Entropy & Expected Touchdowns in Fantasy Football

Information Theory (Winter 2020)

by David Mendoza

March 18, 2020

Introduction

Fantasy football is loaded with tons of information. Players get scored on touchdowns, running yards, receiving yards, receptions, 2-point conversions, fumbles, interceptions, field goals, and many more statistics. To make matters more complicated, every fantasy football league customizes scoring rules.

Most leagues award 6 points for every touchdown scored so it is the most compensated statistic. For this project, the following analysis was followed:

  • Looking at the top 10 quarterbacks, running backs, wide receivers, and tight ends for the 2019-2020 season, the amount of touchdowns per game for every game played was recorded.
  • From those games, the probability mass function for touchdowns per game was deduced.
  • With the probability mass function, the expected value for touchdowns and entropy was calculated.

It is important to note that this analysis only looks into the expected value and entropy of touchdowns per game. It does not take other important scoring metrics like rushing/receiving yards and receptions. This analysis is useful to find the players that have the most opportunities to score touchdowns, which are heavily rewarded.

Results

I. Quarterbacks

Player Name Games w/ 0 TD Games w/ 1 TD Games w/ 2 TD Games w/ 3 TD Games w/ 4 TD Games w/ 5 TD Games w/ 6+ TD Total Games
Lamar Jackson 1 4 2 4 2 3 0 16
Dak Prescott 3 2 4 5 2 0 0 16
Russell Wilson 1 5 5 2 2 1 0 16
Deshaun Watson 2 3 3 5 1 1 0 15
Jameis Winston 1 5 5 2 2 1 0 16
Josh Allen 0 3 11 0 1 0 0 15
Patrick Mahomes 1 6 1 5 1 0 0 14
Kyler Murray 3 5 5 3 0 0 0 16
Aaron Rodgers 3 6 4 1 1 0 1 16
Carson Wentz 0 8 4 4 0 0 0 16

Table 1. Touchdowns per game for the top 10 quarterbacks of the 2019-2020 season

Player Name 0 TD Prob. 1 TD Prob. 2 TD Prob. 3 TD Prob. 4 TD Prob. 5 TD Prob. 6+ TD Prob.
Lamar Jackson 0.0625 0.25 0.125 0.25 0.125 0.1875 0
Dak
Prescott
0.1875 0.125 0.25 0.3125 0.125 0 0
Rusell
Wilson
0.0625 0.3125 0.3125 0.125 0.125 0.0625 0
Deshaun Watson 0.133 0.2 0.2 0.333 0.067 0.067 0
Jameis Winston 0.0625 0.3125 0.3125 0.125 0.125 0.0625 0
Josh
Allen
0 0.2 0.733 0 0.067 0 0
Patrick Mahomes 0.071 0.429 0.071 0.357 0.071 0 0
Kyler
Murray
0.1875 0.3125 0.3125 0.1875 0 0 0
Aaron Rodgers 0.1875 0.375 0.25 0.0625 0.0625 0 0.0625
Carson
Wentz
0 0.5 0.25 0.25 0 0 0

Table 2. Probability mass function for touchdowns per game for the top 10 quarterbacks of the 2019-2020 season

Player Name Expected TDs Expected Points Entropy
Lamar Jackson 2.6875 16.125 2.453
Deshaun Watson 2.202 13.212 2.367
Russell Wilson 2.125 12.75 2.299
Jameis Winston 2.125 12.75 2.299
Dak Prescott 2.0625 12.375 2.227
Josh Allen 1.934 11.604 1.054
Patrick Mahomes 1.926 11.556 1.867
Carson Wentz 1.75 10.5 1.5
Kyler Murray 1.5 9 1.954
Aaron Rodgers 1.3125 7.875 2.234

Table 3. Expected touchdowns, points, and entropy for the top 10 quarterbacks of the 2019-2020 season

Table 3 shows shows the top 10 quarterbacks rearranged by expected touchdown total. Here are some things that stand out:

  • Lamar Jackson has the most uncertainty in the amount of touchdowns he’ll score but he also has the highest expected touchdown total. This is because he has a probability of at least 12.5% of scoring 1, 2, 3, 4, or 5 touchdowns. A player like this is highly valued because he has a good possibility of scoring multiple touchdowns.
  • Josh Allen has the 6th highest expected touchdown total, but he has the lowest uncertainty since he scored 2 touchdowns on 73.3% of the games he played. A player like this is not attractive at first sight, but his consistency is highly dependable.
  • Although Dak Prescott was the 2nd ranked quarterback, he is 5th in expected touchdowns. A player like this is risky since he has an expected touchdown total that is lower than other quarterbacks that are ranked lower.

