The OERA function resulting from a symbolic solution to the Cover/Keilers Offensive Earned Run Average equation set is enclosed by the horizontal lines. Save this file as a text file and edit out the html preceeding and following the C++ source code.

// oera_sym.c
// Copyright (c) 1997-1998 by John F. Jarvis
// This surce code may be freely copied and distributed as long as
// proper credit is given.
// This software is provided "as is" without any express or 
// implied warranties, including, without limitation, the implied
// warranties of merchantibility and fitness for a particular purpose.
#include <stdio.h>
 
// Offensive Earned Run Average
// Thomas M. Cover, Carroll W. Keilers
// Operations Reseach, Vol 25, No 5, Sep-Oct 1977 pp 729-740
// symbolic solution to equation set by S. King using Mathematica
 
typedef double basetype;
const int STATES = 24; // 3 outs only in symbolic function
 
double oera(int /* outs */,int pflag, double bf, double sn, double db,
	double tr, double hr, double bb, double *er)
{ // parameters:
  // outs: number of outs in an inning but ignored in this version
  // pflag: use != 0 value to obtain printing from the function
  // bf: batters facing pitching = at bats + walks
  // sn, db, tr, hr: numbers of singles, doubles, triples, home runs
  // bb: walks. can add hit by pitch counts here and to bf if desired
  // er: NULL or array long enough to store solution vector
  // return value is expected runs per game defined 9*e[0]
 double e[STATES];
 int i;
 
 basetype p1,p2,p3,p4,pb,p0;
 basetype p1e2,p1e3;
 basetype pbe2,pbe3;
 basetype p0e2;
 
 p1 = sn/bf; // probablities of each event
 p2 = db/bf;
 p3 = tr/bf;
 p4 = hr/bf;
 pb = bb/bf;
 p0 = 1.0 - (p1+p2+p3+p4+pb); // probability of an out
 if(p0<=0.0){
 	printf("oera p0 = %8.5f, <=0\n",p0);
 	return 0.0;
 }
 
 p1e2 = p1*p1;
 p1e3 = p1*p1e2;
 pbe2 = pb*pb;
 pbe3 = pb*pbe2;
 p0e2 = p0*p0;
 
e[0] = -1+1/p0-(2*(-1+p0))/p0-p2-p3-p0*(1+p0)*(p2+p3)-pb-(p2+p3+p0*(1+p0
+2*p2+3*p0*p2+2*p3+3*p0*p3))*pb-(1+p2+p3+p0*(2+3*p2+3*p3+p0*(3+6*p2+6*p3
)))*pbe2-(1+3*p0+6*p0e2)*pbe3-p1*(1+p0+p0e2+2*(1+p0*(2+3*p0))*pb+2*(1+3
*p0+6*p0e2)*pbe2)-p1e2*(1+pb+p0*(2+3*pb+p0*(3+6*pb)));
 
e[1] = -1+1/p0-(2*(-1+p0))/p0+p4+p0*p4+p0e2*p4+(-1+p4+p0*(-1-p0+2*p4+3*
p0*p4))*pb+(-1+p4+p0*(-2+3*p4+p0*(-3+6*p4)))*pbe2+p1*((-1+p2+p3+p4)*
(1+pb)+p0*(-1+2*p2+2*p3+2*p4-2*pb+3*(p2+p3+p4)*pb)+p0e2*(-1+3*p2+3*p3+
3*p4-3*pb+6*(p2+p3+p4)*pb));
 
e[2] = e[4]=  -1+1/p0-(2*(-1+p0))/p0+p4+p0*p4+p0e2*p4+(-1+p4+p0*(-1-p0+2*
p4+3*p0*p4))*pb+(-1+p4+p0*(-2+3*p4+p0*(-3+6*p4)))*pbe2-p1e2*(1+pb+p0*(2+
3*pb+p0*(3+6*pb)))-p1*pb*(1+pb+p0*(2+3*pb+p0*(3+6*pb)));
 
e[3] = e[5] = -1+1/p0-(2*(-1+p0))/p0+(2+p1+p0*(2+2*p0+2*p1+3*p0*p1))*p4-pb+(-(
p0*(1+p0))+(2+p1+p0*(4+3*p1+6*p0*(1+p1)))*p4)*pb+(1+3*p0+6*p0e2)*p4*pbe2
+(p2+p3)*(1+p1+p0*(1+p0+2*p1+3*p0*p1)+pb+(p1+p0*(2+3*p0+3*p1+6*p0*p1))*pb);
 
e[6] = -1+1/p0-(2*(-1+p0))/p0+p2+p3+2*p4+p0*(1+p0)*(p2+p3+2*p4)-pb+(p2+p3+
2*p4+p0*(-1+2*p2+2*p3+4*p4+p0*(-1+3*p2+3*p3+6*p4)))*pb+(1+3*p0+6*p0e2)*
p4*pbe2+p1*(1+p0+p0e2-(1+3*p0+6*p0e2)*pbe2)-p1e2*(1+pb+p0*(2+3*pb+p0*(3+6*pb)));
 
