top of page

Assessing Player Performance in Fantasy Football Using Trimmed Confidence Intervals and Percentile Bootstrap Methods

I wrote this for an assignment in the fall of 2023. It's not perfect conceptually, but it does have good insights regarding gauging player performance. 

Introduction

There is often much debate about whether certain sports players are better than others in the media, among groups of friends and fans alike. Fantasy sports have introduced methods of summarizing a player’s performance in each game and cumulatively throughout a season which are often used as talking points to support one’s argument that player A is superior to player B. For the purposes of this paper, the focus will be on fantasy football but the methods and talking points likely apply to all fantasy sports. 

​​

The standard method for ranking players based on prior performance is the average number of fantasy points scored in each game, but this is a poor method of comparison due to the small number of games played in an NFL season. Outlier performances tend to sway fantasy team owners into thinking that the typical performance for a specific player is much different than reality. Using median fantasy points (MFP) scored as a measure of player performance is not a new concept as there have been many people pushing for its widespread use (Ashbrock, 2022), but it is highly unlikely that the majority of people will make the change given that the average fantasy points (AFP) for every single player readily available on every platform for every player, while MFP requires some work. 

​

MFP is preferable to AFP due to its robustness and consistency in representing a player’s performance. Unlike the average, which is highly sensitive to outliers and can be misleading in a sport with a limited number of games like the NFL, the median is more resistant to such extremes. This robustness is crucial because it means that at least 50% of a player’s performance is at or above a certain point level.

Sample

Two quarterbacks (QB), two running backs (RB), two wide receivers (WR), and two tight ends (TE) were chosen based on their ranking of total points scored in a season to show how this number can be misleading. Position rankings and scoring for each player were pulled from ESPN.com post-Week 11 and before Week 12 of the 2023-2024 NFL season as this was when this study was conducted. I strategically chose two players from each position who scored roughly the same number of total points but displayed a notable difference in the average and median fantasy points per game. By choosing players with these criteria, the study highlights the variability and consistency in player performance, a critical aspect of team building in fantasy sports. 

  • Quarterbacks 

    • Sam Howell, Washington Commanders

    • Brock Purdy, San Francisco 49ers

  • Running backs

    • Raheem Mostert, Miami Dolphins 

    • Tony Pollard, Dallas Cowboys

  • Wide Receivers

    • D.K. Metcalf, Seattle Seahawks

    • Jakobi Meyers, Las Vegas Raiders

  • Tight ends

    • Cole Kmet, Chicago Bears

    • Dalton Schultz, Houston Texans

 

Scoring

  • Standard Point Per Reception (PPR) Scoring (via ESPN)

​

Analysis

Each player in each position group will be compared using percentile bootstrap of the median and trimmed confidence interval methods to determine which player has had a more productive season so far. I hypothesize that the player with the worse position ranking will have had a more productive season because the median points scored are greater. 

Descriptives/Assumptions

Quarterbacks

​​​

​​

​​

​​

​​

​​​

​​

​​

​​

​​

​​

​​

  • Sam Howell, Washington Commanders (Position Rank = #6, Avg. Pts. = 18.65, Median Pts. = 18.52)

​

​

​

​

​

​

​

​

​

​

​

​

  • Brock Purdy, San Francisco 49ers (#9, 18.55, 19.30)

​

​

​

​

​

​

​

​

​

​

​

​

Runningbacks

​

​

​

​

​

​

​

​

​

​

​

​

  • Raheem Mostert, Miami Dolphins (#2, 18.48, 14.50)

​

​

​

​

​

​

​

​

​

​

​

​

  • Tony Pollard, Dallas Cowboys (#6, 14.21, 16.05)

​

​

​

​

​

​

​

​

​

​

​

​

Wide Receivers

​

​

​

​

​

​

​

​

​

​

​

​

  • D.K. Metcalf, Seattle Seahawks (#16, 15.56, 13.50)

​

​

​

​

​

​

​

​

​

​

​

​

  • Jakobi Meyers, Las Vegas Raiders (#21, 14.09, 15.50)

​

​

​

​

​

​

​

​

​

​

​

​

Tight Ends

​

​

​

​

​

​

​

​

​

​

​

​

​

  • Cole Kmet, Chicago Bears (#6, 12.22, 9.60)

​

​

​

​

​

​

​

​

​

​

​

​

  • Dalton Schultz, Houston Texans (#8, 10.32, 11.10)

​

​

​

​

​

​

​

​

​

​

​

​​

​

As evident by the histograms and Q-Q plots, the assumption of normality is violated by each player’s distribution of fantasy points scored. To analyze this, a percentile bootstrap of the median difference of each player, and a trimmed 95% confidence interval. 