II. Running Backs

Player Name Games w/ 0 TD Games w/ 1 TD Games w/ 2 TD Games w/ 3 TD Games w/ 4+ TD Total Games
Christian McCaffrey 5 5 4 2 0 16
Aaron
Jones
6 4 4 1 1 16
Ezekiel
Elliot
6 6 4 0 0 16
Austin
Ekeler
8 6 1 1 0 16
Derrick
Henry
4 5 5 1 0 15
Dalvin
Cook
3 9 2 0 0 14
Leonard Fournette 13 1 1 0 0 15
Nick
Chubb
11 3 1 1 0 16
Alvin
Kamara
11 0 3 0 0 14
Saquon Barkley 7 4 2 0 0 13

Table 4. Touchdowns per game for the top 10 running backs of the 2019-2020 season

Player
Name
0 TD Probability 1 TD Probability 2 TD Probability 3 TD Probability 4+ TD Probability
Christian McCaffrey 0.3125 0.3125 0.25 0.125 0
Aaron
Jones
0.375 0.25 0.25 0.0625 0.0625
Ezekiel
Elliot
0.375 0.375 0.25 0 0
Austin
Ekeler
0.5 0.375 0.0625 0.0625 0
Derrick
Henry
0.267 0.333 0.333 0.067 0
Dalvin
Cook
0.214 0.643 0.143 0 0
Leonard Fournette 0.867 0.067 0.067 0 0
Nick
Chubb
0.6875 0.1875 0.0625 0.0625 0
Alvin
Kamara
0.786 0 0.214 0 0
Saquon Barkley 0.538 0.308 0.154 0 0

Table 5. Probability mass function for touchdowns per game for the top 10 running backs of the 2019-2020 season

Player Name Expected TDs Expected Points Entropy
Derrick Henry 1.2 7.2 1.827
Christian McCaffrey 1.1875 7.125 1.924
Aaron Jones 1.1875 7.125 2.031
Dalvin Cook 0.929 5.574 1.287
Ezekiel Elliot 0.875 5.25 1.561
Austin Ekeler 0.6875 4.125 1.531
Saquon Barkley 0.616 3.696 1.42
Nick Chubb 0.5 3 1.325
Alvin Kamara 0.428 2.568 0.749
Leonard Fournette 0.201 1.206 0.701

Table 6. Expected touchdowns, points, and entropy for the top 10 running backs of the 2019-2020 season

Table 6 shows shows the top 10 running backs rearranged by expected touchdown total. Here are some things that stand out:

  • Derrick Henry is the 5th ranked running back, but he has the highest expected touchdown total. This is a good player to chase when looking for upside!
  • Leonard Fournette’s expected touchdown total is much lower than the rest of the list. This makes Fournette a player that should be avoided due to his low probability of scoring touchdowns.
  • Dalvin Cook has the 8th highest entropy because he scored 1 or 2 touchdowns in 78.6% of his games. Although ranked 6th, this is a very valuable player due to his consistency in touchdown scoring.

III. Wide Receivers

Player Name Games w/ 0 TD Games w/ 1 TD Games w/ 2 TD Total Games
Michael Thomas 8 7 1 16
Chris Godwin 8 3 3 14
Julio Jones 11 2 2 15
Cooper Kupp 7 8 1 16
Deandre Hopkins 10 3 2 15
Keenan Allen 11 4 1 16
Julian Edelman 11 4 1 16
Allen Robinson 11 3 2 16
Kenny Golladay 7 7 2 16
Amari Cooper 8 6 1 15

Table 7. Touchdowns per game for the top 10 wide receivers of the 2019-2020 season

Player Name 0 TD Probability 1 TD Probability 2 TD Probability
Michael Thomas 0.5 0.4375 0.0625
Chris Godwin 0.571 0.214 0.214
Julio Jones 0.733 0.133 0.133
Cooper Kupp 0.4375 0.5 0.0625
Deandre Hopkins 0.667 0.2 0.133
Keenan Allen 0.6875 0.25 0.0625
Julian  Edelman 0.6875 0.25 0.0625
Allen Robinson 0.6875 0.1875 0.125
Kenny Golladay 0.4375 0.4375 0.125
Amari Cooper 0.533 0.4 0.067

