티스토리 뷰


톰탱고 TomTango 레버리지 인덱스 Leverage Index (LI)


톰 탱고의 레버러지 인덱스 테이블입니다.

레버리지 인덱스Leverage Index는 특정한 아웃카운트, 특정한 온베이스 주자상황 각각이 얼마나 팀의 승패에 큰 가중치를 가지고 있는지를 측정할 수 있는 통계적 도구입니다.


테이블이 row는 주자상황과 아웃카운트 상황이고, 테이블의 column은 득점차 상황입니다.  

테이블은 홈팀 입장의 숫자입니다.   따라서 1회초의 경우, 홈팀이 이기고 있는 상황에 대한 LI값은 없습니다. 


LI는 보통 불펜투수의 투구이닝에 경기상황의 중요도에 따른 가중치를 곱해주기 위해 사용합니다.  당연하겠지만, 8회 5점을 리드한 상황에서 1이닝 무실점을 기록한 불펜투수의 기록과, 8회 동점 상황의 1사 만루 상황에 등판해서 실점없이 이닝을 마친 불펜투수의 기록이 동등하게 취급될 수는 없기 때문입니다.


LI는 사용되는 방법에 따라 다음 몇가지로 구분해서 부릅니다.


phLI - 핀치히터가 타석에 들어섰을 때의 레버리지인덱스

gmLI - 구원투수가 등판했을 때의 레버리지인덱스

inLI - 투수가 이닝을 시작할 때의 레버리지인덱스

exLI - 투수가 마운드에서 내려올때의 레버리지 인덱스

boLI - 아웃카운트 by 주자상황 각각에 대한 레버리지 인덱스


톰 탱고의 LI 테이블은, 그가 theBook 에서 소개했고 이후 사용하고 있는 24PA 상황에 대한 WPA: Wins Probability Above 모델에 기초합니다.  

참고포스트 -  http://baseball-in-play.com/21

승리확율 WPA:Wins Probability Above 로 본 게임의 재구성: 

8월20일 넥센전 8회말 봉중근의 병살유도의 가치


24PA 는 수없이 다양하고 복잡해보이는 야구경기의 상황은, 그럼에도 불구하고 3종류의 아웃카운트상황과 8종류 (1루, 2루, 3루, 12루, 13루, 23루, 만루, 주자없음)의 온베이스 주자상황의 조합 3*8=24종류의 타석상황을 뜻합니다. 


여기에 다시 24PA상황 각각의 득점차 조건을 조합할 경우, WPA 모델이 됩니다.  특정 PA상황, 특정 이닝, 특정 점수차 에서 홈팀은 통계적으로 얼만큼의 승리확율을 가지고 있었는지 계산됩니다.  WPA 모델에 기초해서 경기 중에 벌어지는 다양한 상황의 승패결정중요도 계산해서 메트릭스로 만들어둔 것이 레버리지인덱스입니다. 


경기 후반 점수차가 많이 날 경우 그 타석의 결과는 경기 승패에 별로 영향을 미치지 못할 것입니다.  이럴 경우 레버리지인덱스(LI) 는 낮습니다.   반대로 경기 후반 박빙 승부가 될 경우, 이 순간의 타석결과가 승패를 뒤집을 가능성은 매우 높습니다.  이럴 때 레버리지인덱스는 높은 값이 됩니다.  


레버리지인덱스란, 경기의 그 순간 승패결정의 중요도를 숫자로 계산해둔 것입니다.  평균적인 상황을 1.0 으로 합니다.  경기가 시작되는 시점은 거의 1.0에 가깝습니다.  만약 어떤 상황의 레버리지인덱스가 3.0이라면 이것은 승패결정의 중요도가 평균적인 상황에 비해 3배 높다는 뜻입니다.  


레버리지인덱스가 가장 높은 순간은 1점차 9회말 2아웃 만루 상황입니다.  물론 레버리지인덱스 없이도, 이런 상황이 승패결정에 매우 중요하다는 것은 누구나 압니다.  그런데 레버리지인덱스는 그 중요함이 "얼마나 더 높은지"를 통계적으로 측정한 것입니다.  1점차 9회말 2아웃만루 상황은 평균적인 상황에 비해 승패결정 중요도가 11배 정도 높습니다.  


