Not all sets of data are created equal. Most importantly for fantasy football, not all data sets are normal. That means the mathematics used to understand normal data sets, like mean (or average), standard deviation, and more advance z-scores or Pearson’s coefficient of correlation can be misleading.

Looking at a player’s Mean Points Per Game (PPG) provides a single number that misrepresents that player’s “typical” game. Using Median Points Per Game is more robust to outliers by definition. Additionally, when combined with upper and lower quartiles, it better represents what is “typical”.

Below is a searchable and sortable data set of Median and Mean Points Per Game as well as Total Points, Games Over Average, and Upper and Lower Quartiles. Helpful tips and more notes on the math are provided below the dashboard. 

Helpful Tips

-Use the filters to limit the table of player names. You can search for a specific player using the Name drop-down and search field. You can also narrow the table by selecting a specific team or position. 

-Use the sliders to adjust the time frames in which you are viewing. You can adjust the week slider to view just the start of the season or the fantasy playoffs. You can select a range of years but keep in mind that selecting multiple years will aggregate all of the data. Can also select any single year. 

-The table is sortable by each column header and will automatically update based on the filter selections. Clicking on a player will focus in on them and the charts below will adjust to only display that player’s stats. 

-Use Ctrl+Click to select more than one player at a time. Please note selecting too many players will make the charts below difficult to read. Selecting fewer than 5 players at a time is recommended.

-When reading the candlestick chart (directly below the table), the green box represents the middle 50% of a player’s games. The top of the box is the upper quartile (75th percentile) and the bottom of the box is the lower quartile (25th percentile). The length of the blue line extending from the top of the box is what I use as a player’s ceiling as it represents the range of scores in which the player’s top 25% of games fall.

Conversely, the bottom of the box is a good representation of a player’s floor as it represents the score at which 75% of the player’s games exceeded. Finally, the blue line extending out of the bottom of the box is the player’s bust impact and extends from their lowest 25% of scores to their lowest score. 

-The bottom chart is a distribution of the selected players’ scores. It provides a more detailed look at how many games a player scores within a given score range. You can identify how many of the games in the top 25% of a player’s scores were “game winners” of 30 points or more.

More Math

Fantasy football enthusiasts are quick to reject total points scored as it is more an indicator of a healthy season than fantasy scoring efficiency. However, the push for PPG is flawed in that to calculating PPG requires total points. Using Median Points per Game though obviously correlated with total points doesn’t require total points in its calculation. Furthermore, the fundamental argument for not using mean is that fantasy scores are not a normal distribution. Weekly scores are overly distributed around the 0-10 range but extend out way further and at a greater frequency than would be expected by a normal curve. 

Take for instance the Empirical Rule which states that 99.7% of all observations in a normal curve should fall within three standard deviations of the mean. In the data set provided (using only RB, WR, and TE), three standard deviations from the mean (6.15 PPR points) was 28.62 points. Anyone who has been playing fantasy football knows a 30-point week is a “week winner” yet it is not out of the ordinary as the Empirical Rule would suggest.

In fact, there were at least one or more 30-point scores for every week of the fantasy season in 2022 with over 80% of the weeks having three or more players exceeding 30 points. Our Consistency Score metric digs a bit deeper into weekly booms and busts in fantasy football. 

On the other side of the curve, we should expect to see 15.9% of scores less than one standard deviation from the mean (-1.35 PPR points) according to the Empirical Rule. However, only 0.05% of scores in this data set were below this threshold. Similarly, in a normal curve, you would expect 50% of the observations to be below the average. Yet again though, in this data set over 63% of the weekly player scores were below the 6.15 PPR mean. If this doesn’t convince you that weekly fantasy scoring is not a normal curve perhaps the chart below will.

Median

By the definition of median, it will always represent the value in which 50% of the observations are above and 50% of observations are below. When a data set is a normal distribution the average and median will be the same value. In a non-normal distribution, like weekly fantasy scoring, the median will be closer to the greatest density of values based on its definition. For the data above, the median is almost 3 PPR points less than the mean. 

Evaluating Individual Players

Only 57 of 562 players had medians greater than their means in 2022. This implies that their distribution is actually the reverse of the chart above, i.e. they would have a greater amount of games above their mean as opposed to less than it. In the dashboard, you can filter by the percentage of games above average to be able to exploit this misconception.

Take, for instance, Courtland Sutton who scored an average PPG of 10.63 and a median PPG of 12.3 points. The argument here is not that Sutton had a great season or won your fantasy matchups last season. However, he scored over his average in 66% of the games he played. If you started him with the expectation that he would score 10 points you would have been too low more times than not. 

On the flip side, look at Mike Evans who had an average PPG of 15.03 and a median PPG of 10.4. He only had 33% of his games above his inflated average. If you expected him to score 15 points (or even 12.6 points his average before his 48.7 points in Week 17), you would have been disappointed in all but four games (5 if using 12.6 as his mean).

Comparing a player’s mean and median scores is incredibly helpful but does not paint the entire picture. Since I first published a piece on Median Points Per Game, I have heard arguments that fantasy managers want to know the impact of outlier games. Because the mean is greatly influenced by these outliers, these fantasy managers would prefer the mean. Additionally, the issue here is that there is no way of telling from the single value of the mean if a player has massive positive or negative outliers. Or, whether the mean is a true representation of what that player typically scores. 

To further explain this, take teammates Evans and Chris Godwin into consideration. In 2022, their Average PPG scores were within .2 points of each other but Godwin had over a 3-point advantage in median PPG. Of the 13 games they both played Evans only outscored Godwin five times. Simply looking at mean PPG would imply that on a week-to-week basis, they were scoring the same and not hinting at Evans’ explosive scoring potential.

If looking only at median PPG you would be able to better discern Godwin as the more consistent player. However, you would fail to see the level of consistency and Evans’ explosiveness would also be faded. This is where the candlestick charts (sometimes referred to as box-and-whisker plots) are helpful. 

In the candlestick charts above you can see that Evans has a much greater range of outcomes than Godwin. However, Godwin has a much more predictable scoring. The extent of Evans’ upper whisker captures his big games as the whisker captures the top 25% of his scores. While both of them have similar upper quartiles (the top of the box) Godwin has a clear advantage in his floor again almost 3 PPR points greater than Evans. This information can be critical in roster construction.

All things considered, Median Points Per Game in and of itself will not win you a fantasy football championship (it’s my belief that no single value will). However, it along with Upper and Lower Quartiles can be instrumental in increasing your likelihood of winning.

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