e[7] = -1+1/p0-(2*(-1+p0))/p0+2*p2+2*p3+3*p4+p0*(1+p0)*(2*(p2+p3)+3*p4)+
(1+p0*(2+3*p0))*(p2+p3+2*p4)*pb+(1+3*p0+6*p0e2)*p4*pbe2+p1*(1+p2+p3+p4+p0*
(1+2*p2+2*p3+2*p4+p0*(1+3*p2+3*p3+3*p4))+(1+3*p0+6*p0e2)*(p2+p3+p4)*pb);
 
e[8] = -1+1/p0-(-1+p0)/p0-p2-p0*p2-p3-p0*p3-(1+p0+p2+2*p0*p2+p3+2*p0*p3)*
pb-(1+p2+p3+p0*(2+3*p2+3*p3))*pbe2-(1+3*p0)*pbe3-p1e2*(1+pb+p0*(2+3*pb))-
p1*(1+2*pb*(1+pb)+p0*(1+4*pb+6*pbe2));
 
e[9] = -1+1/p0-(-1+p0)/p0+p4+p0*p4+(-1-p0+p4+2*p0*p4)*pb+(-1+p4+p0*
(-2+3*p4))*pbe2+p1*((-1+p2+p3+p4)*(1+pb)+p0*(-1+2*p2+2*p3+2*p4-2*pb+
3*(p2+p3+p4)*pb));
 
e[10] = e[12] = -1+1/p0-(-1+p0)/p0+p4+p0*p4+(-1-p0+p4+2*p0*p4)*pb+(-1+p4
+p0*(-2+3*p4))*pbe2-p1e2*(1+pb+p0*(2+3*pb))-p1*pb*(1+pb+p0*(2+3*pb));
 
e[11] = e[13] = -1+1/p0-(-1+p0)/p0+(2+p1+2*p0*(1+p1))*p4-pb+(-p0+(2+p1+
p0*(4+3*p1))*p4)*pb+(1+3*p0)*p4*pbe2+p2*(1+p0+p1+2*p0*p1+(1+2*p0+p1+3*
p0*p1)*pb)+p3*(1+p0+p1+2*p0*p1+(1+2*p0+p1+3*p0*p1)*pb);
 
e[14] = -1+1/p0-(-1+p0)/p0+p2+p0*p2+p3+p0*p3+2*p4+2*p0*p4+(-1+p2+p3+
2*p4+p0*(-1+2*p2+2*p3+4*p4))*pb+(1+3*p0)*p4*pbe2+p1*(1+p0-(1+3*p0)*pbe2)-
p1e2*(1+pb+p0*(2+3*pb));
 
e[15] = -1+1/p0-(-1+p0)/p0+2*p2+2*p3+2*p0*(p2+p3)+3*p4+3*p0*p4+(1+2*p0)
*(p2+p3+2*p4)*pb+(1+3*p0)*p4*pbe2+p1*(1+p0+p2+2*p0*p2+p3+2*p0*p3+p4+2*p0
*p4+(1+3*p0)*(p2+p3+p4)*pb);
 
e[16] = -1+1/p0-p2-p3-pb-p1e2*(1+pb)-pb*(1+pb)*(p2+p3+pb)-p1*(1+2*pb*(1+pb));
 
e[17] = -1+1/p0+p1*(-1+p2+p3+p4)*(1+pb)-pb*(1+pb)+p4*(1+pb+pbe2);
 
e[18] = e[20] = -1+1/p0-p1e2*(1+pb)-pb*(1+pb)-p1*pb*(1+pb)+p4*(1+pb+pbe2);
 
e[19] = e[21] = -1+1/p0-pb+(1+p1)*p2*(1+pb)+(1+p1)*p3*(1+pb)+p4*(2+p1+(2+p1)*pb+pbe2);
 
e[22] = -1+1/p0+p1+p2+p3+2*p4-pb-p1*pbe2-p1e2*(1+pb)+pb*(p2+p3+p4*(2+pb));
 
e[23] = -1+1/p0+3*p4+p2*(2+pb)+(2+pb)*(p3+p4*pb)+p1*(1+p2+p3+p4+(p2+p3+p4)*pb);
 
if(pflag != 0){
 	printf("bf %6.0f sn %6.0f db %6.0f tr %6.0f hr %6.0f bb %6.0f\n",bf,sn,db,tr,hr,bb);
 	printf("p0 %6.4f p1 %6.4f p2 %6.4f p3 %6.4f p4 %6.4f pb %6.4f\n",p0,p1,p2,p3,p4,pb);
 	printf("outs ");
 	for(i=0;i<8;i++) printf("   %1d%1d%1d  ",i&01, (i&02)>>1, (i&04)>>2);
 	for(i=0;i<STATES;i++){
 		if((i%8)==0) printf("\n %1d  ",i/8);
 		printf(" %7.5f",e[i]);
 	}
 	printf("\n");
 }
 if(er!=NULL) for(i=0;i<STATES;i++) er[i] = e[i];
 
 return 9.0*e[0];
}
.