(Updated Sept. 2)
A reader requests the optimal strategy for maximizing his pool winnings. He writes:
I’m in a small pool that pays both weekly and at the conclusion of the season. To maximize my payoff, I need to win weeks and finish on top. 60% of the funds are paid weekly, the rest after week 17. I need enough variability to win weeks, but not too much, first place pays 20% of the pot.
Five obstacles argue against tuning your strategy too precisely: risk, noise, user error, modeling other entries in your pool, and the bias/variance tradeoff.
The accuracy of picking favorites to win outright varies over time. Typically it ranges between 60% and 70%. Some years it is as low as 57% or as high as 75% over the course of a season. We can go three years without getting a single week when all the favorites win. So even using the highest expected point model, such as WinThatPool’s, is no guarantee you will win your pool by season-end, although in most small pools (say, fewer than 20 entries) it should always rank near the top. In pools with 50 to 100 entries, depending on the others’ skill and on the year you should finish in or near the top five, but coming out #1 is not guaranteed.
An NFL season entails only 256 games spread among 17 weeks. That is a small sample size, with lots of room for bad streaks for the best model and good streaks by useless models. Better to join a pool whose season stretches into the playoffs.
Have you ever entered the wrong side of a game you picked correctly just because Yahoo! or ESPN or poolhost displayed the game wrong, or at least differently from how you expected? It only takes one of those slip-ups to put you permanently behind. I have seen other pool members forget to pick the winner of the Monday night game in time and miss out on winning that week. It happens.
Modeling other entries in your pool
There is a right way to do this, and it is beyond most entrants’ capabilities. It is quite complex, and it entails simulation. In 2009 WinThatPool used to recommend confidence pool picks to optimize winning that week’s pool. Such recommendations depend heavily on the size of the pool, that is, the number of other entries. If demanded by enough readers, WinThatPool might add that feature back.
WinThatPool’s recommendations are effectively unbiased, which is ideal for maximizing points over the course of a season. Lots of entries pick the right favorites but their confidence ranks are biased. Unbiased confidence ranks are what you want for a season-long prize. Compare WinThatPool’s picks to, say, Brian Burke’s win probabilities on AdvancedFootballAnalytics(AFA). Which teams will win is seldom in disagreement between our picks, but in the past Burke’s probabilities have been biased – that is his 80% and 90% picks have not won 80% and 90% of the time. If you applied his picks in a confidence pool, you probably finished out of the running for a season-long pot.
Weekly strategy: Deviate on one heavy favorite
The corollary is WinThatPool’s recommendations are a starting point (hence the slogan, “your starting point for winning office pools”). If you really want to risk your season-long ranking by going against the model, select one of the highest confidence games that week and pick the underdog without changing the confidence points. For week 1 in 2014, that might mean picking Buffalo over @Chicago, and leaving it at 14 points. Your expected point total is worse than picking @Chicago, but if the upset occurs so few of your pool-mates will pick Buffalo that you’re in a good position for the Week 1 pot. Another possibility is to use a different, biased set of confidence ranks. For example, you could simply apply AFA’s picks, but so many people read those picks in the NYTimes chances are you won’t be the only one doing so.
By the way, I am not complaining about AFA or its model. AFA (formerly known as Advanced NFL Stats) is an innovative sports analytics blog. Brian Burke has influenced how the game is played – how many sports sites can say that? Burke was an early critic of received wisdom that too often resulted in overly conservative play. I credit him with evolving how fans, commentators, and even coaches think about football strategy and tactics, and specifically for catalyzing the growing tendency for NFL coaches to go for it on fourth down.
Update – I would add that AFA’s in-game modeling is revolutionary, and one of the primary reasons so many pay attention to AFA.
Best strategy? Start with the season-end strategy and switch if necessary
If after several weeks you fall too far behind you can always switch from the season strategy to the weekly strategy, but you probably cannot do the opposite unless you win Week 1. Figure out in advance what your expected winnings are for the weekly pot and the season pot by assuming a 1/n chance, where n is the number of entries. Compare your expected winnings for 17 chances at the weekly prize with one at the season prize. Pick either strategy and pursue that. If you start out with the season-end strategy, you will probably contend for the season pot, and maybe through a combination of other users’ errors and noisy luck, you might also win a week.