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# The new strike zone's (potential) effect on batters

Looking at hypothetical wOBA changes under MLB's potential new strike zone definition.

Back in January, it was reported that Major League Baseball was considering changing the rulebook definition of the bottom of the strike zone, raising it from the hollow below the knee to the top of the knee. According to Commisioner Manfred, this would be done in response to the ever-dropping nature of the strike zone, which has steadily proceeded downward through at least the PITCHF/x era (as shown by BtBS alum Jon Roegele). Anthony Castrovince recently published an article at MLB.com that illustrated just how significant the change has been, and over at FanGraphs August Fagerstom recently looked at which pitchers would be worst-affected by the change. Although recent news indicates that there probably won't be a change for this season, I'd still like to take a look at what such a change might mean from the batter's perspective.

First, let's remind ourselves what we're talking about. Here are two strike zone plots, similar to what Jon reports for his size-of-strike-zone data. The principal difference is that he uses a strict threshold of 50% of taken pitches being called strikes, while I'm using color to illustrate likelihood of a taken pitch being called a strike. Since I used 1" squares, by summing the probabilities I can get a strike zone size in square inches. By my method, I find that the strike zone in 2009 was 463 square inches, while in 2015 it was 498 square inches.

The dashed lines you see represent the average PITCHF/x "sz_bottom" parameter in each season (19.2 in 2009, 19.0 in 2015). PITCHF/x operators are instructed to set this parameter to the hollow of the knee, and while we should expect a little error, I'm judging it to be close enough to the true strike zone bottom for each batter. Using this cutoff, we can compare the strike zone size above and below to confirm that the low strike really is what's making a difference in total size. Unsurprisingly (since it's what everyone else has found, too), this is indeed the case -- only 20% of the increase came in the "above the knee" strike zone, which went from 453 sq. inches in 2009 to 458 in 2015, while the remaining 80% was in the "below the knee" zone, whose size jumped from 10 sq. inches to 40 in 2015.

Okay, with that framework/background in mind, let's focus in on the specific areas we're talking about for this strike zone change. I was unable to find the average size of a knee, so I had to estimate on myself. I'm 6'5" and the distance between the top of my knee and the bottom was maybe 3.5", so I'm going to go with 3" as the default knee size for MLB players. I'd like to examine which hitters could potentially benefit the most (or be hurt the most) by a sudden 3" upward shift in the bottom of the zone.

To do that, I'm going to have to make some assumptions -- decide for yourself whether they're valid (or even plausible) or not. First: I'm going to say that the new strike zone boundary won't change a hitter's performance *when he swings*, regardless of where the pitch is. Second, I'm not going to be able to deal with how the new zone will affect sequencing, frequency of each possible count, or anything like that, with the result of those assumptions being that the change in strike zone won't lead to any change in when a plate appearance ends. Everything I'll talk about only refers to pitches that conclude plate appearances, and yield a walk, strikeout, or batted ball. Those assumptions are a little tough to justify in some circumstances, but for the most part aren't terribly unreasonable, I think.

Third, and this is a much bigger leap, I'm going to say that the result of a taken pitch in the 3" zone between the old boundary and new (higher) boundary will match the result of a taken pitch in the 3" zone immediately below the old strike zone boundary. This relies on hitters and umpires immediately learning the new strike zone just as well as they knew the old one, which... let's just go with it, for the sake of argument if nothing else. Fourth, and now we're firmly, undeniably in "go with it for the sake of argument" territory, I'll need to address how often a batter will swing at a pitch that's in the new out-of-zone band. Give that we're talking about an area outside of the (future) rulebook strike zone, swing frequency is bound to decrease; however, batters can also probably square up the ball better in this zone than they could in the old, lower "just out of the zone" band, so swing frequency won't fall that much. I'm going to start out using the harmonic mean of the batter's old swing rates in the new band and old band. Fifth, and last, I need to address the frequency with which a plate appearance-ending pitch will be in the new out-of-zone band, since it's unlikely there will be exactly the same number of pitches there now that it's out of the zone. I've decided that I'm going to set the pitch frequency to what the frequency of the old out-of-zone band was, and distribute the now-locationless pitches across the new strike zone according to a batter's current pitch frequency in other bands.