Table 8. Probability mass function for touchdowns per game for the top 10 wide receivers of the 2019-2020 season

Player Name Expected TDs Expected Points Entropy
Kenny Golladay 0.6875 4.125 1.419
Chris Godwin 0.642 3.852 1.412
Cooper Kupp 0.625 3.75 1.272
Michael Thomas 0.5625 3.375 1.272
Amari Cooper 0.534 3.204 1.274
Deandre Hopkins 0.466 2.796 1.241
Allen Robinson 0.4375 2.625 1.2
Julio Jones 0.399 2.394 1.103
Keenan Allen 0.375 2.25 1.122
Julian Edelman 0.375 2.25 1.122

Table 9. Expected touchdowns, points, and entropy for the top 10 wide receivers of the 2019-2020 season

Table 9 shows shows the top 10 wide receivers rearranged by expected touchdown total. Here are some things that stand out:

  • Kenny Golladay is the 9th ranked wide receiver, but he has the highest expected touchdown total. A player like this is a valuable boom or bust. On 56.25% of his games, he scored 1 or 2 touchdowns.
  • Amari Cooper follows a similar trend. Cooper is ranked 10th but has the 5th highest expected touchdown total.
  • Although Julio Jones is ranked 3rd, he has the 8th highest expected touchdown total. A player like this is likely to be overvalued since he doesn’t score many touchdowns.

IV. Tight Ends

Player Name Games w/ 0 TDs Games w/ 1 TDs Games w/ 2 TDs Total Games
Travis Kelce 10 6 0 16
George Kittle 9 5 0 14
Darren Waller 14 1 1 16
Zach Ertz 10 4 1 15
Mark Andrews 7 6 2 15
Austin Hooper 8 4 1 13
Jared Cook 7 5 2 14
Tyler Higbee 11 3 0 14
Hunter Henry 8 3 1 12
Dallas Geodert 9 5 0 14

Table 10. Touchdowns per game for the top 10 tight end of the 2019-2020 season

Player Name 0 TD Probability 1 TD Probability 2 TD Probability
Travis Kelce 0.625 0.375 0
George Kittle 0.643 0.357 0
Darren Waller 0.875 0.0625 0.0625
Zach Ertz 0.667 0.267 0.067
Mark Andrews 0.467 0.4 0.133
Austin Hooper 0.615 0.308 0.077
Jared Cook 0.5 0.357 0.143
Tyler Higbee 0.786 0.214 0
Hunter Henry 0.667 0.25 0.0833
Dallas Geodert 0.643 0.357 0

Table 11. Probability mass function for touchdowns per game for the top 10 tight ends of the 2019-2020 season

Player Names Expected TDs Expected Points Entropy of TDs
Mark Andrews 1.267 7.602 1.429
Austin Hooper 1.231 7.386 1.239
Jared Cook 1.214 7.284 1.432
Zach Ertz 1.201 7.206 1.16
Hunter Henry 1.167 7.002 1.188
Darren Waller 1 6 0.669
Tyler Higbee 0.786 4.716 0.749
George Kittle 0.643 3.858 0.94
Dallas Geodert 0.643 3.858 0.94
Travis Kelce 0.625 3.75 0.954

Table 12. Expected touchdowns, points, and entropy for the top 10 tight ends of the 2019-2020 season

Table 12 shows shows the top 10 tight ends rearranged by expected touchdown total. Here are some things that stand out:

  • Travis Kelce is the 1st ranked tight end, but he has the lowest expected touchdown total. This may seem strange, but it is due to other scoring statistics like receiving yards and receptions. This is why it is important to take this analysis with a grain of salt!
  • Darren Waller, ranked 3rd, has the lowest entropy among all tight ends. This is because he doesn’t score a lot of touchdowns but has steady production similar to Travis Kelce.
  • Austin Hooper and Jared Cook are ranked much lower than their expected touchdown total rank. This is because the tight end position is usually a boom or bust in terms of touchdowns. There are many tight ends that are touchdown threats despite not being valuable in other categories like receiving yards or receptions.

Conclusion

This analysis is a useful way to learn which players are consistent in terms of scoring touchdowns. Chasing touchdowns is not the most important thing in fantasy football, but it is the fastest way to score a lot of points. Good fantasy football teams usually have a combination of players that can go off for a lot of touchdowns and players that have a steady floor from other scoring categories.

References

NFL Fantasy Scoring Leaders