february 19, 2010 how to catch a tiger: understanding putting performance on the pga tour jason...
TRANSCRIPT
February 19, 2010
How to Catch a Tiger:
Understanding Putting Performance on the PGA TOUR
Jason AcimovicMIT Operations Research Center, [email protected]
Douglas FearingMIT Operations Research Center, [email protected]
Professor Stephen GravesMIT Sloan School of Management, [email protected]
February 19, 2010
Agenda
2
• Introduction– Project Question
– Applications
– Approach and contribution
• Golf and data overview
• Putting model
• Off-green model
• Situational analysis
February 19, 2010
Project Question
• How well do people perform on tasks?– Tasks differ from each other
– Not everyone performs every task
– Even the same task can be different from person to person
3
February 19, 2010
Applications
• Evaluating employees in a distribution center– Pickers in a warehouse vary in skill (picks per hour)
– Pick zones vary in difficulty (books vs. electronics)
– Difficulty also varies by hour of day and day of week
– Pickers shift around, but not enough to ensure perfect mixing
– How do you compensate the best employees and identify underperformers?
• Golf putting– Different golfers play different tournaments
– Greens vary in their difficulty
– Different golfers start on the green from different distances
– How do we identify the best putters?
4
February 19, 2010
Project approach and contribution
• Develop statistical models to predict strokes-to-go
• Correct for player skill and course difficulty
• Evaluate incremental value of each shot taken relative to the expectation for the field– Compare predicted strokes-to-go before and after shot
• Aggregate shot value across players, shot types, etc. to better understand player performance
• Compare our model to current metrics, namely, Putting Average
• Paper: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1538300 (or email us)
5
February 19, 2010
Agenda
6
• Introduction
• Golf and data overview– Strokes-to-go example
– ShotLink data
• Putting model
• Off-green model
• Situational analysis
February 19, 2010
Quick golf primer
• The goal is to get from the tee to the pin in the fewest number of strokes
• 18 holes in a round of golf
• Typically 4 rounds in a tournament
• Lowest total score wins
7
TeeTee
GreenGreen
FairwayFairway
February 19, 2010
Strokes-to-go example
Shot Location Strokes-To-Go
1 4.4
3 1.8
2 3.0
Shot Gain
0.4
0.8
0.2
8
4.4 – 3.0 – 1 = 0.4
February 19, 2010
ShotLink Data
9
• Every tournament, 250 volunteers gather data on every shot– Lasers pinpoint the ball location to within an inch
– Field volunteers gather qualitative characteristics
• Data is used for both real time reporting as well as detailed analyses
• 5 Million shot data points
• 2 Million putt data points
February 19, 2010
Visual explanation of ShotLinkTM dataset
CourseYearRound NumberHole NumberTee LocationBall LocationPin LocationPlayerShot NumberLocation TypeBall LieHole ParStimp ReadingGreen Length
X Coordinate
Y Coordinate
Z Coordinate
16th Hole on Colonial
10
X Coordinate
Y Coordinate
Z Coordinate
February 19, 2010
Data for the 14th hole at Quail Hollow – 1 day
11
February 19, 2010
Agenda
12
• Introduction• Golf and data overview• Putting model
– Empirical data
– Two stage model• Holing out submodel
• Distance-to-go submodel
– Markov chain
– Correct for hole difficulty and player skill
– Putts-gained per round and results
• Off-green model• Situational analysis
February 19, 2010
Empirical mean and std. dev. of putts-to-go
Mean Std. Dev.
13
February 19, 2010
Two-stage model to predict putts-to-go
• First stage sub-model– From anywhere on the green, the first model predicts the
probability of sinking the putt
14
Probability of 0.1 of making it in on this putt
February 19, 2010
• Second stage sub-model– If the golfer misses the putt, the second model calculates
the distribution of the distance-to-go for the green
If I miss, I have a 0.0021 probability of being in this blue area. (calculate this for entire green)
Second stage finds conditional distance-to-go
15
February 19, 2010
• We can calculate the putts-to-go distribution from anywhere on the green
Combine and …
16
Consider only distance in our
model
Consider only distance in our
model
February 19, 2010
Empirical probabilities of holing out
17
Empirical probability of holing out vs. distance
February 19, 2010
Normal regression is inappropriate
• With Ordinary Least Squares regression, “one” might predict the probability of making a putt based on starting distance….
• But…– We want to predict a probability with a range between 0 and 1
– Errors are not normal
18
0 1Y d
February 19, 2010
One-putt logistic regression model
• Y – putts-to-go
• d – initial distance to the pin
• Fitted model parameters:
• Probability:
19
41 5
1
0 4
[ 1| ]
1 e logxp ( )+
P Y d
d dd
L
0 5, ,
February 19, 2010
Model holing out as a logistic regression
20
Model probability of holing out vs. distance
February 19, 2010
2nd-stage problem, determining distance-to-go
• What happens if we miss the first putt?
