Verify the accuracy of the scoring formula "RC" using actual professional baseball data

  1. Introduction

United States sports writer and pioneer of baseball Sabermetrics [Bill James](https://ja.wikipedia.org/wiki/%E3%83%93%E3%83%AB%E3%83 % BB% E3% 82% B8% E3% 82% A7% E3% 83% BC% E3% 83% A0% E3% 82% BA) has created a formula to predict the team's score.

Number of points=  (Number of hits+Number of walks)× Number of base hits ÷(At bat+Number of walks)

The score estimated by this formula was named ** RC (Runs Created) **. James substituted the past season records of various MLB teams on the right side of the equation to see if it matched the actual score. As a result, this formula was effective regardless of which team was applied, and the score could be predicted with extremely high accuracy. But there is one question.

--It was MLB data that James used to verify the accuracy of this formula. Is it possible to accurately predict the score for the NPB team using this formula?

Therefore, this time, we verified the accuracy of this score formula RC using the actual NPB team data.

  1. Data and Program 2.1. Data The data used are the season results of the 12 teams of Nippon Professional Baseball (NPB) from 2005 to 2016. Data is the homepage of Nippon Professional Baseball http://npb.jp/ Obtained from. For example, the 2016 Central League season results http://npb.jp/bis/2016/stats/tmb_c.html Obtained from, processed the format as follows and saved.

2016C_bat.csv


Carp, .272, 143, 5582, 4914, 684, 1338, 203, 35, 153, 2070, 649, 118, 52, 91, 29, 500, 13, 47, 1063, 85, .421, .343
Yakult, .256, 143, 5509, 4828, 594, 1234, 210, 20, 113, 1823, 565, 82, 24, 85, 33, 524, 10, 39, 907, 117, .378, .331
Giants, .251, 143, 5356, 4797, 519, 1203, 217, 19, 128, 1842, 497, 62, 26, 112, 23, 389, 11, 35, 961, 100, .384, .310
DeNA, .249, 143, 5364, 4838, 572, 1205, 194, 21, 140, 1861, 548, 67, 34, 81, 18, 373, 7, 54, 1049, 92, .385, .309
Dragons, .245, 143, 5405, 4813, 500, 1180, 209, 21, 89, 1698, 473, 60, 28, 108, 28, 410, 7, 46, 1001, 103, .353, .309
Tigers, .245, 143, 5401, 4789, 506, 1171, 204, 17, 90, 1679, 475, 59, 25, 88, 38, 435, 17, 51, 1149, 99, .351, .312

(The data is https://github.com/AnchorBlues/python/tree/master/baseballdata I put the processed one in

2.2. Program The programming language Python was used for data reading, analysis, and visualization.

NPB.py


#coding:utf - 8

import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

fy = 2005
ly = 2016
Yn = ly - fy + 1

Bat_Column = ['Average', 'Game', 'PA', 'AB', 'Score', 'Hit', \
			  'TwoBase', 'ThreeBase', 'HR', 'TB', 'RBI', 'Steel', \
			  'MissSteal', 'Bunt', 'SF', 'BB', 'IntentionalWalk', \
			  'DeadBall', 'StrikeOut', 'DoublePlay', 'SLG', 'OBP']

# PA :Plate Appearance Number of at-bats
# AB :At Bat at bat
# TB :Total Bases Number of bases
# RBI :RBI
# SF :Sacrifice Fly Sacrifice fly
# IntentionalWalk :Intentional walk

N = len(Bat_Column)

class Bat_Data():
	def __init__(self, Data, Year, Team):
		self.Year = Year
		self.Team = Team
		for i in range(0, N):
			setattr(self, Bat_Column[i], Data[:, i])

		self.OPS = self.SLG + self.OBP
		self.NOI = (self.SLG / 3.0 + self.OBP) * 1000
		self.BABIP = (self.Hit - self.HR) / (self.AB + self.SF - self.HR - self.StrikeOut)
		self.RC = (self.Hit + self.BB) * self.TB / (self.AB + self.BB)
		self.IsoP = self.SLG - self.Average
		self.IsoD = self.OBP - self.Average



class TEAM:
	def __init__(self, ID, Name, maker):
		self.ID = ID
		self.Name = Name
		self.maker = maker


team = [0] * 12
team[0] = TEAM(0, 'Carp', '>')
team[1] = TEAM(1, 'Tigers', '<')
team[2]= TEAM(2, 'Giants', '^')
team[3] = TEAM(3, 'Dragons', 'v')
team[4] = TEAM(4, 'DeNA', 'd')
team[5] = TEAM(5, 'Yakult', 'D')
team[6] = TEAM(6, 'Fighters', '8')
team[7] = TEAM(7, 'Lotte', 'H')
team[8] = TEAM(8, 'Lions', 'h')
team[9] = TEAM(9, 'Eagles', '*')
team[10] = TEAM(10, 'Orix', 'p')
team[11] = TEAM(11, 'Hawks', 's')


