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The last column in this series wondered about the possibility of an NBA-like referee scandal happening with Major League umpires. The structure of the game makes that difficult, but I’d like to back that up with research. Now, with data in hand, I’d like to explore if there are umpires who are kind to either favorites or underdogs. With help from Retrosheet, home-plate umpires from 2000 through 2006 will be scored on the probability of the winning percentage of game favorites fitting the expectation. This covers the time period since the mass resignation of umpires in 1999.

The following formula calculates the probability of the favorite in a game winning:

prob = FWPct*(1- UWPCT)/((FWPct*(1- UWPCT) + UWPct*(1- FWPCT))

Where:

  • FWPct is the winning percentage of the favorite.
  • UWPCT is the winning percentage of the underdog.

Note that in this formula, teams with 1.000 winning percentages always win, teams with .000 winning percentages always lose, and teams with the same winning percentage are expected to play .500 ball against each other.

For this study, the two winning percentages are simply the team’s winning percentage for the season. The favorite in a game is the team with the higher winning percentage, or the home team if the percentages are the same. For example, any time Cleveland played Detroit in 2005, the Indians were the favorite with a .574 winning percentage and Detroit was the underdog with a .438 winning percentage. That meant the probability of the Indians defeating the Tigers in a game was .634 (11.4 expected wins). They were 12-6 vs. Detroit that season, a .667 winning percentage.

The probability of the favorite winning is calculated for each game, and those probabilities are summed over all games to get the expected number of wins. Over the entire dataset of 16997 games, favorites were expected to win 9993.6 games. They actually won 9950, which is well within the 95% confidence interval. The overall probability of a favorite winning an individual game was .588. The cumulative probability of winning no more than 9950 games is .25, so it is within the 50% confidence interval. The formula underestimates the number of wins, but not significantly.

The same calculation is done for each home-plate umpire. The probability of the favorite winning is summed over all games for a particular umpire to become the expected number of wins. That’s compared to the actual wins with that person behind the plate, and the cumulative binomial probability is calculated for winning no more than that number of games. The following table contains all umpires who appeared behind the plate for at least 100 games in the seven years covered by the study:

Umpire Name Games Expected Wins Actual Wins Difference (Exp-Act) Probability
Marty Foster 227 134.06 115 19.06 0.006
Jim Reynolds 235 136.85 119 17.85 0.011
Lance Barksdale 210 123.60 107 16.6 0.012
Kerwin Danley 199 117.41 103 14.41 0.023
Alfonso Marquez 238 139.86 125 14.86 0.030
Paul Emmel 229 136.37 122 14.37 0.032
Ted Barrett 237 139.22 125 14.22 0.036
Joe Brinkman 187 109.65 98 11.65 0.050
Dan Iassogna 247 144.95 133 11.95 0.070
Hunter Wendelstedt 233 135.57 124 11.57 0.071
Ron Kulpa 236 139.91 130 9.91 0.106
Jim Wolf 211 125.11 117 8.11 0.143
Andy Fletcher 222 129.60 122 7.6 0.167
Chuck Meriwether 235 138.28 132 6.28 0.221
Tony Randazzo 233 137.11 131 6.11 0.227
CB Bucknor 236 139.86 134 5.86 0.238
Fieldin Culbreth 232 135.58 130 5.58 0.249
Randy Marsh 218 127.61 123 4.61 0.285
Sam Holbrook 140 81.61 78 3.61 0.296
Larry Young 226 131.99 128 3.99 0.318
Gary Darling 169 99.37 96 3.37 0.326
Mike Everitt 234 137.57 134 3.57 0.341
Bill Miller 239 140.46 137 3.46 0.347
Dana DeMuth 226 132.31 129 3.31 0.351
Jeff Nelson 230 133.91 131 2.91 0.372
Larry Poncino 172 100.11 98 2.11 0.400
Charlie Reliford 196 116.14 114 2.14 0.404
Rick Reed 199 118.10 116 2.1 0.407
Mark Hirschbeck 103 60.63 59 1.63 0.408
Jerry Meals 242 144.06 142 2.06 0.418
Brian Gorman 237 141.01 139 2.01 0.419
Paul Nauert 134 77.57 76 1.57 0.424
Mike Reilly 220 130.80 129 1.8 0.427
Eric Cooper 240 141.34 140 1.34 0.455
Tim Welke 235 137.18 136 1.18 0.463
Paul Schrieber 220 128.61 128 0.61 0.493
Jerry Layne 213 125.47 125 0.47 0.500
Mark Carlson 243 142.40 142 0.4 0.504
Jim Joyce 200 118.19 118 0.19 0.516
Marvin Hudson 232 136.05 136 0.05 0.523
Bruce Froemming 234 136.04 136 0.04 0.523
Tim Tschida 239 140.74 141 -0.26 0.538
Terry Craft 150 87.83 88 -0.17 0.542
Angel Hernandez 235 137.61 138 -0.39 0.545
Doug Eddings 242 142.51 143 -0.49 0.550
Brian Runge 194 113.61 114 -0.39 0.550
Joe West 172 101.65 102 -0.35 0.551
Bill Welke 232 137.34 138 -0.66 0.560
Mike Fichter 123 72.24 73 -0.76 0.589
Gerry Davis 228 134.70 136 -1.3 0.594
Tim Timmons 242 142.00 144 -2 0.627
Larry Vanover 170 100.83 103 -2.17 0.660
Steve Rippley 101 60.32 62 -1.68 0.669
Dale Scott 233 136.03 139 -2.97 0.677
Tim McClelland 235 138.48 142 -3.52 0.702
Laz Diaz 239 140.05 144 -3.95 0.720
Mike DiMuro 169 100.20 104 -3.8 0.749
Gary Cederstrom 230 133.54 139 -5.46 0.787
Bill Hohn 135 79.47 84 -4.53 0.810
Jeff Kellogg 216 128.91 135 -6.09 0.820
Derryl Cousins 220 127.76 134 -6.24 0.821
Greg Gibson 232 137.07 144 -6.93 0.839
Jerry Crawford 204 120.51 127 -6.49 0.840
Ed Rapuano 234 137.98 145 -7.02 0.841
Ed Montague 222 131.12 138 -6.88 0.843
Mark Wegner 231 134.85 142 -7.15 0.846
Bruce Dreckman 136 80.62 86 -5.38 0.848
Wally Bell 242 141.99 151 -9.01 0.893
Chris Guccione 225 133.75 144 -10.25 0.929
Matt Hollowell 118 69.28 77 -7.72 0.939
Rob Drake 175 102.90 113 -10.1 0.949
Mike Winters 236 139.49 152 -12.51 0.958
John Hirschbeck 211 124.43 137 -12.57 0.967
Phil Cuzzi 241 143.16 159 -15.84 0.985
Brian O’Nora 228 134.13 150 -15.87 0.987