21
z
February 19, 2010
Empirical mean and std. dev. of distance-to-go
Mean Std. Dev.
22
February 19, 2010
Empirical distributions of distance-to-go
From 10 ft. From 30 ft.
23
February 19, 2010
Distance-to-go gamma regression model
• d – initial distance to the pin
• z – distance-to-go (assuming a miss)
• Fitted model parameters:
• Mean:
• Density:
24
0 3,Shape ( ) ,,k 2
2 30 1exp{ log }d d d d
( | ) ( ; , )df z d gamma z k
1 dzk
k
d
ekzk
/
( )
February 19, 2010
Distance-to-go model: mean and std. dev.
Mean Std. Dev.
25April 21, 2023
February 19, 2010
Distance-to-go model distributions
From 10 ft. From 30 ft.
26
February 19, 2010
Putts-to-go as Markov chain
27
distanceH
p = 1
p = [ 1 + exp(…) ]-1 g (z|d) = (1 - [ 1 + exp(…) ]-1) x f(z|d)
z
Whereg(z|d): probability density of ending up at z conditioned on starting at d
f(z|d) probability density of ending up at z conditioned on missing and starting at d(from the distance-to-go gamma regression model)
d
Probability of holing out in n putts is probability of reaching absorbing state in n transitions
Probability of holing out in n putts is probability of reaching absorbing state in n transitions
February 19, 2010
Making it within n putts (model prediction)
• Over 90% of golfers 2-putt or better within 35 ft.
• Only a 1.6% chance of 4-putting or worse at 100 ft.
28
Two-Stage Model Within N Putts
February 19, 2010
Two-stage model mean and std. dev.
Mean Std. Dev.
29
February 19, 2010
Comparing putt quality
• Greens vary in difficulty– Fast vs. slow greens
– Type and length of grass
• Good putts on a hard green should be valued more than the same on an easy green
• Adjust parameters for each hole to the logistic and gamma regression models
30
February 19, 2010
Revised logistic and gamma regressions
• Every player p and hole h have their own dummy variables and specific holing-out probabilities*
– Ip is the indicatory variable, and is equal to 1 if observation i contains player p and is zero otherwise.
– Instead of a regression with 6 parameters, we now have thousands of parameters• E.g., there is a β0h parameter for every hole
31
1
0
54
0 1 4
1 0
.{ log
( 1)
..
1 exp}p h
p
ip p h
h
d
I d I
d d
P Y
*The actual analysis accounts for the number of observations per player and per hole, so that the model is more complex for players about whom we know more.
The gamma regression is adjusted similarly
The gamma regression is adjusted similarly
February 19, 2010
Visualizing player skill level differences
32
• Comparison of above average (Brent Geiberger), below average (John Huston), and field average putter for an average green
February 19, 2010
Visualizing green difficulty differences
• Comparison of an easy green (Bay Hill #9), difficult green (Sawgrass #1), and average green based on a field average golfer
33
February 19, 2010
Calculating putts gained per round
• Calculate the gain associated with each putt– Relative to the putts-to-go for each specific hole
– Example: Golfer starts at 12 ft. and takes 2 putts to sink ball• Expected putts-to-go: 1.71
• Actual number of putts: 2
• Relative gain: (- 0.29)
• Sum the relative gains for each player
• Divide by the number of rounds played
34
12 feet1.71 putts to go
February 19, 2010
Top 10 putts gained per round
35
Rank GolferPutts Gained /
RoundNumber of
RoundsPutts Gained / Round Stdev
1 Tiger Woods 0.69 230 0.12
2 David Frost 0.67 113 0.16
3 Fredrik Jacobson 0.56 248 0.11
4 Nathan Green 0.55 197 0.12
5 Aaron Baddeley 0.53 303 0.10
6 Jesper Parnevik 0.50 315 0.10
7 Stewart Cink 0.49 375 0.09
8 Darren Clarke 0.45 107 0.17
9 Ben Crane 0.44 273 0.11
10 Willie Wood 0.42 72 0.20
February 19, 2010
Putting average is the most popular metric today
• Putting Average– Average number of putts per green*
• When a golfer reaches a green– Count the putts it takes to get it in the hole
– Average this among all his green appearances
– Regardless of how close he starts on the green
36
*Actually, a green in regulation, which means the green was reached in no more than (par – 2) strokes
February 19, 2010
Comparing with putting average
37
GolferPutts Gained /
RoundPG/RRank Putting Average
PARank
Tiger Woods 0.69 1 1.71 1
David Frost 0.67 2 1.77 60
Fredrik Jacobson 0.56 3 1.74 4
Nathan Green 0.55 4 1.74 5
Aaron Baddeley 0.53 5 1.74 3
Jesper Parnevik 0.50 6 1.76 47
Stewart Cink 0.49 7 1.75 12
Darren Clarke 0.45 8 1.75 19
Ben Crane 0.44 9 1.75 17
Willie Wood 0.42 10 1.77 92
February 19, 2010
Understanding the discrepancies
• Insert first-putt distance histograms for most severe outlier.
