path: root/src/fantasy-football-part1.Rmd

---
title: 'Fantasy Football: Science or Luck? (Part 1)'
date: 2013-04-02
output:
  html_document:
    css: style.css
    highlight: pygments
---

# Introduction

I've always been an (American) football statistics junkie. 
As a child I collected and carefully studied thousands of football cards - I always had the most important datapoints memorized.
Every Monday morning on the school bus, September to January, I pored over the box scores from the previous NFL Sunday to see which teams and players had succeeded or failed.

Fantasy football was a logical continuation of this interest.
In case some readers are unfamiliar with the game, I will provide a brief explanation. 
A group of 8-12 friends, family, or random people on the internet form a league before the start of the NFL season. 
Using one of a [variety of draft formats](http://www.nfl.com/fantasyfootball/help/drafttypes), each participant selects a team of players to represent them. Teams go head to head each week of the season. 
The performance of the players on each team (in the real-life NFL) is scored based on a standard system; for example, a touchdown is typically worth 6 points and 10 yards rushing is worth a single point. 
Points are totaled and the team with the higher total score wins the week. 
Typically there is a playoff system and a final fantasy 'Super Bowl'. You can read more about fantasy football [here](https://en.wikipedia.org/wiki/Fantasy_football_%28American%29) if you are interested.

After many years of experience, my anecdotal observations indicate fantasy football success is more a roll of the dice rather than an exact science.
In each individual year or league, the draft order, total points scored, and even final regular season rank seems to have little bearing on the overall winner. 
Seldom do the same players win the championship or even make the playoffs in consecutive years (a far cry from the actual NFL, where 9 of the past 13 Super Bowls have been won by a set of only 4 teams). 
Still, these observations are exactly as I described them (anecdotal). Given enough data, interesting patterns may yet lurk underneath.

Luckily for my curiosity, there is some data available to test for these patterns. 
Over several late nights, I dug through the archives of the fantasy football leagues I participated in going back to 2006.
Unfortunately, CBS Sportsline (where I played prior to 2006) did not keep any records, though I checked thoroughly after dusting off my late 1990s era AOL username and password. 
My analysis of this dataset will be broken into several parts, as I have time to complete them. 
The complete raw dataset is available [here](https://kenkellner.com/files/fantasy_football_results.csv).

```{r}
src_url = 'https://kenkellner.com/files/fantasy_football_results.csv'
if (!file.exists('../data/fantasy_football_results.csv')){
	dir.create('../data')
	download.file(src_url,'../data/fantasy_football_results.csv')
}

rawdata = read.csv('../data/fantasy_football_results.csv',header=T)
```

# Variation in Player Success

The two most important questions I'm interested in are (1) which fantasy players  are successful, and (2) what behaviors or patterns make them successful? 
In order to begin to answer those questions, I needed to answer an even more fundamental question - how should we define individual fantasy football success?

# Win Percentage

The most straightforward method of defining fantasy 'success' is to examine the player's regular season record.
However, since the number of competing players and the number of games played can vary between years and leagues, it makes more sense to use a simple win percentage (e.g., .500) for each player in each year.
Below is a histogram displaying the mean win percentage (averaged across all years/leagues for which I have data) for the 20 players I have at least 3 years of data for. 
Taller bars mean more players fell in that range of win percentage:

```{r,message=FALSE,warning=FALSE}
#Re-create missing graphdata-----------------------------------
library(tidyverse)

players_keep = rawdata %>%
	group_by(Player) %>%
	summarize(n = n()) %>%
	filter(n>2) %>%
	pull(Player)

rawdata_keep = rawdata %>% filter(Player%in%players_keep)

leaguestats = rawdata_keep %>%
	group_by(League) %>%
	summarize(MnPts = mean(Total.Points,na.rm=T),
			  SdPts = sd(Total.Points,na.rm=T))

graphdata = rawdata_keep %>%
	left_join(leaguestats,by='League') %>%
	mutate(PtsZ = (Total.Points - MnPts) / SdPts) %>%
	group_by(Player) %>%
	summarize(TotPtsZ = mean(PtsZ, na.rm=T),
			  WinPct = mean(Win.pct..reg.),
			  PlayoffPct = mean(Playoffs),
			  ChampPct = mean(Champion))
#--------------------------------------------------------------

hist(graphdata$WinPct, prob=TRUE,main='Mean player win %',
	 xlab='Win Percentage',col=rgb(220,57,18,max=255))    

#Draw smoothed density line
lines(density(graphdata$WinPct,adjust=1.8),lwd=3,col="black") 

#Add identification info
text(0.6,7,"1. Mark S. (.625)")
text(0.6,6.5,"2. Ken (.600)")
text(0.6,6,"3. Tom S. (.550)")
text(0.6,5.5,"4. Tom G. (.540)")
text(0.6,5,"5. Steve (.530)")
```

