Umpire Research
This page is meant to be a comprehensive resource for academic social science and/or operations research using MLB umpire data, often referred to as PITCHf/x or Statcast.
There is also a large collection of excellent work outside of the academic space on umpires, and I encourage anyone interested in this topic to search websites like The Hardball Times, Fangraphs, and Baseball Prospectus (among others) for additional sources. I have attempted to lay out a comprehensive body of work from these websites on this page as well and will continue to do so as I move forward (please note that I have not updated the non-academic works list since 2018, but am in the process of doing so and welcome suggestions for any missed references below).
Economics & Social Science Research
Thornton-Lugo, M.A., McCarter, M.W., Clark, J.R., Luse, W., Hyde, S.J., Heydarifard, Z., & Huang, L.S.R. (2022). Makeup calls in organizations: An application of justice to the study of bad calls. Journal of Applied Psychology. [Article Link]
Snowden, H. (2021). Would "robot umpires" reduce discrimination? Measuring racial bias in Major League Baseball umpires. Claremont Colleges Senior Theses. [Article Link]
Archsmith, J.E., Heyes, A., Neidell, M.J., & Bhaven, N. (2021). The dynamics of inattention in the (baseball) field. NBER Working Paper. [Article Link]
Fesselmeyer, E. (2019). The impact of temperature on labor quality: Umpire accuracy in Major League Baseball. SSRN Working Paper. [Article Link]
Zimmerman, D.L., Tang, J., & Huang, R. (2019). Outline analysis of the called strike zone in Major League Baseball. Annals of Applied Statistics, 13, 2416-2451. [Article Link]
Archsmith, J., Heyes, A., & Saberian, S. (2018). Air quality and error quantity: Pollution and performance in a high-skilled, quality-focused occupation. Journal of the Association of Environmental and Resource Economists, 5, 827-863. [Article Link]
Lopez, M. & Mills, B.M. (2018). Opportunistic shirking behavior during unpaid overtime. Applied Economics Letters. [Article Link]
Bradbury, J.C. (2018). Monitoring and employee shirking: Evidence from MLB umpires. Journal of Sports Economics. [Article Link]
Hunter, D.J. (2018). New metrics for evaluating home plate umpire consistency and accuracy. Journal of Quantitative Analysis in Sports. [Article Link]
Deshpande, S.K. & Wyner, A. (2018). A hierarchical Bayesian model of pitch framing. Journal of Quantitative Analysis in Sports, 13, 95-112. [Article Link]
Mills, B.M. & Salaga, S. (2018). A natural experiment for efficient markets: Information quality and influential agents. Journal of Financial Markets, 40, 23-39. [Article Link]
Mills, B.M. (2017). Policy changes in Major League Baseball: Improved agent behavior and ancillary productivity outcomes. Economic Inquiry, 55, 1104.1118. [Article Link]
Mills, B.M. (2017). Technological innovations in monitoring and evaluation: Evidence of performance impacts among Major League Baseball umpires. Labour Economics, 46, 189-199. [Article Link]
Green, E. & Daniels, D.P. (2017). Bayesian Instinct. SSRN Working Paper Abstract ID #2916929. [Article Link]
Chen, D.L., Moskowitz, T.J., & Shue, K. (2017). Decision making under the gambler's fallacy: Evidence from asylum judges, loan officers, and baseball umpires. The Quarterly Journal of Economics, 131, 1181-1242. [Article Link]
Hamrick, J. & Rasp, J. (2015). The connection between race and called strikes and balls. Journal of Sports Economics, 16, 714-734. [Article Link]
Tainsky, S., Mills, B.M., & Winfree, J. (2015). An examination of potential discrimination among MLB umpires. Journal of Sports Economics, 16, 353-374. [Article Link]
Kim, J.W. & King, B.G. (2014). Seeing stars: Matthew effects and status bias in Major League Baseball umpiring. Management Science, 60, 2619-2644. [Article Link]
Mills, B.M. (2014). Social pressure at the plate: Inequality aversion, status, and mere exposure. Managerial and Decision Economics, 35, 387-403. [Article Link]
Parsons, C.A., Sulaeman, J., Yates, M.C., & Hamermesh, D.S. (2011). Strike three: Discrimination, incentives, and evaluation. American Economic Review, 101, 1410-1435. [Article Link]
Smith, E.E. & Groetzinger, J.D. (2010). Do fans matter? The effect of attendance on the outcomes of Major League Baseball games. Journal of Quantitative Analysis in Sports, 6(1).