Make sense? I know there are a TON of assumptions there, but this is all speculative anyway, and I couldn't see a way around them. The point of those assumptions is to allow the calculation of a new hypothetical wOBA for each batter last season under the higher bottom of the strike zone, and see which players would get the biggest hypothetical benefit. Putting them all together, here's how my calculation works. Using 2015 data, I divide the strike zone into four vertical bands; band 1 is more than 3 inches below the bottom of the strike zone, band 2 is between zero and three inches below the zone, band 3 is between zero and three inches above the bottom of the zone, and band 4 is everything above that. I see how many plate appearance-ending pitches occurred in each of those bands; I then change the number that occurred in band 3 to the same number as there were in band 2, and then distribute the missing pitches to the other bands proportionally. I'll illustrate this using Andrew McCutchen's data as an example.

McCutchen had 54 pitches in the old Band 2, so the new Band 2 (formerly Band 3) also is set to 54 pitches. The missing 14 pitches are then distributed proportionally between the other two zones.

So then, with the new pitch counts for each of the three new bands, I'll figure out the new wOBA. For new bands 1 and 3, I use the old wOBAs for old bands 1 and 4. For new band 2, I calculate a swing rate by taking the average from old bands 2 and 3. For the new wOBA on swings, I use the batter's overall wOBA on swings, and for the new wOBA on taken pitches I use the old wOBA on takes from old band 2. I can then get an overall wOBA by taking a weighted average across all bands (using total PAs for the weights). Continuing with the McCutchen example, here's how it works out.

So McCutchen's new wOBA is (66*.388 + 42*.425 + 12*.558 + 555*.399)/(66+42+12+555), or .402.

Across the whole league, looking just at qualified batters, the range of absolute wOBA changes runs from +.0316 at the highest to -.0114 at the worst, while the percent change runs from +9.6% to -3.7%. Putting it on a runs scale via wRC, the range is +12.2 to -9.2. Looking at the list, it's not immediately clear to me if there's a certain style of hitter that's more prevalent at the top and/or bottom of the list. It's certainly not a good hitter/bad hitter divide; the top ten(ish, depending on sorting metric) contains McCutchen, Jose Bautista, Didi Gregorius, and Jace Peterson, while the bottom of the list includes David Ortiz, Yadier Molina, Jimmy Rollins, and Lorenzo Cain. I think I'll leave it to the reader and/or next researcher to see if there's a pattern to be found.

Here's the table that lists the change for all qualified batters. Please note that the 2015 unchanged wOBA numbers may differ very slightly from what you find elsewhere, as I'm working off of home-built linear weights.