#2 Bat_Consolidate Data instances into one instance
def Docking(Data1, Data2):

	data = np.zeros((Data1.Average.shape[0] + Data2.Average.shape[0], N))
	for i in range(0, N):
		data[:, i] = np.r_[getattr(Data1, Bat_Column[i]), getattr(Data2, Bat_Column[i])]

	year = np.r_[Data1.Year, Data2.Year]
	team = np.r_[Data1.Team, Data2.Team]
	Data_new = Bat_Data(data, year, team)
	return Data_new


def get_data(League, year):
	fname = './baseballdata/' + str(year) + League + '_bat.csv'
	Data = np.loadtxt(fname, delimiter = ',', usecols = range(1, N + 1))
	Year = np.ones(6) * year
	Team = np.loadtxt(fname, delimiter = ',', usecols = range(0, 1), dtype = str)
	Data = Bat_Data(Data, Year, Team)
	return Data


def get_all_data(League):
	for i in range(Yn):
		year = i + fy
		tmp = get_data(League, year)
		if i == 0:
			Data = tmp
		else:
			Data = Docking(Data, tmp)

	return Data

# Data.Column_From the name, the team name is Team_Extract only the one with name.
def PickUp_Data_of_a_team(Data, Column_name, Team_name):
	return getattr(Data, Column_name)[np.where(getattr(Data, 'Team') == Team_name)]


def draw_scatter(plt, Data, X_name, Y_name, regression_flg = 0, Y_eq_X_line_flg = 0, \
				 title = 'Scatter plot', fsizex = 10, fsizey = 8):

	fig, ax = plt.subplots(figsize = (fsizex, fsizey))
	plt.rcParams['font.size'] = 16

	for i in range(0, len(team)):
		x = PickUp_Data_of_a_team(Data, X_name, team[i].Name)
		y = PickUp_Data_of_a_team(Data, Y_name, team[i].Name)
		year = PickUp_Data_of_a_team(Data, 'Year', team[i].Name)
		if x != np.array([]):
			CF = ax.scatter(x, y, c = year, s = 50, marker = team[i].maker, \
							label = team[i].Name, vmin = fy, vmax = ly)

		if i == 0:
			X = x
			Y = y
		else:
			X = np.r_[X, x]
			Y = np.r_[Y, y]

	plt.colorbar(CF, ticks = list(np.arange(fy, ly + 1)), label = 'year')
	plt.legend(bbox_to_anchor = (1.35, 1), loc = 2, borderaxespad = 0., scatterpoints = 1)
	ax.set_title(title)
	ax.set_xlabel(X_name)
	ax.set_ylabel(Y_name)

	#Draw a regression line
	if regression_flg == 1:
		slope, intercept, r_value, _, _ = stats.linregress(X, Y)
		xx = np.arange(450, 750, 1)
		yy = slope * xx + intercept
		ax.plot(xx, yy, linewidth = 2)

	# y=Draw a straight line of x
	if Y_eq_X_line_flg == 1:
		xx = np.arange(450, 750, 1)
		yy_d = xx
		ax.plot(xx, yy_d, color = 'k')

	print 'Correlation=', np.corrcoef(X, Y)[0, 1]
	return plt

For example, if you want to retrieve the 2016 Central League data, do the following:

In [1]:import NPB
In [2]:Data_2016C=NPB.get_data('C',2016)   #When you want to be in the Pacific League'C'To'P'To.
In [3]:Data_2016C.Average  #Output the batting average of each of the 6 teams in the 2016 Central League

Out[3]: array([ 0.272,  0.256,  0.251,  0.249,  0.245,  0.245])
  1. Result 3.1. Average vs Score First, let's look at the correlation between the most common batting average, batting average, and the number of points scored. Take out the team data (144 samples in total) of all 12 teams from 2005 to 2016, and draw a scatter plot with "Batting average (Average)" on the horizontal axis and "Score" on the vertical axis. Try.
In [1]:import matplotlib.pyplot as plt
In [2]:Data_C=NPB.get_all_data('C')   #Extract all data from the Central League
In [3]:Data_P=NPB.get_all_data('P')   #Get all the Pacific League data
In [4]:Data=NPB.Docking(Data_C,Data_P) #Integrate data from both leagues
In [5]:plt=NPB.draw_scatter(plt,Data,'Average','Score') #Draw a scatter plot of batting average and score
In [6]:plt.show()

The output figure is as follows. image

Also, the correlation coefficient is Correlation= 0.825987845723 The result was that.

3.2. RC vs Score For the same data as 3.1., Now draw a scatter plot with "RC" on the horizontal axis and "Score" on the vertical axis.

In [7]:plt=NPB.draw_scatter(plt,Data,'RC','Score',regression_flg=1,Y_eq_X_line_flg=1) #Draw a scatter plot of RC and scores. Furthermore, the regression line and y=Draw a straight line of x.
In [8]:plt.show()

The output figure is as follows. image

Also, the correlation coefficient is Correlation= 0.953524104544 The result was that. From the value of the correlation coefficient, it can be seen that there is an extremely strong correlation between RC and the score. Furthermore, the regression line (blue line in the above figure) is very close to the straight line of "y = x" (black line in the above figure). (The regression line was y = 0.95 * x-6.3)

  1. Conclusion As a result of verifying with the past team data of NPB, it was found that the official score RC can predict the score number of the NPB team with extremely high accuracy. The RC formula devised by Bill James has now been improved in terms of coefficient values, etc., and the number of stolen bases is also used as an explanatory variable (see Wikipedia page [see below]). However, the great thing about the scoring formula devised by Bill James is that the score can be estimated accurately only by ** base ability (= number of hits + walks) x advance ability (= number of bases) **. I think. There are no coefficients on each explanatory variable, and the form of the equation is very simple. The fact that we discovered that we can estimate the number of points with such a simple formula is still worth noting.

References

-[Moneyball [Complete Edition](by Michael Lewis)](https://www.amazon.co.jp/s/ref=nb_sb_noss?__mk_ja_JP=%E3%82%AB%E3%82%BF% E3% 82% AB% E3% 83% 8A & url = search-alias% 3Daps & field-keywords =% E3% 83% 9E% E3% 83% 8D% E3% 83% BC% E3% 83% 9C% E3% 83% BC % E3% 83% AB) -Nippon Professional Baseball

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