MacMahon, C. & Starkes, J.L. (2008). Contextual influences on baseball ball-strike decisions in umpires, players, and controls. Journal of Sports Sciences, 26, 751-760.
Rader, B.G. & Winkle, K.J. (2008). Baseball's great hitting barrage of the 1990s (and beyond) reexamined. NINE: A Journal of Baseball History and Culture, 17, 70-96. [Article Link]
Insley, H.R. (2001). Major league umpired association: Is collective bargaining the answer to or the problem in the contractual relationships of professional sports today. Capital University Law Review, 29, 601-624. [Article Link]
---------------------------------------------------------
Books and Book Chapters
Mills, B.M. (2017). Umpire analytics. In The SABR Book of Umpires and Umpiring. L. Gerlach & B. Nowlin (Eds.). Phoenix, AZ: SABR.
Sievert, C. & Mills, B.M. (2017). Using publicly available baseball data to measure and evaluate pitching performance. In the Handbook of Statistical Methods for Design and Analysis in Sport. J. Albert, M. Glickman, T. Swartz, & R. Koning (Eds.). Boca Raton, FL: Chapman & Hall/CRC Press.
Moskowitz, T.J. & Wertheim, L.J. (2011). Scorecasting: The Hidden Influences Behind How Sports are Played and Games Are Won. New York, NY: Crown Archetype. [CHAPTERS: "Whistle Swallowing" and "Comforts of Home"]
Bradbury, J.C. (2007). The Baseball Economist: The Real Game Exposed. New York, NY: Penguin Group. [CHAPTER 4: "Lobbying for Balls and Strikes"]
---------------------------------------------------------
The Traveling Umpire Problem and Other Academic Work
Chandrasekharan, R.C., Toffolo, T.A.M., & Wauters, T. (2019). Analysis of a constructive matheuristic for the traveling umpire problem. Journal of Quantitative Analysis in Sports. [Article Link]
Bender, M. & Westphal, S. (2016). A combined approximation for the traveling tournament problem and the traveling umpire problem. Journal of Quantitative Analysis in Sports, 12, 139-149. [Article Link]
Oliveira, L., Souza, C.C., & Yunes, T. (2014). Improved bounds for the traveling umpire problem: A stronger formulation and a relax-and-fix heuristic. European Journal of Operations Research, 236, 592-600. [Article Link]
Trick, M.A & Yildiz, H. (2012). Locally optimized crossover for the traveling umpire problem. European Journal of Operations Research, 216, 286-292. [Article Link]
Trick, M.A., Yildiz, H., & Yunes, T. (2012) Scheduling Major League Baseball umpires and the traveling umpire problem. Interfaces, 42, 232-244. [Article Link]
Beyer, J.A., Rowson, S., & Duma, S.M. (2012). Concussions experienced by Major League Baseball catchers and umpires: Field data and experimental baseball impacts. Annals of Biomedical Engineering, 40, 150-159. [Article Link]
Guziec, A. (2002). Tracking pitches for broadcast television. IEEE Computer, 35, 38-43. [Article Link]
---------------------------------------------------------
Work in the Public Analytics Space
Allen, D. (2009a). Does the umpire know the count? Baseball Analysts. [Article Link]
Armstrong, J. (2021). Peer learning among MLB umpires. Fangraphs. [Article Link]
Baggett, A. (2015). Conceptualizing the MLB strike zone using PITCHf/x data. Exploring Baseball Data with R. [Article Link]
Bergman, S. (2018). Umpires ejections and player ethnicity: An analysis. The Hardball Times. [Article Link]
Bonney, P. (2016). Who watches the watchers? Introducing umpire consistency score. In The Hardball Times Baseball Annual 2016. Joe Distelheim, Jason Linden, Greg Smions, & Paul Swydan (Eds.). Fangraphs & The Hardball Times.
