Statistics Lecture 25. Advanced Statistical Research in Baseball. Administrative Notes. Measuring Fielding in Baseball: Present and Future

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1 Administrative Notes Statistics Lecture 25 Advanced Statistical Research in Baseball Homework 7 due in recitation on Friday, April 24 Recitation on Friday, April 24 th is mandatory Recitation on Friday, May 1 st is optional and will just be final exam review Q and A My office hours on Tu April 28 th are only 3-4pm No office hours on Tu May 5 th but instead I will hold office hours 3-5pm on Monday May 4th April 23, 215 Stat Lecture 25 - Baseball! 1 April 23, 215 Stat Lecture 25 - Baseball! 2 Administrative Notes Final Exam is Tuesday, May 5th (3-5pm) Covers Chapters 1-8 and 1 in textbook Bring ID cards to final! Allowed: Calculators, double-sided 8.5 x 11 cheat sheet List of additional textbook study problems will be posted Rooms are same as the midterm: Stat 111 Lecture Last Name Midterm Exam Room 11am 12pm Everyone MEYERSON HALL B1 2 3pm A-F MEYERSON HALL B1 2 3pm G-Z COHEN HALL G17 Measuring Fielding in Baseball: Present and Future Shane T. Jensen Department of Statistics, The Wharton School, University of Pennsylvania April 23, 215 April 23, 215 Stat Lecture 25 - Baseball! 3 Quantifying Fielding Performance in Baseball Overall goal: accurateevaluationofthefielding performance of each major league baseball player Historical Method: Errors Errors only punishes for bad plays, no corresponding reward for good plays No accounting for relative difficulty of each play Historical Method: Fielding Percentage Percentage of time a player properly handles the ball Ambiguity in the denominator: players with poor range could have high FP due to less opportunities Available Data Ball-in-play data available from Baseball Info Solutions Each season has balls-in-play (BIP) IhaveworkedwithBIPdatafrom2-8(sevenseasons) Three BIP types: 42%grounders,33%flys,25%liners BIP velocity information as ordinal category Flyballs Caught by CF Flyballs Not Caught by CF Need to take into account the relative difficulty of individual balls-in-play (BIP)

2 Current Methods: Ultimate Zone Rating Ultimate Zone Rating: dividesfieldupintozones and tabulates success/failures of each fielder within zones Current Methods: Ultimate Zone Rating cont d Difference between fielders success rate and average success rate calculated for each zone Differences weighted by run value and then aggregated zone for overall rating Advantage: UZRzonesareproxyfordifficultyofBIP Advantage: runssaved/costisaneasytointerpretscale Disadvantage: zonesareanadhocdiscretizationofthe continuous fielding surface Other Current Methods Plus-Minus system (John Dewan): uses zones like UZR Average success rate s k calculated within each zone k Fielder gets credit of 1 s k for each successful play, debit of s k for each unsuccessful play in zone Aggregating over zones gives plus-minus value Version with run values: defensive runs saved (DRS) Probabilistic Model of Range (David Pinto): uses angles to represent BIP direction (instead of zones) Predicted outs for each direction calculated over all players Actual outs for each direction calculated for individual players and compared to predicted Different PMR charts for grounders vs. liners vs. flys Big Zone Metric (Peter Jensen): Uses publicly