JapaneseJapaneseSociety Society ofComputationalof Computational Statistics

Pitching PredictionBy Multinomial Logit Model In

Nippon Professional Baseball

Keisuke Koike'` Hiroyasu Abet and Hiroshi Yadohisai

Abs tract - In Nippon Prefessional Baseball. it is importartt for players to recelve useful lnfgrmation. It has been reported that pitchers's records were better this year than last year. On the other hand. batters's records haye worsened overal1 for the same period. Therefore. we created a pitching model by multinornial logit model to provide usefu1 information to batters. Fi rst, we justify the use ef the multinomial logit rnodel and explain relevant terms used in the moder, Secend. we defifte a pitching prediction model by ernpleying multinomial logit model and variables used for this paperafter which we describe the applied data, Finally we presenC the conclusions.

Keyword: Pitching Prediction; Multinomint Lagit Model; pitch.

1 Introduction

RecentLy in Nippon Professiona1 Baseball, a strategic approach to the game based on analysis of various data has become populac and members of the coaching team have developed strategtes for pitchers and batters. In this papeny we aim to provide information that is usefu1 from the perspective of batters. The general purpose ofbatters is to hit the ball. From this perspective, important information for batters would increase their hitting probabilities. One way to do this is to predict the pitches of each pitcheny which can vary widely Therefore, we built a pitching model for the purpose of pitch prediction, In this papeny we utiLize a multinomial logit model similar to that known in the marketing field. In essence, we believe that a pitcher selects from a variety of pitches in the same manner in which customers choose a commercial product. ln addition, a personalized pitch model is created by each pitcher.

2 Pitchmodel

2.1 Definitionofterms

We build the pitch model based on data from Nippon Professional Baseball, which was made available by Data Stadium Inc. Here we define the variables used and explain the input data,

Definition 2.1 Vbriety ofpitch N The variety ofpitches is defined as a set of changtug halls that are throzvn by the pitchen Tlhere are several dijferent types. such as the jiistbalt, curveball, slideL changeup, forkball, sinicec cutte" and scnuball, among others. Howeven in this papeny we classijied the above mentioned types into three catagories. We eategorize thefostball and screzvball into a group called fbstball-related; the curveball, slider and cutter into a group calted curve-related; and theforkbalt. changeup, sinker, and others into a group calledfoll-related.

- - - N = {1 : Fastball related,2 : Curve related, 3 : Fall related}. <2,1)

'Graduate School of Culture and information Science. Doshisha University} Kyoto 610-0394, Japan, E- mail:dileOe7@mai14,deshisha.ac.jp +Graduate School of Culture and Information Seience, Doshisha UniversitM Kyoto 61e-0394, Japan tDepartment of Culture and Informatien Science, Doshisha University Kyoto 610-0394, Japan

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Definition 2.2 Pitch location M The location pitch consists of 5 areas, which are high-and-inside. Iow-and-inside, high-and-outside, down- and-outside, and centen We dojine a set M of these 5 areas to attow us to consider the retationship between high and lotv and in and out, as shown in Figure 1,

2oo 16e ]?oi so40o

1: high-and-inside

0 2: low-and-inside

3: high-and-outside 0

4: low-and-outside

5: center

0 1

The dark area is the strike zone, and the iight area is the ball zene.

Figure 1: Pitch location

Definition 2.3 Pitching Y Pitchingisdefinedas a set ofordered pairs that consist ofa variety ofpitches N and pitch locations M. Vthi define the set ofpitchiug asfollows:

Y=((m,n)1mEM,nEN]. {2.2)

In this there are 15 papeny different combinations of pitches because there are 5 pitch areas and 3 categories of pitching.

Definition 2.4 Pinch indicator P Pinch indicator represents a scenariofor a base runner on second or third base at i-th pitch. We define pinch indicato4 Pi asfollows:

are On the second or thrrdbase) p, = (S E8ftrhUenrns)er(S) (2 3) Definition 2.5 Count VZiriable T:hecount varinble isdojinedas a number pair ofthe of balls and the number ofstrikes. The number of balls isb = O,1.2,and = {b 3}, while the number clf strikes is s {s O, 1, and 2) as foliozvs:

b,･,s- xts) c,,, . (g [g:,: (2.4) Where xib describes the ball count at i-th pitch, and xi, describes the strike count at i-th pitch,

We use Coo as the omitted variable, then it is omitted in table 1.

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PiCnoCneCi]oCioiCillC,?1C,31Cio2Ci12CmCi32 o1oooooooooo oo1ooooooeoo ooo1oooooooo ' '::::'''''''''''''

1oooooeooooo looooooooooo o1oooooooeoo Thble 1: Data used in model estimation

2.2 Multinomiallogitmedel

We built a pitch model using variables of P and Cib,. In this pape- we employ a multinomial logit -- fi- model. With the i-th throw) the probability of each pitch yi (m, n) is described as Pr(yi (m, n)), Then, the model is represented as follows:

=exp(Vimn) pr(yiiD ' (2.5) £ (k,o.,y exp( viks)