Boyle, W., O'Rourke, S., Long, J. & Pavlidis, H. Robo strike zone: It's not as simple as you think. Baseball Prospectus. [ Article Link]
Carleton, R. (2016a). Baseball therapy: The knee. Baseball Prospectus. [Article Link]
Carleton, R. (2016b). Baseball therapy: The dark side of pitch framing? Baseball Prospectus. [Article Link]
Carleton, R. (2016c). Baseball therapy: Framing the at-bat. Baseball Prospectus. [Article Link]
Davis, N. & Lopez, M. (2015). Umpires are less blind than they used to be. FiveThirtyEight. [Article Link]
Fast, M. (2010). The internet cried a little when you wrote that on it. The Hardball Times. [Article Link]
Fast, M. (2011a). Spinning yarn: How accurate is PitchTrax? Baseball Prospectus. [Article Link]
Fast, M. (2011b). Spinning yarn: Home plate umpire positioning. Baseball Prospectus. [Article Link]
Fast, M. (2011c). NLCS umpire charts and data. Baseball Prospectus. [Article Link]
Fast, M. (2011d). Spinning yarn: The real strike zone Part 1. Baseball Prospectus. [Article Link]
Fast, M. (2011e). Spinning yarn: The real strike zone Part 2. Baseball Prospectus. [Article Link]
Fast, M. (2011f). Spinning yarn: Removing the mask encore presentation. Baseball Prospectus. [Article Link]
Hale, J. (2007a). A zone of their own. The Hardball Times. [Article Link]
Hale, J. (2007b). A gentle massage. The Hardball Times. [Article Link]
Hale, J. (2009). Strikeouts are fascist (walks, too). The Mockingbird. [Article Link]
Judge, J., Pavlidis, H., & Brooks, D. (2015). Moving beyond WOWY: A mixed approach to measuring catcher framing. The Hardball Times. [Article Link]
Kalk, J. (2009). That was a strike? The Hardball Times. [Article Link]
Karegeannes, J. (2004). Confessions of a QuesTec operator: How the system works, how it can be improved. Baseball Prospectus. [Article Link]
Lang, E. (2015). Analyzing the strike zone as a three-dimensional volume. The Hardball Times. [Article Link]
Lindbergh, B. (2014). Rung up: Are postseason umpires actually baseball’s most accurate? Grantland. [Article Link]
Lindholm, S. (2014). How well do umpires call balls and strikes? Beyond the Box Score. [Article Link]
Lopez, M. & Mills, B.M. (2018). Everyone wants to go home during extra innings - maybe even the umpires. FiveThirtyEight. [Article Link]
Mata, M. (2015). On the nature of the strike zone in two and three dimensions. The Hardball Times. [Article Link]
Mathewson, J.D. (2010a). Benefit of the doubt: Odd patterns in umpire compensation. Beyond the Box Score. [Article Link]
Mathewson, J.D. (2010b). Benefit of the doubt: How pitch speed and movement affect the zone.Beyond the Box Score. [Article Link]
Mathewson, J.D. (2011). Benefit of the doubt: Mo and the wide zone. Beyond the Box Score. [Article Link]
Mills, B.M. (2015). Measuring strike zone contour areas. Exploring Baseball Data with R. [Article Link]
Mills, B.M. (2016). Are the umpires at it again? The Hardball Times. [Article Link]
Molyneux, G. (2016). Umpires aren’t compassionate, they’re Bayesian. Baseball Prospectus. [Article Link]
Moore, C. (2009). Bayesian umpires. Baseball Analysts. [Article Link]
Nathan, A., Kensrud, J., Smith, L., & Lang, E. (2014). Testing TrackMan. Baseball Prospectus. [Article Link]
Pavlidis, H. & Brooks, D. (2014). Framing and blocking pitches: A regressed, probabilistic model. Baseball Prospectus. [Article Link]
Roegele, J. (2014). The strike zone during the PITCHf/x era. The Hardball Times. [Article Link]
