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Underdogs and Risk

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More from Advanced NFL Stats, this time an analysis of game strategy for underdogs.When facing a team of superior talent, should an NFL team play more conservatively and hope for mistakes from the favorite? Nope. Remember to click through and read the piece, as I'll provide a high-level summary.

If you approximate NFL scoring using a normal distribution, you find that an underdog will lose x% of the time, based on the differential in scoring expectation. The more conservative a team plays, the narrower their scoring distribution becomes. Conservative play effectively lowers the risk of falling into the lower tail of a team's scoring distribution, but also saws off the chances of landing in the upper tail.

Playing more aggressively flattens out a team's scoring distribution. The probability of hitting a team's scoring average drops, and that weight then spreads into the tails. If the other team has more talent and a higher expected score, increasing the odds of surpassing that average makes sense. The risk of a loss decreases, but the risk of getting embarrassed increases. 

How do teams actually play their cards?

This is more evidence coaches do not coach to maximize their team’s chances of winning. My theory is coaches are delaying elimination until the latest point in the game—that is, trying to “stay in the game” for as long as possible. Underdog coaches minimize risk all game long hoping for a miracle along the way. They seem to be reducing the chances of being blown out, but this is not consistent with giving their team the best chance to win.