I've gathered a reasonable amount of data, so you can see the ever-present [normal distribution](https://en.wikipedia.org/wiki/Normal_distribution), or bell curve, beginning to take shape. 
However, it's [skewed](https://en.wikipedia.org/wiki/Skewness) - there is a higher concentration of players below .500 and a small number (2) well above .500.
It seems most people fall right around the expected average (as many games won as lost) or just above - but it's much more unlikely to have a mean win percentage above 0.550. 
I'm not surprised by the positions of my fellow players on this graph - my longtime opponents Steve and Tom G. are above .500, and Mark S. has set the curve. 
Still, it's clear that none of us have dominated our fantasy leagues the way some top NFL teams have over the same time period (11 teams have a win percentage greater than .550 over the last 6 years, led by New England with 0.760). 
The parity I see in the graph above is preliminary evidence that fantasy football success seems to be more about luck than skill. 
Of course, regular season win percentage doesn't fully measure fantasy football success - ultimately we are interested in who wins the league outright.

# Proportions of Seasons Ending in Championship

The second statistic I used to measure 'success' is the proportion of leagues in which a player won a championship (calculated simply as number of championships won divided by total leagues played). 
This method might improve on the previous metric by ignoring all the variation inherent within the regular season and focusing only on the winner. 
However, it has issues of its own which are immediately apparent in the histogram below:

```{r}
hist(graphdata$ChampPct, breaks=5,prob=TRUE,main='How often do players win the title?',xlab='% of League Championships',col=rgb(255,153,0,max=255)) 

#Draw smoothed density line
lines(density(graphdata$ChampPct,adjust=0.9),lwd=3,col="black")

#Add identification info
text(0.25,8,"1. Colin (.333)")
text(0.25,7,"2. Terry (.250)")
text(0.25,6,"2. Stef (.250)")
text(0.25,5,"4. Tom G. (.200)")
text(0.25,4,"5. 2-way tie (.167)")
```

This distribution is nearly uniform, with the exception of a spike at 0 (perhaps best modeled as [zero-inflated](https://en.wikipedia.org/wiki/Zero-inflated_model)?).
Most players don't win more than the 10% of leagues they'd be expected to win by chance (in an average 10-team league). 
A single championship greatly changes your position in the ranking - no player in the dataset won more than 2 total championships regardless of how many leagues they were in (Colin, Tom G., and Ken each had 2). 
I'd argue that this method of defining success relies too much on chance (I'll explain this further later on), though Colin's 2 championships in 6 leagues is impressive.

# Proportion of Seasons in Playoffs

The third metric I used to define success is the percentage of seasons in which a given player made into the 4-team playoffs. 
This method accounts for regular season success, and is less dependent on the random outcome of a single championship game.
It also standardizes between leagues with differences in variation among win percentages (e.g. between a league where almost everyone has a record near .500 and a league where a couple teams are near 0 and a couple near 1). 
Here's the resulting distribution:

```{r}
#Recreate missing playoffpct chart-----------------
hist(graphdata$PlayoffPct, breaks=5,prob=TRUE,main='How often to players reach the playoffs?',xlab='% of Leagues in Playoffs',col=rgb(16,150,24,max=255)) 

#Draw smoothed density line
lines(density(graphdata$PlayoffPct,adjust=0.9),lwd=3,col="black")

#Add identification info
text(0.8,1.6,"1. Mark S. (.833)")
text(0.8,1.4,"2. Stef (.750)")
text(0.8,1.2,"3. Colin (.667)")
text(0.8,1,"4. Ken. (.563)")
text(0.8,0.8,"5. 4-way tie (.500)")
```

If playoff entry was completely random, you would expect most people to have a percentage between 0.33 and 0.5 depending on the number of teams in the league. 
The distribution has a mode in that area (around 0.45), but it also appears to be bimodal. 
There are a large number of players who never or almost never make the playoffs, and a skew towards a small number of players who nearly always make it. 
Once again, Mark S. is at the top, suggesting a link between mean regular season record and playoff entry (not at all surprising).