Roegele, J. (2014). The strike zone expansion is out of control. The Hardball Times. [Article Link]
Roegele, J. (2015). The expanded strike zone: It’s baaaack. The Hardball Times. [Article Link]
Roegele, J. (2015). The commissioner speaks: Imagining a redefined strike zone. The Hardball Times. [Article Link]
Roegele, J. (2016). The 2016 strike zone. The Hardball Times. [Article Link]
ssp3nc3r. (2018). Modeling Umpire Calls. P( ssp3nc3r | Columbian ). [Article Link]
Steiner, N. (2009). Measuring the umpire’s effect on the game. The Hardball Times. [Article Link]
Tango, T. (2015). Evaluating the effectiveness of an umpire…effectively. Tangotiger Blog. [Article Link]
Turkenkopf, D. (2008). A strike is a strike, right? Beyond the Box Score. [Article Link]
Walsh, J. (2007a). Strike zone: Fact vs. fiction. The Hardball Times. [Article Link]
Walsh, J. (2007b). The eye of the umpire. The Hardball Times. [Article Link]
Walsh, J. (2010). The compassionate umpire. The Hardball Times. [Article Link]
Walsh, J. (2011). That was a strike? In The Hardball Times Baseball Annual 2011. Joe Distelheim, Bryan Tsao, Jeremiah Oshan, & Carolina Bolado Hale (Eds.).Chicago, IL: ACTA Sports.
Weinstock, J. (2012). Which umpire has the largest strike zone. The Hardball Times. [Article Link]
---------------------------------------------------------
Data Tools
Baseball Savant Statcast Search
Brooks Baseball PITCHf/x Tool
Bill Petti's baseballr Package
Carson Sievert's pitchRx Package
Retrosheet's Umpire Pages
This page is meant to be a comprehensive resource for academic social science and/or operations research using MLB umpire data, often referred to as PITCHf/x or Statcast.
There is also a large collection of excellent work outside of the academic space on umpires, and I encourage anyone interested in this topic to search websites like The Hardball Times, Fangraphs, and Baseball Prospectus (among others) for additional sources. I have attempted to lay out a comprehensive body of work from these websites on this page as well and will continue to do so as I move forward (please note that I have not updated the non-academic works list since 2018, but am in the process of doing so and welcome suggestions for any missed references below).
Economics & Social Science Research
Thornton-Lugo, M.A., McCarter, M.W., Clark, J.R., Luse, W., Hyde, S.J., Heydarifard, Z., & Huang, L.S.R. (2022). Makeup calls in organizations: An application of justice to the study of bad calls. Journal of Applied Psychology. [Article Link]
Snowden, H. (2021). Would "robot umpires" reduce discrimination? Measuring racial bias in Major League Baseball umpires. Claremont Colleges Senior Theses. [Article Link]
Archsmith, J.E., Heyes, A., Neidell, M.J., & Bhaven, N. (2021). The dynamics of inattention in the (baseball) field. NBER Working Paper. [Article Link]
Fesselmeyer, E. (2019). The impact of temperature on labor quality: Umpire accuracy in Major League Baseball. SSRN Working Paper. [Article Link]
Zimmerman, D.L., Tang, J., & Huang, R. (2019). Outline analysis of the called strike zone in Major League Baseball. Annals of Applied Statistics, 13, 2416-2451. [Article Link]
Archsmith, J., Heyes, A., & Saberian, S. (2018). Air quality and error quantity: Pollution and performance in a high-skilled, quality-focused occupation. Journal of the Association of Environmental and Resource Economists, 5, 827-863. [Article Link]