available MLB Gameday data instead of BIS Data is less resolute, so larger zones are used Continuous Fielding Curves Zone-based methods break up the field into discrete bins for computational convenience High-resolution data could also be used to fit smooth fielding curves to the continuous playing surface Even more sophisticated approach embeds smooth fielding curves within a Bayesian hierarchical model Allows for principled sharing of information within and between individual players Count Data The outcome of each play is either a success or failure: { 1 if the j th BIP hit to the i th player leads to out S ij = if the j th BIP hit to the i th player leads to hit Observed successes and failures are modeled as Binary outcomes from an underlying probability p ij Each p ij is a function of available data for that BIP: (x, y) ij location, velocity V ij and type of the BIP These probability functions will be smooth parametric curves that can vary between different players Representation for Different BIP Types Two-dimensional curves needed for flys/liners: success depends on velocity, direction and distance to BIP One-dimensional curves needed for grounders: success depends on velocity, direction and angle to BIP Backward Flyballs and Liners Forward CF Location at (,324) Distance BIP Location 15 5 SS Location Grounders Grounder Trajectory Left Right θ Angle 5 5

3 Logistic regression for each smooth curve Logistic regression used to model smooth curves for probability p ij of successfully fielding BIP j by player i Logistic regression for fly-balls/liners: ( ) pij log 1 p ij = β i + β i1 D ij + β i2 D ij F ij + β i3 D ij V ij D ij =distancetobip,v ij =vel,f ij = 1ifforward(vs.back) Logistic regression for grounders: ( ) pij log 1 p ij = β i + β i1 θ ij + β i2 θ ij L ij + β i3 θ ij V ij θ ij =angletobip,v ij =velocity,l ij = 1ifleft(vs.right) Individual Grounder Curves Compare curves of individual fielders β i of to aggegrate model β + for all fielders at that position P(Success) P(Success) for Everett, Jeter vs. average SS Average Jeter Everett Individual Fly/Liner Curves Compare curves of individual fielders β i of to aggegrate model β + for all fielders at that position Numerical Summary of Overall Performance Beyond comparing curves between players, we can derive an overall numerical estimate of fielder performance SAFE: Spatial Aggregate Fielding Evaluation For each player, aggregate differences between individual curve (based on β i )andoverallcurve(basedonµ) Aggregation done by numerical integration over fine grid of values (1D grid for grounders, 2D grid for flys/liners) Estimates and standard errors of β i gives us the mean and 95% confidence interval of SAFE for each player Differential Weighting in SAFE Our full aggregation also weights grid points by BIP frequency, run value, andshared consequence P(Success) Runs (a) P(Success) for Jeter vs. Average Average Jeter (c) Run Consequence for Grounders Density Responsibility Fraction (b) Density Estimate of Grounder Angle (d) Shared Responsibility of SS SAFE value: runs saved/cost of fielder vs. average Results for Corner Infielders: Best/Worst Posterior SAFE values Ten Best 1B Player-Years Ten Best 3B Player-Years Doug Mientkiewicz, ( 2.8, 11.3 ) Marco Scutaro, ( 1., 16.6 ) Andy Phillips, ( 2.6, 11.4 ) Mark Bellhorn, ( 4., 17.1 ) Rich Aurilia, ( 2.7, 1.2 ) Hank