Fantasy Football
Optimization
Kennon Young, Nick Ashton, Austin Cline
Informal Definition
• Current player performance projections lack accuracy and are
unreliable in properly predicting offensive player’s weekly
performance via their individual statistical performance which is
measured by number of touchdowns, yards gained after a catch,
rushing yards, etc. These measures are important in predicting a
weekly performance but fall short of incorporating other player
performance in what is known to be a team sport.
Formal Definition
- Minimize:
- Where
𝑛
𝑖=1(𝑝𝑖
− 𝑎𝑖 ) 2
- n = is the number of players we are considering
- 𝑖 = is the individual player considered during each iteration
- 𝑝𝑖 = is the sum of the StrengthOfSchedule and ComplimentPlayer Algorithm
Result, where StrengthOfSchedule is weighted 30% and ComplimentPlayer is
weighted 70%
- 𝑎𝑖 = the actual result, in yards, of how player I finished at the end of the 2014
season
Fantasy Omatic
• Only source that investigated this problem
• Utilized Strength of Schedule and Linear Regression in an attempt to
solve the problem
• Our idea was largely formulated around these two concepts of
Strength of Schedule and implementing Linear Regression analysis
Data Representation (Defense)
seattle13 = 16
carolina13 = 15
cincinnati13 = 14
newOrleans13 = 13
sanFrancisco13 = 12
arizona13 = 11
houston13 = 10
nyGiants13 = 9
cleveland13 = 8
buffalo13 = 7
nyJets13 = 6
baltimore13 = 5
pittsburgh13 = 4
tennessee13 = 3
losAngeles13 = 2
detroit13 = 1
tampaBay13 = 0
washington13 = -1
denver13 = -2
indianapolis13 = -3
miami13 = -4
oakland13 = -5
sanDiego13 = -6
kansasCity13 = -7
greenBay13 = -8
newEngland13 = -9
atlanta13 = -10
jacksonville13 = -11
philidelphia13 = -12
chicago13 = -13
minnesota13 = -14
dallas13 = -15
seattle14 = 16
detroit14= 15
denver14 = 14
buffalo14 = 13
sanFrancisco14 = 12
nyJets14 = 11
kansasCity14 = 10
baltimore14 = 9
sanDiego14 = 8
carolina14 = 7
indianapolis14 = 6
miami14 = 5
newEngland14 = 4
minnesota14 = 3
greenBay14 = 2
houston14 = 1
losAngeles14 = 0
pittsburgh14 = -1
dallas14 = -2
washington14 = -3
oakland14 = -4
cincinnati14 = -5
cleveland14 = -6
arizona14 = -7
tampaBay14 = -8
jacksonville14 = -9
tennessee14 = -10
philidelphia14 = -11
nyGiants14 = -12
chicago14 = -13
newOrleans14 = -14
atlanta14 = -15
Data Representation (Wide Receivers)
#Demaryius Thomas
demaryiusThomas_2013 = [161, 52, 94, 86, 57, 78, 82, 75, 108, 121, 41, 106, 88, 45, 123, 113]
demaryiusThomas_2013_Defense = [baltimore13, nyGiants13, oakland13, philidelphia13, dallas13, jacksonville13, indianapolis13, washington13, sanDiego13,
kansasCity13,newEngland13,kansasCity13, tennessee13, sanDiego13, houston13, oakland13]
demaryiusThomas_2013_passerRating = [141.1, 105.5, 135.8, 146.0, 129.6, 92.9, 96.1, 94.3, 135.2, 94.1, 70.4, 118.2, 107.8, 92.4, 113.2, 145.8]
demaryiusThomas_2014 = [48, 62, 31, 226, 124, 171, 105, 127, 108, 103, 87, 63, 11, 123, 115, 115]
demaryiusThomas_2014_Defense = [indianapolis14, kansasCity14, seattle14, arizona14, nyJets14, sanFrancisco14, sanDiego14, newOrleans14, oakland14,
losAngeles14, miami14, kansasCity14, buffalo14, sanDiego14, cincinnati14, oakland14]
demaryiusThomas_2014_passerRating = [111.9, 143.9, 85.7, 110.2, 117.9, 157.2, 124.2, 80.9, 111.9, 75.3, 135.4, 85.3, 56.9, 125.6, 61.8, 80.1]
#AJ Green
ajGreen_2013 = [162, 41 ,46, 51, 61, 103, 155, 115, 128, 151, 7, 83, 72, 93, 97, 61]
ajGreen_2013_Defense = [chicago13, pittsburgh13, greenBay13, cleveland13, newEngland13, buffalo13, detroit13, nyJets13, miami13, baltimore13,
cleveland13, sanDiego13, indianapolis13, pittsburgh13, minnesota13, baltimore13]
ajGreen_2013_passerRating = [97.2, 81.7, 105.5, 58.2, 81.1, 105.9, 135.9, 125.7, 55.4, 52.2, 62.7, 83.6, 120.5, 86.4, 136.2, 62.2]
ajGreen_2014 = [131, 0, 102, 81, 0, 0, 0, 44, 23, 127, 121, 57, 224, 49, 0, 82]
ajGreen_2014_Defense = [baltimore14, atlanta14, tennessee14, newOrleans14, carolina14, indianapolis14, baltimore14, jacksonville14, cleveland14, newOrleans14,
houston14, tampaBay14, pittsburgh14, cleveland14, denver14, pittsburgh14]
ajGreen_2014_passerRating = [98.7, 116.6, 68.9, 117.4, 93.5, 55.4, 89.3, 79.1, 2.0, 143.9, 84.6, 60.6, 128.8, 53.6, 93.1, 83.7, 83.5]
Strength Of Schedule
Goal: Manipulate players production based of the difficulty of the
defense they played.