Lopez, M. & Mills, B.M. (2018). Opportunistic shirking behavior during unpaid overtime. Applied Economics Letters. [Article Link]
Bradbury, J.C. (2018). Monitoring and employee shirking: Evidence from MLB umpires. Journal of Sports Economics. [Article Link]
Hunter, D.J. (2018). New metrics for evaluating home plate umpire consistency and accuracy. Journal of Quantitative Analysis in Sports. [Article Link]
Deshpande, S.K. & Wyner, A. (2018). A hierarchical Bayesian model of pitch framing. Journal of Quantitative Analysis in Sports, 13, 95-112. [Article Link]
Mills, B.M. & Salaga, S. (2018). A natural experiment for efficient markets: Information quality and influential agents. Journal of Financial Markets, 40, 23-39. [Article Link]
Mills, B.M. (2017). Policy changes in Major League Baseball: Improved agent behavior and ancillary productivity outcomes. Economic Inquiry, 55, 1104.1118. [Article Link]
Mills, B.M. (2017). Technological innovations in monitoring and evaluation: Evidence of performance impacts among Major League Baseball umpires. Labour Economics, 46, 189-199. [Article Link]
Green, E. & Daniels, D.P. (2017). Bayesian Instinct. SSRN Working Paper Abstract ID #2916929. [Article Link]
Chen, D.L., Moskowitz, T.J., & Shue, K. (2017). Decision making under the gambler's fallacy: Evidence from asylum judges, loan officers, and baseball umpires. The Quarterly Journal of Economics, 131, 1181-1242. [Article Link]
Hamrick, J. & Rasp, J. (2015). The connection between race and called strikes and balls. Journal of Sports Economics, 16, 714-734. [Article Link]
Tainsky, S., Mills, B.M., & Winfree, J. (2015). An examination of potential discrimination among MLB umpires. Journal of Sports Economics, 16, 353-374. [Article Link]
Kim, J.W. & King, B.G. (2014). Seeing stars: Matthew effects and status bias in Major League Baseball umpiring. Management Science, 60, 2619-2644. [Article Link]
Mills, B.M. (2014). Social pressure at the plate: Inequality aversion, status, and mere exposure. Managerial and Decision Economics, 35, 387-403. [Article Link]
Parsons, C.A., Sulaeman, J., Yates, M.C., & Hamermesh, D.S. (2011). Strike three: Discrimination, incentives, and evaluation. American Economic Review, 101, 1410-1435. [Article Link]
Smith, E.E. & Groetzinger, J.D. (2010). Do fans matter? The effect of attendance on the outcomes of Major League Baseball games. Journal of Quantitative Analysis in Sports, 6(1).
MacMahon, C. & Starkes, J.L. (2008). Contextual influences on baseball ball-strike decisions in umpires, players, and controls. Journal of Sports Sciences, 26, 751-760.
Rader, B.G. & Winkle, K.J. (2008). Baseball's great hitting barrage of the 1990s (and beyond) reexamined. NINE: A Journal of Baseball History and Culture, 17, 70-96. [Article Link]
Insley, H.R. (2001). Major league umpired association: Is collective bargaining the answer to or the problem in the contractual relationships of professional sports today. Capital University Law Review, 29, 601-624. [Article Link]
---------------------------------------------------------
Books and Book Chapters
Mills, B.M. (2017). Umpire analytics. In The SABR Book of Umpires and Umpiring. L. Gerlach & B. Nowlin (Eds.). Phoenix, AZ: SABR.
Sievert, C. & Mills, B.M. (2017). Using publicly available baseball data to measure and evaluate pitching performance. In the Handbook of Statistical Methods for Design and Analysis in Sport. J. Albert, M. Glickman, T. Swartz, & R. Koning (Eds.). Boca Raton, FL: Chapman & Hall/CRC Press.
