/* Baseball example from Section 8.3 and Chapter 8, Exercise 4
*/
#include <iostream>
#include <iomanip>
#include <fstream>
#include <cmath>
using namespace std;
ofstream ans("baseball.ans");
const int r=18; /* Number of players */
const int n=45; /* Number of times at bat */
int main (void)
{
ans.setf(ios::showpoint);
int i;
double Xbar,Ybar,S,lambda,MSP,MSE,MSEEfron,MSPEfron,Eff,EffP,
P0,S1,Mu,lambda1,MSP1,MSE1,MSEStein,MSPStein,Eff1,EffP1;
double Y[r],X[r],P[r],Ave[r],ML[r],Theta[r],Efron[r],
RetransEfron[r],Stein[r],RetransStein[r];
int M[r]={
18,17,16,15,14,14,13,12,11,11,10,10,10,10,10,9,8,7
};
int Atbats[r]={
367,426,521,275,418,466,586,138,510,
200,277,270,435,538,186,558,408, 70
};
int Hits[r]={
127,127,144, 61,114,126,154, 29,137,
46, 73, 69,132,142, 42,159,129, 14
};
char Name[r][12]={
"Clemente","F Robinson","F Howard", "Johnstone", "Berry",
"Spencer", "Kessinger", "L Alvardo","Santo", "Swoboda",
"Unser", "Williams", "Scott", "Petrocelli","E Rodriguez",
"Campaneris","Munson","Alvis"
};
char Team[r][6]={
"Pitts","Balt","Wash","Cal","Chi","Cal","Chi","Bos","Chi",
"NY","Wash","Chi","Bos","Bos","KC","Oak","NY","Mil"
};
char League [r][3]={
"NL","AL","AL","AL","AL","AL","NL","AL","NL",
"AL","AL","AL","AL","AL","AL","AL","AL","NL"
};
Xbar=Ybar=MSE=MSP=0;
for (i=0; i < r; i++)
{
Y[i]=double(M[i])/double(n);
X[i]=2*sqrt(double(n))*asin(sqrt(Y[i]));
Xbar+=X[i]/r;
Ybar+=Y[i]/r;
P[i]=double(Hits[i])/double(Atbats[i]);
Theta[i]=2*sqrt(double(n))*asin(sqrt(P[i]));
MSE+=(X[i]-Theta[i])*(X[i]-Theta[i])/r;
MSP+=(Y[i]-P[i])*(Y[i]-P[i])/r;
};
S=0;
for (i=0; i < r; i++)
S+=(X[i]-Xbar)*(X[i]-Xbar);
lambda=(r-3)/S;
ans << " i Name Team League Y P "
<< "Atbats X Theta" << endl;
for (i=0; i < r; i++)
{
ans << setw(2) << i+1 << " ";
ans.setf(ios::left);
ans << setw(12) << Name[i] << setw(6) << Team[i]
<< setw(3) << League[i] << " ";
ans.setf(ios::right);
ans << setw(6) << setprecision(3) << Y[i]
<< setw(6) << P[i]
<< setw(3) << Atbats[i] << " "
<< setw(6) << setprecision(4) << X[i]
<< setw(6) << Theta[i] << endl;
}
ans << endl;
MSEEfron=MSPEfron=0;
for (i=0; i < r; i++)
{
Ave[i]=P[i];
ML[i]=Y[i];
Efron[i]=lambda*Xbar+(1-lambda)*X[i];
RetransEfron[i]=sin(Efron[i]/(2*sqrt(double(n))))*
sin(Efron[i]/(2*sqrt(double(n))));
MSEEfron+=(Efron[i]-Theta[i])*(Efron[i]-Theta[i])/r;
MSPEfron+=(RetransEfron[i]-P[i])*(RetransEfron[i]-P[i])/r;
}
Eff=MSE/MSEEfron;
EffP=MSP/MSPEfron;
ans << " i Name Team League Ave ML RetransEfron"
<< endl;
for (i=0; i < r; i++)
{
ans << setw(2) << i+1 << " ";
ans.setf(ios::left);
ans << setw(12) << Name[i] << setw(6)
<< Team[i]
<< setw(3) << League[i] << " ";
ans.setf(ios::right);
ans << setw(6) << setprecision(3) << Ave[i] << setw(6)
<< ML[i] << setw(3) << RetransEfron[i] << endl;
}
ans << endl;
ans << "Ybar Xbar S lambda" << endl;
ans << Ybar << " " << Xbar << " " << S
<< " " << lambda << endl;
ans << endl;
ans << "MSE MSEEfron Eff MSP "
<< "MSPEfron EffP" << endl;
ans << setw(7) << setprecision(4) << MSE << " " << MSEEfron
<< " " << Eff << " " << setw(8) << MSP
<< " " << MSPEfron << " " << EffP << endl;
ans << endl;
/* Remainder of program concerns Chapter 8, Question 4 */
P0=0.25;
Mu=2*sqrt(double(n))*asin(sqrt(P0));
S1=0;
for (i=0; i < r; i++)
S1+=(X[i]-Mu)*(X[i]-Mu);
lambda1=(r-2)/S1;
MSEEfron=MSPEfron=0;
MSEStein=MSPStein=0;
for (i=0; i < r; i++)
{
Stein[i]=lambda1*Mu+(1-lambda1)*X[i];
RetransStein[i]=sin(Stein[i]/(2*sqrt(double(n))))*
sin(Stein[i]/(2*sqrt(double(n))));
MSEStein+=(Stein[i]-Theta[i])*(Stein[i]-Theta[i])/r;
MSPStein+=(RetransStein[i]-P[i])*(RetransStein[i]-P[i])/r;
}
Eff1=MSE/MSEStein;
EffP1=MSP/MSPStein;
ans << " i Name Team League Ave ML RetransStein"
<< endl;
for (i=0; i < r; i++)
{
ans << setw(2) << i+1 << " ";
ans.setf(ios::left);
ans << setw(12) << Name[i] << setw(6)
<< Team[i]
<< setw(3) << League[i] << " ";
ans.setf(ios::right);
ans << setw(6) << setprecision(3) << Ave[i] << setw(6)
<< ML[i] << setw(3) << RetransStein[i] << endl;
}
ans << endl;
ans << "Ybar Xbar S1 lambda1" << endl;
ans << Ybar << " " << Xbar << " " << S1
<< " " << lambda1 << endl;
ans << endl;
ans << "MSE MSEStein Eff1 MSP "
<< "MSPStein EffP1" << endl;
ans << setw(7) << setprecision(4) << MSE << " " << MSEStein
<< " " << Eff1 << " " << setw(8) << MSP
<< " " << MSPStein << " " << EffP1 << endl;
}
/* */