As everyone knows, the biggest story of this football season has been the New England Patriots' quest to go undefeated. Assuming the Pats win this week, should they go all-out in the final game or rest their star players for the playoffs?
Ordinarily I don't like jeopardizing team results for personal glory, but you have to ask yourself: Which is more important to the team, going 16-0 or winning the Super Bowl? After all, a Super Bowl win doesn't mean that much in the abstract; it is only because football fans lionize the Bradshaws and Montanas of the world that we think it's such a huge deal. After all, 41 teams have won a Super Bowl. None have gone 16-0 in the regular season.
If the Pats absolutely had to lose one game, they'd probably rather do so in Week 17 than in the playoffs. But that's not the case here; playing their hardest in Week 17 only has a small chance of costing them anything.
Let's say that Tom Brady getting hurt reduces the Pats' chances of winning each game by 25%. So if he sits in Week 17, the Patriots will go undefeated 60% of the time rather than 85%.
Meanwhile, there's perhaps a 2% chance that Brady will be seriously hurt in Week 17 and miss the playoffs. The market currently puts the Pats at about 56% to win the Super Bowl; if Brady goes down, that number dips to 18% using these assumptions.
With the 2% probability of a serious injury costing them 38% of their chance at a championship, the Pats are costing themselves less than 1% of a Super Bowl title in expected value by letting Brady play the whole game, while giving up 25% of their chance to go undefeated.
You can use slightly different numbers if you like, but you will reach the same conclusion: Unless winning the Super Bowl is much, much more important than going 16-0, the right move for is to go for the undefeated season.