies by random chance is quite small.
For Steelers/49ers/Cowboys fans looking to boast further of your teams greatness - the odds of any one individual team winning 5 Super Bowls were 1.088%. The odds of a given team winning 6, 7, or 8 Super Bowls in that time, by chance alone, were 0.223%, 0.039%, and 0.006%.
Here’s the relevant C code.
February 11th, 2006 at 11:11 am
I’m not a football fan by any mean, but there’s also the possibility that what brings the victory is money. Winning the Superbowl (and performing well in general) brings more money to the team, which can hire better player, who play better, which brings more money and so on. Being in a large city with lots of football fans would certainly help on this front too.
February 11th, 2006 at 4:07 pm
The amount of money winning the SB brings in is trivial in the grand scheme of things.
What the original post fails to model is that teams stay reasonably intact over a short (3-5 years) period of time. This was especially true before the last 10 years. The Steelers of the 70s won 4 of 6, the 49ers of the 80s won 4 in 9 years, the Cowboys of the 90s won 3 in 4 years. In each of those cases, the team was fairly stable and was dominant.
What this means in terms of statistics is that
1) Your model is flawed. Distribution is not random because teams tend to remain intact, and
2) The current statistical sample is way too small. 40 Super Bowls doesn’t tell you anything. After 1000 Super Bowls, I would guess that you will see a near normal distribution (as if you had done it randomly). By then, every team would have had a chance to go through a dominant period.
February 11th, 2006 at 5:36 pm
I don’t argue with #1 or #2, except to attribute a bit more of the dominance of the 70s Steelers, 80s 49ers and 90s Cowboys to their players and management, rather than specific players (not discounting the players, just saying that it takes exceptional management to maintain the excellence, and keep the players focused after the first Super Bowl win.
But yeah, I was basically trying to prove that Super Bowl victory patterns in the last 40 years are far from normal, and, as a corellary, teams like my boyhood favorites, the Cardinals (football) are atrociously bad not because of a series of misfortunes, but because of a pattern of incompetence. I’ve got no analysis here of the ‘outside-the-bell-curve’ status of bad teams like the Cardinals and Saints, but they’ve got to be at least as far to the left of the bell curve as the Cowboys and Steelers are to the right.