# Playoff Seeding

What I haven't accounted for above is playoff seeding (#1-4). You'd expect that higher seeds, earned with better regular season records, would set you up for a championship. At the very least, you'd expect an equal number of wins from each seed. Here's the breakdown, by percent of championships won:

```{r}
#Recreate missing chart 2 code-------------------------

chart2 = rawdata %>%
	filter(Rank.b.f.Playoffs < 5) %>%
	group_by(Rank.b.f.Playoffs) %>%
	summarize(ChampPct = mean(Champion))

barplot(chart2$ChampPct, main = 'Which Playoff Seed Does Best?',
		xlab = 'Playoff Seed (1=top)', ylab='Proportion of Championships',
		names = 1:4, col=c(rgb(51,102,204,max=255),rgb(220,57,18,max=255),
						   rgb(255,153,0,max=255),rgb(16,150,24,max=255)))
```

This is very surprising - the first seed is actually the *least likely* to win the championship!
Of the 16 leagues I examined, only 1 top seed won the title. 
Second seeds and fourth seeds are much more likely to win than either first or third seeds. 
Granted, I haven't tested for actual statistical differences between the seeds but this is still puzzling.
One suspicion that I have is that lower seeds (particularly 4th seeds) are often teams that are peaking at the end of the season, just managing to sneak into the playoffs. 
In the playoff rounds, they defeat top seeded teams which may have peaked earlier in the season and declined since. 
I have collected data on win streaks and other variables which may allow me to explore this question further.
The takeaway message is that effort, and perhaps skill, play a role in getting a player to the playoffs, but after that it seems to be based mainly on chance.


# Total Points Scored

The fourth and final metric I used is fairly straightforward in theory - total points scored. 
Points scored has the advantage of being the least based on those random, frustrating weeks when you lose 150-145, since points are totaled across all regular season weeks. 
Of course, total points might be completely unrelated to actual wins and championships for that same reason. 
The raw points data requires some adjustment, since every league has different roster and scoring rules. 
Therefore, for each player in each league, I calculated a standardized [Z-score](https://en.wikipedia.org/wiki/Standard_score) which essentially compares that player's points total with the other points totals in that particular league. 
The result is numbers generally between -3 and 3, where a completely average point total is equal to 0 and a point total 1 standard deviation above the mean is equal to 1 (and so on).
Comparison between years and leagues is now possible.

```{r}
hist(graphdata$TotPtsZ, breaks=5,prob=TRUE,main='Total Points Scored',xlab='Z-score of Total Points',col=rgb(51,102,204,max=255))   

#Draw smoothed density line
lines(density(graphdata$TotPtsZ,adjust=2),lwd=3,col="black")

#Add identification information
text(1,.8,"1. Mark S. (1.148)")
text(1,.7,"2. Colin (0.520)")
text(1,.6,"3. Tom S. (0.388)")
text(1,.5,"4. Tom G. (.302)")
text(1,.4,"5. Ken (.280)")
```

Mean Z-score follows a normal distribution much more closely than the previous 2 methods.
Most players have a mean Z-score around 0, indicating an average number of points scored.
Familiar names make up the top-5 ranking, with Mark S. again at the top, more than 1 standard deviation greater than the mean.

# Conclusions from Part I

Clearly, defining fantasy football success is difficult. 
All of these methods have drawbacks, and I've done little to answer the question of luck vs. skill. 
However, there are a few players that seem to rise to the top under every metric - based on these charts alone, I'd give the overall title to Mark. 
A lot more work needs to be done - in my next post, I'll be moving away from looking at individual players in order to answer predictive questions. 
For example, does draft order affect championship chance? 
What about player effort (=number of moves)? 
Pooling all players together will allow me to use more sophisticated modeling approaches to answer these questions.

I'd love to hear any reader ideas or criticism on this analysis so far. I'd also greatly appreciate the contribution of data from additional leagues.