- Rank Defense on a Scale
- Implement linear regression formula that will affect players
production for each game
- Order players based on those results
Strength of Schedule Results
• WR 13
• With Strength of Schedule Considered, Antonio Brown yards are: 1535.0 . Antonio Brown actual yards are: 1499
• With Strength of Schedule Considered, Pierre Garcon yards are: 1170.0 . Pierre Garcon actual yards are: 1346
• With Strength of Schedule Considered, Demaryius Thomas yards are: 1310.0 . Demaryius Thomas actual yards are: 1430
• With Strength of Schedule Considered, AJ Green yards are: 1408.0 . AJ Green actual yards are: 1426
• With Strength of Schedule Considered, Larry Fitzgerald yards are: 1070.0 . Larry Fitzgerald actual yards are: 954
• With Strength of Schedule Considered, Greg Olsen yards are: 900.0 . Greg Olsen actual yards are: 816
• With Strength of Schedule Considered, Eric Decker yards are: 1168.0 . Eric Decker actual yards are: 1288
• With Strength of Schedule Considered, Doug Baldwin yards are: 902.0 . Doug Baldwin actual yards are: 778
• With Strength of Schedule Considered, Emmanuel Sanders yards are: 776.0 . Emmanuel Sanders actual yards are: 740
• With Strength of Schedule Considered, Ashon Jefery yards are: 1391.0 . Ashon Jefery actual yards are: 1421
Compliment Player
Goal: Prove that a Wide Receiver’s Quarterback
affects game production
For each Wide Receiver:
• Determine quarterback reliance based on average yards per game
• Manipulate player’s yards per game by the QB’s Pass Rating, which is
based on certain thresholds, using linear regression
• See if player’s on field production increased or decreased in relation to
the quarter back they play with
Compliment Player Results
ESPN 2013:
Antonio Brown: 93 yards/game
Demaryius Thomas: 89.4 yards/game
AJ Green: 89.1 yards/game
Alshon Jeffery: 88.8 yards/game
…..
…..
Emmanuel Sanders: 46 yards/game
Our 2014 prediction:
Demaryius Thomas: 112 yards/game
Antonio Brown: 110 yards/game
AJ Green: 92 yards/game
Emmanuel Sanders: 75 yards/game
Alshon Jeffery: 73 yards/game
Weighted Optimization
• After running multiple weights on our results from each algorithm we
found:
- 𝑝𝑖 = (30%)(StrengthOfSchedule) + (70%) (ComplimentPlayer)
Confidence Interval
-
Find X Bar
Find Sample Standard Deviation
Find Square Root of sample Size
Calculate low Confidence
Interval
- Calculate High Confidence
interval
Compare: Our Prediction To Actual
Our Combined Weighted prediction:
Antonio Brown: 107 yards/game
Demaryius Thomas: 102.9 yards/game
AJ Green: 90.8 yards/game
Alshon Jeffery: 77 yards/game
Emmanuel Sanders: 67 yards/game
Actual ESPN 2014:
Antonio Brown: 106 yards/game
Demaryius Thomas: 101 yards/game
AJ Green: 94 yards/game
Emmanuel Sanders: 87 yards/ game
Alshon Jeffery: 70 yards/game
Pitfalls
• Quarterback rating does not have a big impact on a running back’s
production
• Unpredictable variables that occur in sports, such as weather, injuries,
and other unforeseen events can have an impact on the desired
results
• Injuries created large holes in our data sets and did not allow for us to
conduct large scale analysis using consistent data
Conclusions
• A player’s schedule difficulty plays a large role in the player’s ranking
among other players
• A good quarterback does not necessarily mean increased production
for players of all positions, only wide receivers will be affected
• With strength of schedule and compliment player equally weighted,
the results were not accurate.
• With a 95% confidence interval had no bearing on accuracy in our
experiment
Conclusion Continued
- Time Complexity
-
Strength Of Schedule: O(n2)
Compliment Player: O(n)
Weighted Optimization: O(n2)
Confidence Interval: O(n2)
Questions
• What were the two methods/ideas used by fantasy-o-matic?
• Strength of schedule and linear regression
• Does a quarterback’s rating have a huge impact on a running back’s
production?
• No, a running back’s stats have little to do with the quarterback’s efficiency
• What was the main pitfall we encountered that limited us from using
large sets of data?
• Player injuries and missed games limited the amount of data we could use