Saturday, January 15, 2011

Simulation and Prediction: Winning Rosters Fantasy Football Playoff pool

The purpose of the fantasy football playoff roster simulation is to search all of the possible combinations of player rosters for the one roster that has the highest chance of beating the other rosters. To do this I have first simulated the expected outcomes of the playoff games using Sagarin ratings. I also collect the expected performance of each player in each given game from available data about their performance this year. Combing the two yields the expected performance of a given roster and then I compare lists of rosters to each other to see which roster beats the other roster the most times.

My goal is to find roster which score a lot of points and which do well in comparison to their competition. Additionally the search is also for rosters which win over the various high probability outcomes of the playoff season. The model is displayed diagrammatically below.

Using the simulations of the NFL playoffs, the average expected points for a given player per game, we can simulate the performance of fantasy football playoff roster against one another. Now that we know the 72 rosters competing in this year's RKB fantasy football playoff pool, the simulations allow us to see what the probability of rosters being in the first two places, those placements are in the money for this playoff pool.

Before the wild card week during creation of my rosters I used a similar technique with 20 roster that I picked to try to choose the best roster. I chose rosters that had players from teams that played the most games and had players with a high average number of points per game. I also tried to cover the different possible superbowl matchups. From the 20 I chose 5 rosters that I felt covered the potential matchups. The chart below shows the performance of those rosters vs. the 72 participants in this years RKB fantasy football playoff pool.

The chart shows the frequency of the first 20 outcomes for first and second place combinations in 10,000 simulations. Green bars are rosters in which I place in the money, red are not. My rosters are 57 (RDK1, NE dominates ATL in SB matchup), 58 (RDK2, GB dominates NE or PIT in SB matchup), 59(RDK3, PIT dominates ATL in SB matchup), 60 (RDK4, NO dominates NE in SB matchup), and for the hometown 61 (RDK5, PHI dominates NE in SB matchup). Rosters are numbered by their alphabetical order on the RKB Fantasy football roster list.

Before the wild card games were played my rosters were in good position to be in the money according to the simulation results. One roster, 57 where NE is in the SB was so popular that two other participants picked exactly the same players for their rosters (2 and 56). Of the 91 different outcomes, 38 of them had my rosters in the money. Those 38 outcomes combined to 75% of the 10,000 simulations with my rosters in the money. But a the wild card week of playoffs has occurred the outcomes have changed.

After the wild card week, I modified the playoff simulator to reflect the fact that IND, KC, NO and PHI were out and reran the simulations. These simulations also included the actual point totals for players who played the first week added to the simulated totals for the games after the first one if a given player played any. Now there are much fewer possible combinations of possible rosters in the money (first or second place), but my rosters still figure prominently in the money. Once again, green bars are rosters in which I place in the money, red are not

Now their are only 20 possible outcomes of first and second place combinations according to the simulation. Of these 20 combinations, 8 have my rosters in the money. Those 8 represent 64% of the 10,000 simulations. This is a decrease from the estimate before the wild card games were played, but the most probably outcome, in which I am in a three way tie for first place, has gone from 11% to 22%.

I could still lose the chance to get money if really unusual events like SEA winning or New England losing occur, but the whole point of this was to have the fewest rosters which cover the most probability of being in the money.

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