Moskowitz, T.J. & Wertheim, L.J. (2011). Scorecasting: The Hidden Influences Behind How Sports are Played and Games Are Won. New York, NY: Crown Archetype. [CHAPTERS: "Whistle Swallowing" and "Comforts of Home"]
Bradbury, J.C. (2007). The Baseball Economist: The Real Game Exposed. New York, NY: Penguin Group. [CHAPTER 4: "Lobbying for Balls and Strikes"]
---------------------------------------------------------
The Traveling Umpire Problem and Other Academic Work
Chandrasekharan, R.C., Toffolo, T.A.M., & Wauters, T. (2019). Analysis of a constructive matheuristic for the traveling umpire problem. Journal of Quantitative Analysis in Sports. [Article Link]
Bender, M. & Westphal, S. (2016). A combined approximation for the traveling tournament problem and the traveling umpire problem. Journal of Quantitative Analysis in Sports, 12, 139-149. [Article Link]
Oliveira, L., Souza, C.C., & Yunes, T. (2014). Improved bounds for the traveling umpire problem: A stronger formulation and a relax-and-fix heuristic. European Journal of Operations Research, 236, 592-600. [Article Link]
Trick, M.A & Yildiz, H. (2012). Locally optimized crossover for the traveling umpire problem. European Journal of Operations Research, 216, 286-292. [Article Link]
Trick, M.A., Yildiz, H., & Yunes, T. (2012) Scheduling Major League Baseball umpires and the traveling umpire problem. Interfaces, 42, 232-244. [Article Link]
Beyer, J.A., Rowson, S., & Duma, S.M. (2012). Concussions experienced by Major League Baseball catchers and umpires: Field data and experimental baseball impacts. Annals of Biomedical Engineering, 40, 150-159. [Article Link]
Guziec, A. (2002). Tracking pitches for broadcast television. IEEE Computer, 35, 38-43. [Article Link]
---------------------------------------------------------
Work in the Public Analytics Space
Allen, D. (2009a). Does the umpire know the count? Baseball Analysts. [Article Link]
Armstrong, J. (2021). Peer learning among MLB umpires. Fangraphs. [Article Link]
Baggett, A. (2015). Conceptualizing the MLB strike zone using PITCHf/x data. Exploring Baseball Data with R. [Article Link]
Bergman, S. (2018). Umpires ejections and player ethnicity: An analysis. The Hardball Times. [Article Link]
Bonney, P. (2016). Who watches the watchers? Introducing umpire consistency score. In The Hardball Times Baseball Annual 2016. Joe Distelheim, Jason Linden, Greg Smions, & Paul Swydan (Eds.). Fangraphs & The Hardball Times.
Boyle, W., O'Rourke, S., Long, J. & Pavlidis, H. Robo strike zone: It's not as simple as you think. Baseball Prospectus. [ Article Link]
Carleton, R. (2016a). Baseball therapy: The knee. Baseball Prospectus. [Article Link]
Carleton, R. (2016b). Baseball therapy: The dark side of pitch framing? Baseball Prospectus. [Article Link]
Carleton, R. (2016c). Baseball therapy: Framing the at-bat. Baseball Prospectus. [Article Link]
Davis, N. & Lopez, M. (2015). Umpires are less blind than they used to be. FiveThirtyEight. [Article Link]
Fast, M. (2010). The internet cried a little when you wrote that on it. The Hardball Times. [Article Link]
Fast, M. (2011a). Spinning yarn: How accurate is PitchTrax? Baseball Prospectus. [Article Link]
Fast, M. (2011b). Spinning yarn: Home plate umpire positioning. Baseball Prospectus. [Article Link]
Fast, M. (2011c). NLCS umpire charts and data. Baseball Prospectus. [Article Link]
Fast, M. (2011d). Spinning yarn: The real strike zone Part 1. Baseball Prospectus. [Article Link]
Fast, M. (2011e). Spinning yarn: The real strike zone Part 2. Baseball Prospectus. [Article Link]
Fast, M. (2011f). Spinning yarn: Removing the mask encore presentation. Baseball Prospectus. [Article Link]