Name Old wOBA New wOBA Diff. Pct. Change ΔwRC
Lucas Duda 0.3533 0.3848 0.0316 8.9 10.5
Brandon Crawford 0.3295 0.3610 0.0315 9.6 10.7
Mitch Moreland 0.3436 0.3750 0.0314 9.2 9.9
Nelson Cruz 0.3969 0.4276 0.0306 7.7 12.2
Stephen Vogt 0.3376 0.3629 0.0253 7.5 7.4
Eric Hosmer 0.3551 0.3801 0.0250 7.0 9.5
Didi Gregorius 0.2930 0.3171 0.0241 8.2 7.7
Adrian Gonzalez 0.3556 0.3790 0.0234 6.6 8.2
Andrew McCutchen 0.3796 0.4022 0.0226 6.0 8.3
Jhonny Peralta 0.3226 0.3436 0.0210 6.5 7.0
Albert Pujols 0.3345 0.3552 0.0207 6.2 7.1
Carlos Santana 0.3315 0.3521 0.0206 6.2 7.1
Jay Bruce 0.3119 0.3313 0.0194 6.2 6.3
Derek Norris 0.3037 0.3231 0.0194 6.4 5.4
Kole Calhoun 0.3133 0.3326 0.0193 6.2 6.6
Jace Peterson 0.2840 0.3033 0.0192 6.8 5.7
Alex Rodriguez 0.3597 0.3784 0.0187 5.2 5.7
Kyle Seager 0.3345 0.3525 0.0180 5.4 5.9
Jose Bautista 0.3864 0.4038 0.0174 4.5 5.4
Shin-Soo Choo 0.3558 0.3729 0.0171 4.8 5.1
Billy Burns 0.3133 0.3304 0.0171 5.4 4.3
Michael Taylor 0.2810 0.2980 0.0170 6.1 4.0
Andrelton Simmons 0.2888 0.3055 0.0167 5.8 4.4
Matt Duffy 0.3268 0.3435 0.0167 5.1 4.6
Robinson Cano 0.3359 0.3525 0.0166 4.9 5.1
Mookie Betts 0.3495 0.3661 0.0166 4.8 4.9
Brock Holt 0.3148 0.3313 0.0165 5.2 3.8
Evan Gattis 0.3174 0.3338 0.0164 5.2 4.4
Miguel Cabrera 0.4177 0.4340 0.0163 3.9 3.7
Brett Gardner 0.3197 0.3356 0.0159 5.0 4.5
Ben Revere 0.3127 0.3284 0.0158 5.0 4.4
Kendrys Morales 0.3611 0.3768 0.0157 4.3 4.3
Mark Trumbo 0.3276 0.3432 0.0157 4.8 3.7
Paul Goldschmidt 0.4275 0.4430 0.0155 3.6 4.6
Xander Bogaerts 0.3351 0.3504 0.0153 4.6 4.2
Joe Mauer 0.3162 0.3314 0.0152 4.8 4.3
Avisail Garcia 0.2916 0.3065 0.0149 5.1 3.7
Kris Bryant 0.3644 0.3791 0.0147 4.0 3.9
Daniel Murphy 0.3298 0.3443 0.0145 4.4 3.1
Salvador Perez 0.2997 0.3142 0.0144 4.8 3.2
Francisco Cervelli 0.3312 0.3454 0.0142 4.3 2.8
Carlos Beltran 0.3459 0.3600 0.0141 4.1 2.9
Bryce Harper 0.4638 0.4775 0.0137 3.0 3.4
Marcus Semien 0.3101 0.3237 0.0135 4.4 3.1
Nolan Arenado 0.3754 0.3887 0.0133 3.6 3.3
Yunel Escobar 0.3429 0.3560 0.0131 3.8 2.7
Dexter Fowler 0.3283 0.3413 0.0130 4.0 3.2
Charlie Blackmon 0.3343 0.3471 0.0128 3.8 3.0
Matt Carpenter 0.3712 0.3840 0.0128 3.4 3.0
Jason Kipnis 0.3505 0.3632 0.0127 3.6 2.8
J.D. Martinez 0.3731 0.3857 0.0126 3.4 2.8
Ryan Braun 0.3652 0.3777 0.0125 3.4 2.4
Manny Machado 0.3664 0.3788 0.0124 3.4 3.0
Adam Eaton 0.3341 0.3465 0.0124 3.7 2.8
Brett Lawrie 0.3010 0.3132 0.0123 4.1 2.4
Logan Morrison 0.2974 0.3092 0.0118 4.0 1.9
Joey Votto 0.4297 0.4415 0.0118 2.7 2.6
A.J. Pollock 0.3695 0.3813 0.0118 3.2 2.5
Josh Donaldson 0.3932 0.4049 0.0117 3.0 2.5
Buster Posey 0.3657 0.3773 0.0116 3.2 2.2
Chris Owings 0.2515 0.2629 0.0114 4.5 1.9
Curtis Granderson 0.3541 0.3650 0.0109 3.1 2.0
Cameron Maybin 0.3065 0.3173 0.0108 3.5 1.6
Nick Markakis 0.3310 0.3417 0.0107 3.2 2.0
Starling Marte 0.3249 0.3356 0.0107 3.3 1.7
Logan Forsythe 0.3419 0.3525 0.0107 3.1 1.7
Brandon Phillips 0.3128 0.3234 0.0106 3.4 1.7
DJ LeMahieu 0.3263 0.3367 0.0104 3.2 1.6
Chris Davis 0.3878 0.3981 0.0103 2.7 1.7
Kolten Wong 0.3004 0.3106 0.0102 3.4 1.5
