Find win expectancy and volatility given inning, out, base, run situation.

wpaCalc.py

## Find win expectancy and volatility given inning, out, base, run situation.

## no. of runs that score with HR in diff. base situations
baseHr = {1: 1,
          2: 2,
          3: 2,
          4: 3,
          5: 2,
          6: 3,
          7: 3,
          8: 4
          }
    
tangoRunExp = {'60': {1: 0.51400000000000001, 2: 0.19400000000000001, 3: 0.14999999999999999, 4: 0.076999999999999999, 5: 0.036999999999999998, 6: 0.017000000000000001, 7: 0.0060000000000000001, 8: 0.0030000000000000001, 9: 0.001, 10: 0.001, 'm': -0.216, 'b': 0.247}, '61': {1: 0.59599999999999997, 2: 0.17599999999999999, 3: 0.13200000000000001, 4: 0.057000000000000002, 5: 0.024, 6: 0.0089999999999999993, 7: 0.0040000000000000001, 8: 0.001, 9: 0.0, 10: 0.0, 'm': -0.11600000000000001, 'b': 0.40600000000000003}, '62': {1: 0.55900000000000005, 2: 0.20599999999999999, 3: 0.158, 4: 0.051999999999999998, 5: 0.017000000000000001, 6: 0.0050000000000000001, 7: 0.002, 8: 0.001, 9: 0.0, 10: 0.0, 'm': -0.19900000000000001, 'b': 0.82799999999999996}, '82': {1: 0.27300000000000002, 2: 0.35499999999999998, 3: 0.17000000000000001, 4: 0.13800000000000001, 5: 0.041000000000000002, 6: 0.014999999999999999, 7: 0.0050000000000000001, 8: 0.001, 9: 0.0, 10: 0.0, 'm': -0.20899999999999999, 'b': 0.78900000000000003}, '80': {1: 0.311, 2: 0.247, 3: 0.17000000000000001, 4: 0.14399999999999999, 5: 0.070999999999999994, 6: 0.031, 7: 0.012999999999999999, 8: 0.0080000000000000002, 9: 0.0030000000000000001, 10: 0.002, 'm': -0.127, 'b': 0.193}, '81': {1: 0.39700000000000002, 2: 0.24399999999999999, 3: 0.151, 4: 0.123, 5: 0.050999999999999997, 6: 0.021000000000000001, 7: 0.0080000000000000002, 8: 0.0030000000000000001, 9: 0.001, 10: 0.0, 'm': -0.14199999999999999, 'b': 0.40200000000000002}, '20': {1: 0.42399999999999999, 2: 0.29899999999999999, 3: 0.14999999999999999, 4: 0.071999999999999995, 5: 0.032000000000000001, 6: 0.012999999999999999, 7: 0.0050000000000000001, 8: 0.002, 9: 0.001, 10: 0.0, 'm': -0.27800000000000002, 'b': 0.71599999999999997}, '21': {1: 0.44400000000000001, 2: 0.32600000000000001, 3: 0.13700000000000001, 4: 0.056000000000000001, 5: 0.021999999999999999, 6: 0.0089999999999999993, 7: 0.0030000000000000001, 8: 0.001, 9: 0.0, 10: 0.0, 'm': -0.26800000000000002, 'b': 0.86299999999999999}, '22': {1: 0.45300000000000001, 2: 0.374, 3: 0.11600000000000001, 4: 0.039, 5: 0.012, 6: 0.0050000000000000001, 7: 0.001, 8: 0.0, 9: 0.0, 10: 0.0, 'm': -0.19400000000000001, 'b': 0.97399999999999998}, '42': {1: 0.49399999999999999, 2: 0.23699999999999999, 3: 0.18099999999999999, 4: 0.059999999999999998, 5: 0.017999999999999999, 6: 0.0070000000000000001, 7: 0.002, 8: 0.001, 9: 0.0, 10: 0.0, 'm': -0.14399999999999999, 'b': 0.84099999999999997}, '40': {1: 0.36199999999999999, 2: 0.25600000000000001, 3: 0.19400000000000001, 4: 0.104, 5: 0.048000000000000001, 6: 0.02, 7: 0.0089999999999999993, 8: 0.0040000000000000001, 9: 0.002, 10: 0.001, 'm': -0.16700000000000001, 'b': 0.45000000000000001}, '41': {1: 0.40100000000000002, 2: 0.25800000000000001, 3: 0.20300000000000001, 4: 0.083000000000000004, 5: 0.034000000000000002, 