One of my colleagues asked me for advice on filling out his NFL confidence pool, and I offered 2 strategies:
1. Assign confidence points by the Vegas money lines, the heaviest favorites getting the top points and on down. This offers the best chance of maximizing total season points.
2. Do the above, but switch one of the top 3 picks to take the underdog. This offers the best chance of winning a weekly top score payout.
Attached is a rough proof, a Monte Carlo simulation with the following assumptions:
Player 1 employs strategy #1.
Player 2 employs strategy #2.
Player 3 employs strategy #1 but reduces top game pick to 1 point, increasing all the rest of the values (this is clearly dominated by strategy #2 and even comes out under average when strategy #2 is not included in the simulation)
Player 4 picks totally randomly (Strategy #4)
Players 5-50 use strategy #5 to pick roughly in line with the Vegas odds, though they pick upsets given Rand^2>Vegas money line. This is a generalized model of the median confidence pool picker.
The #1 strategy gains 3 points on average over the strategy employed by players 5-50.
The #2 strategy is over 2x as likely to win the weekly payout over the strategy employed by players 5-50.
The #1 strategy is 25% as likely to win weekly payouts compared to strategy #5 players, given there are 45 players emulating the median confidence pool model.
The #2 strategy will average 10 less points than strategy #1.
Going completely random (strategy #3) has a better chance to win the weekly total than all but strategy #2.
The money lines in the example were taken from this week's slate (14 games which happen to be without a prohibitive favorite). Even though this is full of assumptions and strategies should vary depending on competition, those that want to skip on the game theory should consider employing strategy #1 early in the season and switching to strategy #2 if they fall behind in the overall standings.
I know there are plenty of areas for improvement here. This went from question through model to post in 2 hours at an airport. Feel free to use the attached to model your own simulations and keep me posted via email or the comments with your strategies and results.
Confidence Pool Sim
Original Author- Erich
Revision Date- 20081023