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The Poisson Distribution and Peyton Manning's Inconsistency
Aug. 31, 2014

Peyton Manning is the most inconsistent quarterback in the NFL. This is a compliment! Last season, his performance was so “inconsistent” with the norm that he set an NFL record for passing touchdowns in a season. In this post, I will explain the mathematics behind why the season-to-season variation in star players’ performances will dwarf that of an average player. This has important fantasy ramifications, as your entire season can be won or lost by the exceptionally good or bad performance of just one star player.

In the media, Peyton is often described as a model of consistency, while his brother Eli has been called one of the most inconsistent quarterbacks in the league. However, let’s quantitatively compare their season-to-season consistency. Eli’s best season was 2010 when he had 31 passing touchdowns, and his worst was 2013 with 18 (a difference of 13 between best and worst seasons, while Peyton’s best and worst seasons differ by a whopping 28 passing touchdowns! In reality, Eli is relatively consistent, while Peyton is a normally excellent player capable of exceptional seasons of true greatness. This is just one example of a general truth about quarterbacks: the players who earn the most touchdowns tend to have the most season-to-season variation in the number of passing touchdowns scored. (Take a look at career stats of other players to confirm this!)

There is a mathematical explanation of this fact: Passing touchdowns in the NFL are a “rare event” (there are very few touchdowns scored per minute on average), which means that the number of passing touchdowns per season follows a Poisson distribution. By searching “Poission Distribution” on Wikipedia, you can see that the variance of a Poisson distribution is equal to its average. Therefore, the more often a quarterback scores on average, the more variation there is in his performance. As we have seen, for star players like Peyton, this variation can be huge. Get Peyton in a good season, and you could get double the performance of an ordinary quarterback!

You can use this information to your advantage in fantasy football. Don’t get too high or low off of recent performances of your star players. If your stars go through a prolonged slump, stay patient; large variation is normal. Then, when one of your stars has an exceptional season, you’ll be riding their “inconsistency” to a league championship.

Use this advice to build a killer lineup at AdvancedSportistics.com!
Who will score the most EPA this week?
Drew Brees
Aaron Rodgers
Andrew Luck
Peyton Manning
Yesterday's Top Winners

Will be posted after NFL Week 1.
Advanced Stat of the Day

Philip Rivers has the highest single-game Expected Points Added with 14.2 in a 33-30 win over Philadelphia on September 15, 2013.