Legend

Red...... Very High-Leverage

Blue..... High-Leverage

Gray..... Medium-Leverage

(empty).. Low-Leverage


"-3"..... Home team is down by 3


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_ _ _20.20.30.40.50.70.70.50.40.2
1 _ _20.30.50.711.31.31.10.80.5
_ 2 _20.40.711.41.81.81.410.7
_ _ 320.50.81.21.62.12.11.61.10.7
1 2 _20.60.91.31.92.52.62.31.71.1
1 _ 320.611.422.72.82.41.81.2
_ 2 320.711.62.22.93.22.721.4
12320.91.42.23.14.14.54.13.22.3
Bottom of Inning 6
123Outs-4-3-2-101234
_ _ _00.81.11.41.61.30.90.60.30.2
1 _ _01.41.92.32.421.30.80.50.3
_ 2 _01.31.7221.61.10.70.40.2
_ _ 301.21.61.81.71.30.80.50.30.2
1 2 _02.22.73.132.31.50.90.60.3
1 _ 3022.52.72.41.71.10.70.40.2
_ 2 301.92.32.42.21.71.10.70.40.2
123033.53.63.12.21.40.90.50.3
_ _ _10.50.811.210.70.40.30.2
1 _ _111.51.92.11.71.10.70.40.3
_ 2 _11.11.51.92.11.81.20.80.50.3
_ _ 3111.41.92.32.11.40.90.50.3
1 2 _11.92.63.13.32.71.81.10.70.4
1 _ 311.82.42.832.61.71.10.70.4
_ 2 311.72.22.52.52.11.40.90.50.3
123133.84.243.32.21.40.80.5
_ _ _20.30.40.60.80.70.50.30.20.1
1 _ _20.60.91.21.51.30.80.50.30.2
_ 2 _20.81.21.621.81.20.80.50.3
_ _ 320.91.31.92.42.21.40.90.60.3
1 2 _21.422.62.92.51.610.60.4
1 _ 321.42.12.73.12.71.81.10.70.4
_ 2 321.62.43.13.52.91.91.20.70.4
12322.73.74.54.942.61.710.6
Top of Inning 7
123Outs-4-3-2-101234
_ _ _00.20.40.711.51.71.410.6
1 _ _00.40.611.62.42.72.31.71.2
_ 2 _00.30.50.81.21.92.321.51.1
_ _ 300.20.40.611.521.91.51.1
1 2 _00.40.71.11.82.73.43.22.61.9
1 _ 300.30.50.81.322.832.51.8
_ 2 300.30.50.81.322.52.62.31.7
12300.40.61.11.72.63.53.93.62.8
_ _ _10.20.30.50.81.21.310.60.4
1 _ _10.30.50.91.422.31.81.30.8
_ 2 _10.30.60.91.42.12.31.81.30.8
_ _ 310.40.71.11.62.42.51.81.30.8
1 2 _10.50.81.32.13.23.63.12.31.6
1 _ 310.50.81.323.13.32.92.21.5
_ 2 310.40.71.11.62.52.82.72.11.4
12310.611.62.63.94.54.43.62.6
_ _ _20.10.20.40.50.80.80.60.30.2
1 _ _20.20.40.611.51.61.20.70.4
_ 2 _20.30.60.91.42.12.21.50.90.6
_ _ 320.40.71.11.72.52.51.71.10.6
1 2 _20.40.81.21.92.93.22.51.71
1 _ 320.50.81.42.13.13.42.61.71.1
_ 2 320.50.91.52.33.43.93.121.2
12320.71.223.14.75.44.53.32.1
Bottom of Inning 7
123Outs-4-3-2-101234
_ _ _00.81.21.61.91.50.80.40.20.1
1 _ _01.422.632.31.20.70.40.2
_ 2 _01.31.82.32.41.80.90.50.30.1
_ _ 301.31.82.221.50.80.40.20.1
1 2 _02.233.63.52.51.30.80.40.2
1 _ 302.12.83.32.81.70.90.50.30.1
_ 2 3022.62.92.61.70.90.50.30.1
12303.344.13.52.31.20.70.40.2
_ _ _10.50.81.11.41.20.60.30.20.1
1 _ _111.52.12.521.10.60.30.2
_ 2 _111.52.12.62.11.10.60.30.2
_ _ 3111.52.12.92.51.30.70.40.2
1 2 _11.92.73.6431.60.90.50.3
1 _ 311.82.63.23.73.11.60.90.50.3
_ 2 311.72.4332.51.30.70.40.2
12313.14.24.94.83.721.10.60.3
_ _ _20.20.40.710.80.40.20.10.1
1 _ _20.50.91.41.81.50.80.40.20.1
_ 2 _20.71.11.82.62.21.10.70.40.2
_ _ 320.81.3232.61.40.80.40.2