32

Vnnn = Ltmn + + rmnPi Z Z llbsmnCits r (2.6) b=e s=o

where Vimn represents the use of (m,n) with the i-th pitch; a'm. represents a constant parameter for pitch(m, n)ijSb,.. represents an impact of the situation with b balls and s strikes on the pitch(m. n); and r.. represents an impact of pinch indicator on the pitch(m, n),

3 Conclusion

ln this papell we focused on building the model of Hideaki Wakui in 2009, who is a pitcher for the Saitama Seibu Lions team. Wk] provide the prediction resuits, such as amn, 5bsmn, and rmn in this paper. Then, P = O, Cee, and y = (1, 1) are designated as the reference categories, fables 2-6 represent the results of [xmn, fibsmn, and rrnn, and t indicates the results of statistial test of each parameters with significance level O.1. Look at the black areas of tables, in the case of Cn and Cn, the probability of y = (4, 3) become low in the table 4, and In the case of P = 1, the probability of center become Iow in the table 5,

4 Acknowledgment

We would like to express our gratitude to Data Stadium Inc. for providing the baseball data,

References

[1] Jim Albert (1994). Exploring Baseball Hitting Data:What About Those Breakdown Statistics? in Authology of Statistics in Sports, Ed. by J.Albert et al, ASA-SIAM, Alexandria. [2] Jim Albert, Jay Bennett (2003). Curve ball Baseball, Statistics, and the Role of Chance in the Game.

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Fastball-relatedCurverelatedFall-related Fastball-reiatedCvrvere]atedFall-velated Cn=1) (n=2) (n=3) (n=1) (n=2) (n=3} rm" O.13 -O.21 -o,ss rt//n o.oo -O.14 -O.37 ti10/nn O.13 O.40 O.15 fi10mfi o.oo -O.62. -O.11 fi2thicn mO.10 -O.49 -9,07 -l.69 b'?o-n ooo -1.39. -O,B9 PS30n,n O.25 -7.69 SS3omn o.oo -B.36 -8.14 t;Olmn O.32 -O.33 -O.94 "Ol,,m o.oo -1,21. -O.33 O.21 tenmri O.13 O.21 ,SITtnn o.oo -O.56 O.U4 e.12 -e.o6 -1.73 fi21nm /E?lmn o.oo -1.50. -O.39 li31mn O.21 -O.55 -B.51 ff']}nm o.oo -1.sot -8.41 6rznn -O.Ol -O.83. -1.65 o.oo -2.Mt -O.93. -O.96. -O.9S //SU2tnn fi]b/m O.52. SUntn o.oo -2.02. fiO.41 O.13 O.12 -O.48 iS22",n fi!2ma'/')]2":ne.oo -2.35. -O.74 rs3?mri O.17 -O.36 -1.81 o.oo -1.46. -1,2S. consf -e.39. -O.47t -1.88. censt o.oo -O,38. mO.S6. ble2:Impactonhigh-and-outsidepitch(m=3) ble3:Impactonhigh-and-insidepitch(m=1)

Fastball-relatedCurverelatedFaX]-related (n=1) {"=2) (n=3) rnm,,.･lt.1..11/g3.1/'1/.',,',･..t./.,'t･.-.1124.,.-e.53 Itlomh-O.21 O.39 O.15 fi1lhmn-O.63 -e.o3 O.29 e3eny,n 1.09 -7.69 -6.69 ffOlnrn O.06 -O.85 -O.53 b'nmn-e.3o -O.59 -LIS PIT"m o.le -O.33 -O.23 fi31mny-O.03 O.16 -8,OO lielntn -O.65 -1.84 O.25 fi7bnn-O.36 10.24 O.37 fi22"in O.11 -O.97 O.32 rs31din-O.8] -o.n -e,32 const-1.76 -l.66 -2.72 Table4:Impactoncenterpitch(m=5)

FastballfelatedCurverelatedFall-related Fastball-re]atedCurverelatedFall-related (n=1} (n=2) (n[.3) (n=1) (n=2) (n=3) r=m -e.29 -O.50- -O.22 rn/n -O.39 -O.30 O.25 fi1thtm O.13 O.19 O.22 QFIOmn -O.29 -1.34 O.09 O.10 -O.48 fi!orffri O.34 Plemh e,lo -O.23 -1.44 fSstinin O.65 -7.so -7.83 -8.19 1`S3on/n O.54 -1.17 Polmn O.49 e,17 O.54 SOImrr O,37 -e.64 O.37 O.36 O.2S ff11nsn O.6S. P'11/prn O.51+ -O.49 O.31 ISII.,-O.04 -O.S9. -e.25 .S21nrn -O.22 -O.92 -1.26t b'31ntn-O.03 -1.15f -1,B6 -O.42 -1.83 -e.86i -O.Ol fi3]otn -8.22 Sozmn O.09 So2mn -O.35 -1.nt O.17 o.3eO.44-O.27 o.le-O.02-O.47//1!l.l.lll,}1･111111//.l,il･gl'i.1illllilil,I-O.36 fiIZ,tntSibvenPszTn /e12,,in O.02 -125. O.38 IS21nrn O.12 -1.or O.28 fi32nm -O.27 -1.s3t -O.47 consi-O.85. -1,11. o.oo const-O.59, -1.13. -1.08} ble5:Impactonlow-and-outsidepitch(m=4) Table6:Impactonlow-and-insidepitch(m=2)

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