Results

Quarterbacks

Trimmed Confidence Interval 

> trimci(qb.difference,tr = .2,alpha = .05) 

[1] "The p-value returned by the this function is based on the" 

[1] "null value specified by the argument null.value, which defaults to 0" 

$ci 

[1] -5.212937 6.624366 $estimate 

[1] 0.7057143 

$test.stat 

[1] 0.2917591 

$se 

[1] 2.418825 

$p.value

[1] 0.7802955 

$n 

[1] 11 

 

Percentile Bootstrap of Median 

> onesampb(qb.difference,est=median,alpha=.05,nboot = 10000) 

$ci 

[1] -3.32 7.28 

$n 

[1] 11 

$estimate 

[1] -1.62 

$p.value 

[1] 0.7506

 

Runningbacks

Trimmed Confidence Interval 

> trimci(rb.difference,tr = .2,alpha = .05) 

[1] "The p-value returned by the this function is based on the" 

[1] "null value specified by the argument null.value, which defaults to 0" 

$ci 

[1] -3.895078 9.523650 

$estimate 

[1] 2.814286 

$test.stat 

[1] 1.026373 

$se 

[1] 2.741972 

$p.value 

[1] 0.3443027 

$n 

[1] 11

 

 

Percentile Bootstrap of Median 

> onesampb(rb.difference,est=median,alpha=.05,nboot = 10000) 

$ci 

[1] -3.5 9.0 

$n 

[1] 11 

$estimate 

[1] 1.3 

$p.value 

[1] 0.7746

 

Wide Receivers

Trimmed Confidence Interval 

> trimci(wr.difference,tr = .2,alpha = .05) 

[1] "The p-value returned by the this function is based on the" 

[1] "null value specified by the argument null.value, which defaults to 0" 

$ci 

[1] -9.744186 10.344186 

$estimate 

[1] 0.3 

$test.stat 

[1] 0.07308443 

$se 

[1] 4.104842 

$p.value 

[1] 0.9441144 

$n

[1] 11 

 

Percentile Bootstrap of Median

> onesampb(wr.difference,est=median,alpha=.05,nboot = 10000) 

$ci 

[1] -6.3 12.9 

$n 

[1] 11 

$estimate 

[1] -2 

$p.value 

[1] 0.758

 

Tight Ends

Trimmed Confidence Interval 

> trimci(te.difference,tr = .2,alpha = .05) 

[1] "The p-value returned by the this function is based on the" 

[1] "null value specified by the argument null.value, which defaults to 0" 

$ci 

[1] -6.139976 9.139976 

$estimate 

[1] 1.5 

$test.stat 

[1] 0.4804161 

$se 

[1] 3.122293 

$p.value 

[1] 0.6479456 

$n 

[1] 11

 

Percentile Bootstrap of Median

> onesampb(te.difference,est = median,.05,nboot=10000) 

$ci 

[1] -4.3 10.1 

$n 

[1] 11 

$estimate 

[1] 0.4 

$p.value 

[1] 0.7412

 

The trimmed confidence interval and percentile bootstrap of the median tests for each position group was not significant, so we reject the null hypothesis that there is a difference in the typical fantasy points scored by these players. 

Conclusion

In a bit of a surprise, none of the tests were significant. Perhaps, if the sample sizes were larger the results may be different. However, this does make sense as fantasy football points are strongly correlated with opportunity and matchups (Hyttenhove). For example, a running back on a less talented team is likely to have fewer rushing attempts than a running back on a more talented team because running the ball takes up more time during a game, thus scoring less fantasy points. 

​

This study is not without its limitations, such as the small sample size of eight NFL players, the focus on a single season, and not accounting for performance variations across seasons such as injuries and team personnel changes. Also, this study only focuses on one scoring system while there are numerous other scoring systems that may have different results as different events are worth more/less points.

 

These results are indicative of the amount of luck involved in fantasy sports. The insignificant results and fluctuation of player performance make it difficult to rely on players to score X amount of points each week, but there are still some strategies to use when choosing players. Analyzing players by their median points scored, instead of average, is still the preferred method as with so few games as a sample, the average number of points is very sensitive to outliers. Another good strategy is acquiring players with favorable matchups against weaker defenses and targeting players on better teams. Although more talented players on less talented teams are more skilled than less talented players on more talented teams, it is likely that the second player has more opportunity to score fantasy points because their team is winning more games, thus the offense is on the field more. 

References

Ashbrock, J. (2022, July 25). Use median points scored in fantasy, not mean (and 2022 QB ranking implications!). The Data Jocks. https://thedatajocks.com/fantasy-football-medianpoints-scored/ 

 

Clay, M. (2023, July 26). Mike Clay’s fantasy football metrics that matter most. ESPN.com. https://www.espn.co.uk/fantasy/football/story/_/id/38069858/fantasy-football-statisticstargets-trends 

 

Hyttenhove, K. (n.d.-b). Fantasy 101: What stats matter?. QB List. https://football.pitcherlist.com/fantasy-101-what-stats-matter/ 

bottom of page