Notice that the probabilities aren’t very normally distributed. The lower half looks okay, but the upper half looks like a normal within a normal. Umpires who are kind to favorites really push their winning percentage up.

ProbDistribution.JPG

The interest of this piece, however, lies at the other end, where favorites losing can make more money for gamblers. There are quite a few umpires with a p-value under .05, with Marty Foster as the most underdog-friendly umpire in the group, so let’s look at him more closely. If gamblers are going to get an umpire to affect a game, they’ll want one with a big payoff, one where the odds are long. Taking into account Foster’s games where the probability of the favorite winning is .65 or higher, we find an innocuous result. Foster was the home plate umpire for 37 such games, and in them, the expectation for wins was 25.7. The actual number of wins was 26. In other words, the variation happens at lower probabilities, where there’s more of a chance for luck to take hold.

The opposite of Foster is Paul Schrieber, who is right on overall, as we expect the favorite to win 128.6 of his games, and they actually won 128. But in games with a high probability of the favorite winning, those teams win just 16 of 33 with an expectation of 22.6 wins. Looking at the individual games, 12 of the 16 underdog wins were by the home team, as were 10 of 16 favorite wins. It almost seems like Schrieber is biased toward the home team.

And that’s the nice thing about this kind of analysis, as a number of biases can be studied. The Yankees biggest underperformance (three wins instead of seven) comes with CB Bucknor behind the plate. At the other end of the spectrum, the Yankees played five games better than expected with Wally Bell calling balls and strikes (17 wins vs. 12). Joe Brinkman hurt home team favorites the most, costing them eight games, while Chris Guccione helped them the most, adding 15 games. Actually, the home-field advantage is pretty clear in the data. The home team rated as the favorite in 8621 games. They won 5370 of those, despite the expectation being for 5058 wins. That’s 312 wins more for home team favorites, a .623 winning percentage versus a .587 expected winning percentage. It’s tough to beat a good team at home.

The good news is the lack of evidence that umpires are intentionally affecting the outcome of games, as the few outliers are probably due to small sample sizes. But this is a nice simple methodology for studying the question. It can be extended to see if umpires have biases against certain teams, or even certain starting pitchers. On the question of gambling, however, I feel a lot better that the probability of an NBA-like referee scandal remains low in baseball.

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