Pro Football Reference Blog

An email from a good buddy of mine (and occasional commenter here):

i am so sick and tired of hearing "its so hard to beat a team three times in a season". idiots. yes, going 3-0 vs a playoff team is hard. BUT NOT IF YOU SPOT TEAM A TWO GAMES YOU MORONS.

He's right, of course. This is essentially the same reason why black isn't necessarily a good bet on a roulette wheel that's come up red on the last ten spins. Yes, it's incredibly unlikely for a wheel to land on red on eleven straight spins, but given that it's already landed on red for the last ten spins, it's not at all unlikely for it to land on red for the eleventh. Likewise, before the season, the Cowboys beating the Giants three times would have been something of a longshot. But now that they've already done two-thirds of the work, it's not.

Anyone making the hard-to-beat-a-team-three-times claim probably is suffering from a failure to understand conditional probability, but that doesn't necessarily make them wrong. Football games are not roulette wheels. In particular, they're not independent. Maybe teams learn more from losses than from wins, or something like that, and it really is hard to beat a team three times, even if you've already beat them twice. That's an empirical question. Let's check it out.

Since the merger, there have been 17 instances of a team trying to beat another team thrice in a season. In 11 of those cases, the team succeeded. Teams, like this year's Cowboys, who have the better record and were therefore playing at home, are 9-3 when trying to beat a team three times in a season. Here's the data:

+------+-------+-----------+-------+-----------+-----+-------+
| year | team1 | t1_record | team2 | t2_record | loc | score |
+------+-------+-----------+-------+-----------+-----+-------+
| 2004 | GNB   | 10-6-0    | MIN   | 8-8-0     | H   | 17-31 |
| 2004 | STL   | 8-8-0     | SEA   | 9-7-0     | R   | 27-20 |
| 2002 | PIT   | 10-5-1    | CLE   | 9-7-0     | H   | 36-33 |
| 2000 | NYG   | 12-4-0    | PHI   | 11-5-0    | H   | 20-10 |
| 1999 | TEN   | 13-3-0    | JAX   | 14-2-0    | R   | 33-14 |
| 1998 | DAL   | 10-6-0    | ARI   | 9-7-0     | H   | 7-20  |
| 1997 | NWE   | 10-6-0    | MIA   | 9-7-0     | H   | 17-3  |
| 1997 | GNB   | 13-3-0    | TAM   | 10-6-0    | H   | 21-7  |
| 1994 | PIT   | 12-4-0    | CLE   | 11-5-0    | H   | 29-9  |
| 1994 | MIN   | 10-6-0    | CHI   | 9-7-0     | H   | 18-35 |
| 1993 | RAI   | 10-6-0    | DEN   | 9-7-0     | H   | 42-24 |
| 1992 | KAN   | 10-6-0    | SDG   | 11-5-0    | R   | 0-17  |
| 1991 | KAN   | 10-6-0    | RAI   | 9-7-0     | H   | 10-6  |
| 1989 | HOU   | 9-7-0     | PIT   | 9-7-0     | H   | 23-26 |
| 1986 | NYG   | 14-2-0    | WAS   | 12-4-0    | H   | 17-0  |
| 1983 | SEA   | 9-7-0     | RAI   | 12-4-0    | R   | 14-30 |
| 1982 | MIA   | 7-2-0     | NYJ   | 6-3-0     | H   | 14-0  |
+------+-------+-----------+-------+-----------+-----+-------+