Playoff Fantasy Football - Games people play

Previously I showed a playoff prediction model using the Sagarin points rating and a random factor to simulate the NFL playoffs. The model revealed two poles of expectations for the Superbowl this year: Without a home advantage, Philadelphia lost to Pittsburgh in the Superbowl. With a home advantage of 2.81, Tennessee beats the New York Giants in the Superbowl. The latest results of the playoffs seem to indicate we are closer to the first situation than the second.

In our earlier problem statement we noted that the key to winning the RKB fantasy football playoff pool is to pick the players which generate the most points. The problem really breaks down to two issues. One: Predicting which teams will play the most games in the playoffs. Two: Picking high scoring players on those teams for a multiplicative effect. Using the previously described model we can predict how many games each playoff team will play so that we can pick players that have the most number of opportunities to score points. The best player lists will have players on teams that play three or four games and not one or tow games.

The chart below (please click the picture or here for larger) shows the number of games each team plays as a fraction of 1000 simulations run at each pair of home advantage and random factor parameter values.

Moving from left to right, the home advantage increase from 0 to 2.81, the number given by the Sagarin ratings. Moving from top to bottom the random factor increase from 0 to 3 to 1000. With no random factor the results are just as the Sagarin ratings would predict (top line of charts). With no home advantage (top left corner) Philadelphia plays four games (blue), Pittsburgh, Atlanta and Baltimore play three games (green) and rest play two (orange) or one (red). With a 2.81 home advantage (top right corner), Tennessee, New York Giants and Minnesota play three games and the rest play two or one.

Adding in a random factor to the simulation now means that there is a distribution of the number of games played instead of one answer as the 1000 simulations end one way or the other. Increasing the random factor to a ridiculously large 1000 is equivalent to saying that the outcome of any game is a 50/50 tossup. The bottom line of charts shows that all home advantage values converge to the same random result. Any team has a 50% chance of playing only one game, and a 25% chance of play two games. Teams with a first round bye have a 25% chance of playing three games, while teams without a buy have a 1 in 8 chance of playing three games and another 1 in 8 chance of playing four games.

More interestingly is how robust are outcomes in which Philadelphia plays four games are to the parameters of the Monte Carlo simulations. Out to a home advantage of 1 (actually 1.2 according to our previous analysis) and up to a random factor of +/- 3, Philadelphia plays four games in more than half of the simulations. These parameters aren't unreasonable, the random factor represents a touchdown and the home advantage is an average over all teams and must have some error in it from team to team. Philadelphia players would have four chances to contribute to a fantasy playoff pool. Other teams that play four games in this parameter region are Baltimore and Atlanta. This analysis was put in place before the playoffs. Atlanta losing in the first round is a big upset according to this model.

With a larger home advantage factor of 2 or 2.81 a good playoff list might contain Tennessee or New York Giants players who will have three games in which to contribute to a playoff pool total score. Several entries into the fantasy pool covering these options would increase the chances of winning.

In a future post, we will determine and simulate which players yield the most points.