Elvis Andrus 0.2883 0.2980 0.0098 3.4 1.4
Jose Abreu 0.3585 0.3679 0.0093 2.6 1.1
Ben Zobrist 0.3505 0.3597 0.0092 2.6 0.9
Christian Yelich 0.3426 0.3515 0.0089 2.6 0.7
Melky Cabrera 0.3059 0.3148 0.0089 2.9 0.9
Ian Kinsler 0.3327 0.3414 0.0087 2.6 0.8
Mike Moustakas 0.3432 0.3519 0.0087 2.5 0.7
Wilson Ramos 0.2660 0.2747 0.0086 3.2 0.6
Joc Pederson 0.3309 0.3393 0.0084 2.5 0.6
Evan Longoria 0.3261 0.3342 0.0081 2.5 0.5
Prince Fielder 0.3611 0.3691 0.0081 2.2 0.5
Alcides Escobar 0.2611 0.2690 0.0079 3.0 0.4
Kevin Kiermaier 0.3065 0.3141 0.0076 2.5 0.2
Trevor Plouffe 0.3177 0.3250 0.0073 2.3 0.1
Todd Frazier 0.3389 0.3461 0.0073 2.1 0.1
Edwin Encarnacion 0.3886 0.3958 0.0073 1.9 0.0
Freddy Galvis 0.2786 0.2858 0.0072 2.6 0.0
Adam Lind 0.3560 0.3633 0.0072 2.0 0.0
Ender Inciarte 0.3191 0.3263 0.0072 2.3 0.0
Anthony Rizzo 0.3741 0.3813 0.0072 1.9 0.0
Brian Dozier 0.3195 0.3265 0.0071 2.2 0.0
Kevin Pillar 0.3050 0.3120 0.0070 2.3 -0.1
Alexei Ramirez 0.2789 0.2855 0.0066 2.4 -0.3
Gregory Polanco 0.3082 0.3147 0.0066 2.1 -0.3
Jason Heyward 0.3464 0.3528 0.0064 1.8 -0.4
Gerardo Parra 0.3302 0.3363 0.0061 1.9 -0.5
Angel Pagan 0.2780 0.2840 0.0060 2.2 -0.5
Troy Tulowitzki 0.3321 0.3377 0.0056 1.7 -0.7
Josh Reddick 0.3380 0.3433 0.0052 1.6 -0.9
Mike Trout 0.4155 0.4199 0.0045 1.1 -1.4
Ian Desmond 0.2889 0.2927 0.0038 1.3 -1.7
Justin Upton 0.3387 0.3420 0.0033 1.0 -1.9
Torii Hunter 0.2999 0.3032 0.0033 1.1 -1.7
Jose Altuve 0.3446 0.3477 0.0031 0.9 -2.2
Billy Butler 0.3073 0.3102 0.0029 0.9 -2.0
Anthony Gose 0.2988 0.3017 0.0029 1.0 -1.8
Nick Castellanos 0.3105 0.3131 0.0027 0.9 -2.1
Jean Segura 0.2646 0.2668 0.0022 0.8 -2.3
David Peralta 0.3781 0.3802 0.0022 0.6 -2.0
Asdrubal Cabrera 0.3184 0.3204 0.0020 0.6 -2.3
Yangervis Solarte 0.3177 0.3195 0.0018 0.6 -2.4
Erick Aybar 0.2757 0.2774 0.0018 0.6 -2.7
Addison Russell 0.3025 0.3039 0.0014 0.5 -2.4
Brandon Moss 0.3067 0.3077 0.0010 0.3 -2.6
Dee Gordon 0.3336 0.3338 0.0002 0.0 -3.6
Neil Walker 0.3223 0.3221 -0.0003 -0.1 -3.5
Matt Kemp 0.3245 0.3238 -0.0007 -0.2 -4.0
Chase Headley 0.3019 0.3009 -0.0010 -0.3 -4.1
Yoenis Cespedes 0.3652 0.3638 -0.0014 -0.4 -4.6
Adam Jones 0.3303 0.3288 -0.0015 -0.5 -4.0
Martin Prado 0.3143 0.3128 -0.0015 -0.5 -3.8
Jose Reyes 0.2933 0.2918 -0.0015 -0.5 -3.6
Carlos Gonzalez 0.3623 0.3602 -0.0021 -0.6 -4.5
Wilmer Flores 0.3010 0.2988 -0.0022 -0.7 -3.8
Aramis Ramirez 0.3078 0.3052 -0.0026 -0.8 -4.0
Starlin Castro 0.2872 0.2846 -0.0026 -0.9 -4.5
Michael Brantley 0.3692 0.3658 -0.0035 -0.9 -5.0
Odubel Herrera 0.3243 0.3206 -0.0037 -1.1 -4.6
Austin Jackson 0.2986 0.2929 -0.0057 -1.9 -5.4
Jimmy Rollins 0.2804 0.2741 -0.0063 -2.2 -6.1
Marlon Byrd 0.3148 0.3083 -0.0065 -2.1 -5.9
David Ortiz 0.3862 0.3781 -0.0081 -2.1 -7.5
Brandon Belt 0.3571 0.3480 -0.0091 -2.5 -7.2
Yadier Molina 0.2887 0.2781 -0.0106 -3.7 -7.5
Lorenzo Cain 0.3550 0.3441 -0.0109 -3.1 -8.5
Adrian Beltre 0.3373 0.3259 -0.0114 -3.4 -9.2
Brian McCann 0.3202 0.3087 -0.0114 -3.6 -7.8

John Choiniere is a researcher and occasional contributor at Beyond the Box Score.You can follow him on Twitter at @johnchoiniere.