# Might median factors per recreation be the way forward for fantasy soccer evaluation?

Fantasy football competition is constantly evolving, but the industry still uses a mysterious seasonal grade for player performance. You’ve heard the arguments, “So-and-so finished as WR23 last year and I could see he finished in the top 15 this year.” The small step forward was the urge for Average Points Per Game, commonly abbreviated as PPG. Viewing a player’s “weekly” production is useful for making weekly squad decisions for cross-season leagues as well as daily fantasy games. There is a better way, however. This results in Median Points Per Game (MPPG is used as an abbreviation). If you don’t remember your math work in middle school, don’t worry, class is about to start!

## Why a season-long finish isn’t helpful

A player’s total score is influenced by far too many variables to be helpful in predicting a player’s future performance. A cumulative number like 150 PPR Points (the typical total PPR number for the RB30) does not provide any insight into how that player came up with that number. There is no consideration of variances and without games being played alongside the total score, there is little context to create. Take Nick Chubb’s 2020 season, for example. He finished with 207.7 PPR points and became RB11. He was one place behind Kareem Hunt who earned 218.5 PPR points. The missing context is that Chubb played four fewer games than Hunt.

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## Why average points per game are better but still not good enough

If we keep our example above, we can calculate the average points per game (APPG) of Chubb and Hunt. Since Chubb played fewer games and had a similar total score, his APPG (17.3) is significantly higher than Hunt’s 13.7. This is helpful as it gives an estimate of the expected performance for Chubb in a given week.

The problem is that for fantasy football this estimate is completely inaccurate. One problem lies in the actual math that is used to compute an average. APPG is simply the total score for the year (or other cumulative time frame) divided by the number of games played. So by using APPG you haven’t broken away from the player’s entire season.

The other math problem is that an average takes on a normal distribution (think the bell curve from middle school science) to be precise. In a normal distribution, the mean and the median are the same, because the mean and the median have the same “weight”. However, if the data is abnormal or “skewed” in one direction, the mean and median will have different values depending on the direction and size of the skewness.

To further prove the errors in using the average in highly abnormal data sets, middle school statisticians and math teachers tell a “joke”. One guy and four of his best friends are at the bar. They all make roughly the same annual income, averaging $ 50,000 a year. For some unknown reason, Bill Gates, who made over $ 7 billion in 2019, walks through the door. Happy day! The guy and his friends all just became billionaires. . . on average. This is a bad joke even by father-joke standards, but it is an attempt to study the effects of introducing a data point that converts a normal curve to a non-normal curve.

## Why median points per game is better

As can be seen in the picture above, the median is closer to the “hump” and the average (mean) remains relatively unchanged. Even in the bad joke above, the median income would reflect the income of the man and his friends much more than the median income, which was the punch line of the joke. If we look at these images above, it should be clear that the median is a more accurate estimate of where the majority of values fall within a data set. To prove this point, the image below is a histogram of Tyler Lockett’s PPR points for each week of the 2020 season. Lockett’s histogram is similar to the third distribution in the image above. As the third distribution detail shows, the mean is greater than the median, although the majority of the values are at the lower end.

Throughout the 2020 season, Lockett’s APPG stood at 16.8, although only six games were above that number. That’s an astonishingly low 37.5% of the games above its average points per game. Lockett’s MPPG was 10.9 and, by definition, half of his games (eight) were above that number. Lockett’s 53-point game was more than likely a game-winner. However, if you knew that 50% of a player’s games would score 10.9 or less PPR points per game, how much would you be interested in having that player on your fantasy list? As a reference, 10.9 PPR points were WR33 at best, WR46 at worst (twice) and would have been WR36 or worse in 16 out of 17 weeks during the 2020 season. Lockett’s 16.6 APPG ranks 12th for 2020, but he hasn’t created a weekly rating that would keep fantasy owners happy outside of three really big weeks. Lockett’s MPPG for the typical fantasy season (weeks 1 through 16) was 10.2, finishing in 48th place; his APPG was 17th at 14.4.

While Lockett is an extreme example of APPG overrating a player, you can use MPPG to find players who are underrated by APPG. Every time a player’s median is above their average, they’ll score more points on a more consistent basis. Brandon Aiyuk is a prime example. Although Aiyuk only played 12 games, he exceeded his average in seven of these games; almost 60% of the time. His average points per game from Week 1 to Week 16 was 15.4, barely outside of the typical weekly WR2 range. However, his MMPG for that period was 18.6, more than three points higher, putting him right in the middle of the WR2 range. Comparing the weeks Lockett and Aiyuk both played, Aiyuk scored six of the eleven times more points than Lockett, even though his APPG was almost one and a half points less.

Median points per game is the next step in developing an understanding of soccer data. It completely breaks from the contextless year-end totals in ways that APPG simply cannot. In addition, it more accurately reflects the main score of a player’s results, which leads to more accurate predictions.

For more info on median points per game, follow me on Twitter as I will be working through the off-season to get the word out as widely as possible.

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