Blalock, 2 1. ( 4.2, 16.5 ) Albert Pujols, ( 3.1, 8.2 ) Sean Burroughs, ( 3.4, 14.2 ) Doug Mientkiewicz, ( 1.8, 9.1 ) David Bell, ( 1.7, 13.3 ) Albert Pujols, ( 1.9, 8.1 ) Scott Rolen, ( 1.9, 12.1 ) Kendry Morales, 6 5. ( -.5, 1.3 ) Hank Blalock, ( 1.4, 11.3 ) Ken Harvey, 3 5. ( 1.5, 8. ) Damian Rolls, (.1, 13.6 ) Howie Kendrick, ( -.8, 9.6 ) Pedro Feliz, (.5, 13.3 ) Albert Pujols, ( 1., 6.8 ) Joe Crede, 2 7. (., 15.8 ) Ten Worst 1B Player-Years Ten Worst 3B Player-Years Richie Sexson, ( -8.2, -1.9 ) Eric Munson, ( -12.4, -2.8 ) Robert Fick, 2-5. ( -11.3, 2. ) Michael Cuddyer, ( -11.4, -2.9 ) Mo Vaughn, ( -9.7, -.3 ) Michael Cuddyer, ( -14.1, -2.3 ) Dmitri Young, ( -9.9,.1 ) Garrett Atkins, ( -12.4, -2.4 ) Tony Clark, ( -11.7, -1.6 ) Fernando Tatis, ( -14.2, -2. ) Fred McGriff, ( -9.4, -2.8 ) Chone Figgins, ( -18.7, -1.4 ) Mike Jacobs, ( -9.4, -2.9 ) Travis Fryman, ( -15.2, -4.4 ) Ben Broussard, ( -1.4, -2.2 ) Joe Randa, ( -17.3, -2.8 ) Nomar Garciaparra, ( -11.1, -3.5 ) Ryan Braun, ( -17.4, -2.9 ) Jason Giambi, ( -13.4, -3.2 ) Jose Bautista, ( -17.4, -5.9 )

4 Results for Middle Infielders: Best/Worst Posterior SAFE values Results for Outfielders: Best/Worst Posterior SAFE values Ten Best 2B Player-Years Ten Best SS Player-Years Julius Matos, ( 12.4, 22.1 ) Pokey Reese, ( 12., 31.2 ) Erick Aybar, ( 1., 24.6 ) Adam Everett, ( 1.4, 27.4 ) Junior Spivey, ( 4.7, 27.1 ) Adam Everett, ( 9., 21.8 ) Tony Graffanino, ( 4.6, 27.6 ) Craig Counsell, ( 6.9, 21.1 ) Adam Kennedy, ( 1.7, 18.6 ) Jorge Velandia, ( 3., 24. ) Willie Bloomquist, ( 4.3, 17.8 ) Alex Cora, ( 3., 24.6 ) Jose Valentin, ( 4.2, 17.9 ) Alex Rodriguez, ( 3.5, 24.4 ) Chase Utley, ( 5.7, 17.5 ) Maicer Izturis, ( 3.8, 22.2 ) Chase Utley, ( 3.1, 17.7 ) Marco Scutaro, ( 4., 2.1 ) CraigCounsell, ( 5.3, 18. ) Brent Lillibridge, ( 5., 19.1 ) Ten Worst 2B Player-Years Ten Worst SS Player-Years Ronnie Belliard, ( -19.5, 2.6 ) Erick Almonte, ( -26.9, 2.3 ) Geoff Blum, ( -17.5, -1.7 ) Derek Jeter, ( -21.7, -5.8 ) Miguel Cairo, ( -17.9, -3.1 ) Michael Morse, ( -23., -4.5 ) Terry Shumpert, ( -22.2,.7 ) Damian Jackson, ( -3.6, -3.5 ) RobertoAlomar, ( -19.3, -4.6 ) Brandon Fahey, ( -22.4, -8.2 ) Enrique Wilson, ( -18.9, -6.2 ) Marco Scutaro, ( -22., -1. ) Alberto Callaspo, ( -2.4, -4.5 ) Derek Jeter, ( -24.8, -6.4 ) DaveBerg, ( -25.1, -2.4 ) Michael Young, ( -23.6, -7.2 ) Luis Rivas, ( -2.9, -6.4 ) Josh Wilson, ( -26.5, -6.4 ) Bret Boone, ( -22.4, -8.1 ) Derek Jeter, ( -29.1, -9.2 ) Ten Best Left Fielders Ten Best Center Fielders Ten Best Right Fielders Name and Year Mean 95% Interva EBrown, (2.2,27.9) JMichaels, (3.3,32.5) GMatthewsJr., ( 5.7, 22.3 ) DDellucci, (5.7,2.4) CFiggins, (3.8,31.2) DMohr, (2.3,28.) RJohnson, (2.3,21.) JHairstonJr., (.3,28.6) TNixon, ( 3.3, 18.1 ) CCrisp, (4.1,17.8) AJones, (2.2,2.7) GMatthewsJr.,5 1.5 ( 2.6, 19. ) SHairston, (1.1,23.5) DGlanville, (-3.1,3.5) RLangerhans,5 1.5 (4.6,19.3) SPodsednik, (6.1,17.8) JPayton,5 1.2 (.,17.8) TNixon,4 9.4 (.7, 19.4 ) MByrd,5 1.7 (.5,22.7) JEdmonds,5 1.1 (-.5,2.5) AEscobar,3 8.7 (-.1,19.3) GVaughn,2 1.7 (1.9,16.9) JGathright,5 1.1 (-6.6,25.) AOchoa,2 8.7 (-2.3,2.9) OPalmeiro,2 1.6 (.8,22.2) DErstad,3 1. (-1.2,2.7) EMarrero,2 8.7 (-.9,2.7) TLong,4 1.3 (-.8,21.7) CPatterson,4 9.8 (1.9,17.9) JDrew,3 8.4 (-1.4,2.8) Ten Worst Left Fielders Ten Worst Center Fielders Ten Worst Right Fielders Name and Year Mean 