Hale, J. (2007a). A zone of their own. The Hardball Times. [Article Link]
Hale, J. (2007b). A gentle massage. The Hardball Times. [Article Link]
Hale, J. (2009). Strikeouts are fascist (walks, too). The Mockingbird. [Article Link]
Judge, J., Pavlidis, H., & Brooks, D. (2015). Moving beyond WOWY: A mixed approach to measuring catcher framing. The Hardball Times. [Article Link]
Kalk, J. (2009). That was a strike? The Hardball Times. [Article Link]
Karegeannes, J. (2004). Confessions of a QuesTec operator: How the system works, how it can be improved. Baseball Prospectus. [Article Link]
Lang, E. (2015). Analyzing the strike zone as a three-dimensional volume. The Hardball Times. [Article Link]
Lindbergh, B. (2014). Rung up: Are postseason umpires actually baseball’s most accurate? Grantland. [Article Link]
Lindholm, S. (2014). How well do umpires call balls and strikes? Beyond the Box Score. [Article Link]
Lopez, M. & Mills, B.M. (2018). Everyone wants to go home during extra innings - maybe even the umpires. FiveThirtyEight. [Article Link]
Mata, M. (2015). On the nature of the strike zone in two and three dimensions. The Hardball Times. [Article Link]
Mathewson, J.D. (2010a). Benefit of the doubt: Odd patterns in umpire compensation. Beyond the Box Score. [Article Link]
Mathewson, J.D. (2010b). Benefit of the doubt: How pitch speed and movement affect the zone.Beyond the Box Score. [Article Link]
Mathewson, J.D. (2011). Benefit of the doubt: Mo and the wide zone. Beyond the Box Score. [Article Link]
Mills, B.M. (2015). Measuring strike zone contour areas. Exploring Baseball Data with R. [Article Link]
Mills, B.M. (2016). Are the umpires at it again? The Hardball Times. [Article Link]
Molyneux, G. (2016). Umpires aren’t compassionate, they’re Bayesian. Baseball Prospectus. [Article Link]
Moore, C. (2009). Bayesian umpires. Baseball Analysts. [Article Link]
Nathan, A., Kensrud, J., Smith, L., & Lang, E. (2014). Testing TrackMan. Baseball Prospectus. [Article Link]
Pavlidis, H. & Brooks, D. (2014). Framing and blocking pitches: A regressed, probabilistic model. Baseball Prospectus. [Article Link]
Roegele, J. (2014). The strike zone during the PITCHf/x era. The Hardball Times. [Article Link]
Roegele, J. (2014). The strike zone expansion is out of control. The Hardball Times. [Article Link]
Roegele, J. (2015). The expanded strike zone: It’s baaaack. The Hardball Times. [Article Link]
Roegele, J. (2015). The commissioner speaks: Imagining a redefined strike zone. The Hardball Times. [Article Link]
Roegele, J. (2016). The 2016 strike zone. The Hardball Times. [Article Link]
ssp3nc3r. (2018). Modeling Umpire Calls. P( ssp3nc3r | Columbian ). [Article Link]
Steiner, N. (2009). Measuring the umpire’s effect on the game. The Hardball Times. [Article Link]
Tango, T. (2015). Evaluating the effectiveness of an umpire…effectively. Tangotiger Blog. [Article Link]
Turkenkopf, D. (2008). A strike is a strike, right? Beyond the Box Score. [Article Link]
Walsh, J. (2007a). Strike zone: Fact vs. fiction. The Hardball Times. [Article Link]
Walsh, J. (2007b). The eye of the umpire. The Hardball Times. [Article Link]
Walsh, J. (2010). The compassionate umpire. The Hardball Times. [Article Link]
Walsh, J. (2011). That was a strike? In The Hardball Times Baseball Annual 2011. Joe Distelheim, Bryan Tsao, Jeremiah Oshan, & Carolina Bolado Hale (Eds.).Chicago, IL: ACTA Sports.
Weinstock, J. (2012). Which umpire has the largest strike zone. The Hardball Times. [Article Link]
---------------------------------------------------------
Data Tools
Baseball Savant Statcast Search
Brooks Baseball PITCHf/x Tool
Bill Petti's baseballr Package
Carson Sievert's pitchRx Package
Retrosheet's Umpire Pages