38
PG/R Percentile Golfer
Putts Gained / Round Putting Average
PA Percentile
9th Stephen Leaney 0.26 1.79 59th
88th Ernie Els -0.63 1.75 5th
•54% for All Players•51% for Stephen Leaney•60% for Ernie Els
Percentage of 1st putts 20 ft. or closer
On average he starts closer to the hole, so his putting average is
inflated by his excellent approach
shots
On average he starts closer to the hole, so his putting average is
inflated by his excellent approach
shots
February 19, 2010
Agenda
39
• Introduction
• Golf and data overview
• Putting model
• Off-green model
• Situational analysis
February 19, 2010
Evaluating off-green performance
• For each hole, calculate “field par”– Empirical average number of strokes corrected for player
skill and hole difficulty
• Calculate total strokes gained per round for each player
• Calculate off-green strokes gained per round
40
(Off-green strokes gained = Total strokes gained – putts gained)
February 19, 2010
Top 10 golfers (on and off green performance)
41
Rank GolferPutts Gained /
RoundOff-Green Gain /
Round Total
1 Tiger Woods 0.69 2.53 3.22
2 Vijay Singh -0.36 2.65 2.29
3 Jim Furyk 0.00 2.03 2.03
4 Phil Mickelson 0.19 1.74 1.94
5 Ernie Els -0.63 2.48 1.85
6 Adam Scott 0.08 1.69 1.77
7 Sergio Garcia -0.67 2.20 1.52
8 David Toms 0.16 1.27 1.43
9 Retief Goosen -0.44 1.84 1.40
10 Stewart Cink 0.49 0.89 1.39
February 19, 2010
Agenda
42
• Introduction
• Golf and data overview
• Putting model
• Off-green model
• Situational analysis– Player specific putts
– Fourth round pressure
– Tiger woods’ fourth round performance
February 19, 2010
Situational putting performance
• Above, we used the general putting model to evaluate putting relative to the field of professionals
• We also have the capability to evaluate a golfer’s putting relative to his own expected performance
• For instance, even if Tiger Woods usually putts better than the field, we can also determine when he putts worse than himself– Does he putt better or worse after the cut?
– Does he putt better or worse for birdie vs. for par?
43
February 19, 2010
Player-specific putts gained – example
• On the 10th green at Quail Hollow, 9 feet from the pin:– Tiger Woods’ personal expected putts-to-go is 1.54
– Vijay Singh’s personal expected putt-to-go is 1.59
– If they each sink it, Tiger gains only 0.54 strokes whereas Vijay gains 0.59 strokes
44
Tiger: E[putts] = 1.54Tiger: E[putts] = 1.54Vijay: E[putts] = 1.59Vijay: E[putts] = 1.59
9ft9ft
February 19, 2010
Advantages of player-specific putts gained
• Easy to test various hypotheses– After calculating the shot value for every putt, we need
only to filter and aggregate the results
• Describes the magnitude in terms of score impact
• Suggests areas for further investigation– Standard deviation of putts gained provides the relative
significance of the effect
45
February 19, 2010
Fourth round pressure
46
• Putting does not seem to be affected by the pressures of being in the fourth round
Putt CountPutts Gained Per
PuttPutts Gained Per
Putt Deviation
3rd Round 359,079 0.00237 0.00027
4th Round 353,979 0.00246 0.00027
Difference 0.00009 0.00038
February 19, 2010
Tiger Woods’ fourth round performance
• A common perception is that Tiger has the ability to kick it up a notch during the final round
• Looking at his putts-gained suggests otherwise
47
Putt CountPutts Gained Per
PuttPutts Gained Per
Putt Deviation
1st Round 1,614 0.00036 0.00386
2nd Round 1,589 0.00847 0.00395
3rd Round 1,654 -0.00293 0.00375
4th Round 1,671 -0.00022 0.00380
February 19, 2010
Conclusion
• Developed a model for putting– Corrected for player skill and hole difficulty
– Intuitive model that describes how putts occur
• Demonstrated the differences between our metric and current putting statistics
• Developed a “field par” which corrects for hole difficulty and quality of field
• Compared on- and off-green performance
• Examined situational putting performance
48