95% Interva KMench,2-1.7 ( -19.4, -2.3 ) CHermansen,2-9.5 (-23.6,4.3) GKapler,5-8.1 (-13.2,-1.6) KMench, ( -14.9, -7.3 ) DRoberts,5-9.8 (-21.,2.2) LWalker,5-8.2 (-17.2,1.2) APiatt, (-16.8,-6.9) RLedee,2-1. (-19.6,.5) JGuillen,5-8.6 (-17.,.7) LBerkman,5-13. ( -16.7, -8.2 ) KGriffeyJr., (-24.4,-1.3) KMench,2-8.6 (-17.7,.7) MRamirez, ( -19.1, -5.4 ) BWilliams, ( -24.5, -3.1 ) EKingsale,4-9.2 (-13.1,-2.9) RSierra, (-16.2,-1.3) SGreen, (-28.3,2.8) WPena,2-9.7 (-17.6,.2) BKielty, (-16.7,-9.1) LTerrero, (-29.4,5.8) CWilson, (-22.1,-2.6 TWomack, (-25.,-5.) BWilliams, ( -23.4, -5.3 ) JGonzalez, (-16.4,-1.4 LBerkman, ( -18.9, -17. ) MGrissom,5-2.3 (-34.2,-9.4) MTucker, (-21.8,-8.1 MRamirez, ( -24.8, ) JCruz, (-36.2,-5.4) Sheffield, ( -21.6, -9.5 Comparing SAFE to Current Methods Summary of Our Approach Decent overall correlation between SAFE and other methods, though magnitudes much less for SAFE BIP data allows more detailed examination of differences between players Parametric approach: smooth probability function reduces variance of results by sharing information between all points near to a fielder SAFE run value aggregates individual differences while weighting for BIP frequency, run value, and shared consequence between positions Publicity and Feedback Player Starting Positions Boston Globe (Gideon Gil, 2/16/8): Numbers tell a glove story Wired (Greta Lorge, 2/16/8): Statistics in the Outfield AP (Randolph E. Schmid, 2/16/8): Baseball s top fielders ranked in new statistical system New York Post had different take on study: You ve Got To Be Kidding! Jeter himself responded in NY Post: Must have been a computer glitch Glossed over reality: we don t actually know where fielders are located when a particular BIP is hit! Each distance/angle is an estimated value, notaknown value since starting location is not truly known Starting location for each position fixed at point with highest overall success probability Problematic when fielders are systematically different in their positioning e.g. 1B when there is a man on base Ideally, would build information about defensive shifts as well

5 Differences between Ballparks Current analysis does not take into account differences in the playing field for different parks Could impact both evaluation of infielders (turf vs. grass) and outfielders (different outfield shapes) Field F/X New system tracks players and BIPs with video cameras Park-specific BIP densities could account for differences in shape but may have higher variance (less data) This data will revolutionize the estimation of fielding ability Field F/X cont d True Defensive Range (TDR) How will Field F/X improve fielding estimation? Real starting positions and speed for each player Real hang time on flys/liners instead of current proxies based on distance/velocity Real trajectories on all BIPs: was that liner to the shortstop 1 feet (catchable) or 2 feet (uncatchable) off the ground? Issue is availability of data. Current access limited to only afewpeople(i mnotcurrentlyoneofthem). Greg Rybarczyk (Hittracker.com) co-authored article in the 211 Hardball Times on "An Introduction to FIELDf/x" True Defensive Range (TDR) uses Fieldf/x location and hang time to evaluate each defensive play Fielders credited/debited for plays based on league-average likelihood of those plays Expect many fantastic advances over the next few years!