6: 0.012999999999999999, 7: 0.0050000000000000001, 8: 0.002, 9: 0.001, 10: 0.0, 'm': -0.17399999999999999, 'b': 0.66900000000000004}, '72': {1: 0.185, 2: 0.54800000000000004, 3: 0.16900000000000001, 4: 0.067000000000000004, 5: 0.023, 6: 0.0060000000000000001, 7: 0.002, 8: 0.0, 9: 0.0, 10: 0.0, 'm': -0.095000000000000001, 'b': 0.78500000000000003}, '71': {1: 0.41299999999999998, 2: 0.32800000000000001, 3: 0.13800000000000001, 4: 0.072999999999999995, 5: 0.029000000000000001, 6: 0.010999999999999999, 7: 0.0050000000000000001, 8: 0.002, 9: 0.001, 10: 0.0, 'm': -0.311, 'b': 0.47799999999999998}, '70': {1: 0.315, 2: 0.35599999999999998, 3: 0.16800000000000001, 4: 0.085999999999999993, 5: 0.043999999999999997, 6: 0.017999999999999999, 7: 0.0070000000000000001, 8: 0.0040000000000000001, 9: 0.002, 10: 0.0, 'm': -0.22900000000000001, 'b': 0.26100000000000001}, '11': {1: 0.59999999999999998, 2: 0.24299999999999999, 3: 0.097000000000000003, 4: 0.036999999999999998, 5: 0.014, 6: 0.0060000000000000001, 7: 0.002, 8: 0.001, 9: 0.0, 10: 0.0, 'm': -0.29599999999999999, 'b': 0.98799999999999999}, '12': {1: 0.67300000000000004, 2: 0.222, 3: 0.070999999999999994, 4: 0.023, 5: 0.0070000000000000001, 6: 0.002, 7: 0.001, 8: 0.0, 9: 0.0, 10: 0.0, 'm': -0.16300000000000001, 'b': 1.014}, '32': {1: 0.68600000000000005, 2: 0.20399999999999999, 3: 0.072999999999999995, 4: 0.025000000000000001, 5: 0.0080000000000000002, 6: 0.002, 7: 0.001, 8: 0.0, 9: 0.0, 10: 0.0, 'm': -0.107, 'b': 0.83199999999999996}, '31': {1: 0.59399999999999997, 2: 0.23400000000000001, 3: 0.104, 4: 0.042000000000000003, 5: 0.017000000000000001, 6: 0.0060000000000000001, 7: 0.0030000000000000001, 8: 0.001, 9: 0.0, 10: 0.0, 'm': -0.191, 'b': 0.69299999999999995}, '30': {1: 0.56599999999999995, 2: 0.22600000000000001, 3: 0.114, 4: 0.052999999999999999, 5: 0.023, 6: 0.01, 7: 0.0040000000000000001, 8: 0.002, 9: 0.001, 10: 0.0, 'm': -0.35799999999999998, 'b': 0.55900000000000005}, '51': {1: 0.73699999999999999, 2: 0.152, 3: 0.067000000000000004, 4: 0.027, 5: 0.010999999999999999, 6: 0.0040000000000000001, 7: 0.001, 8: 0.001, 9: 0.0, 10: 0.0, 'm': -0.27000000000000002, 'b': 0.47699999999999998}, '50': {1: 0.65400000000000003, 2: 0.185, 3: 0.088999999999999996, 4: 0.041000000000000002, 5: 0.017999999999999999, 6: 0.0080000000000000002, 7: 0.0030000000000000001, 8: 0.001, 9: 0.001, 10: 0.0, 'm': -0.37, 'b': 0.35499999999999998}, '52': {1: 0.73199999999999998, 2: 0.17699999999999999, 3: 0.059999999999999998, 4: 0.021000000000000001, 5: 0.0070000000000000001, 6: 0.002, 7: 0.001, 8: 0.0, 9: 0.0, 10: 0.0, 'm': -0.047, 'b': 0.76300000000000001}}

def getRunsInn(rpinn):
    runsinn = {0:   1/((rpinn*.761)+1),
               1:   (rpinn*(0.761**2))/(((rpinn*.761)+1)**2)
               }

    for i in range(2, 11):
        v = (rpinn*(0.761**2)*(((rpinn*.761) - 0.761 + 1)**(i-1)))/(((rpinn*.761)+1)**(i+1))
        runsinn[i] = v
    return runsinn


def getRunExp(rpinn, runsinn):
    runExp = {'10': runsinn
              }
    for i in range(0, 3):
        for j in range(1, 9):
            k = str(j) + str(i)
            if k == '10':   continue
            runExp[k] = {0: ((tangoRunExp[k]['m']*rpinn) + tangoRunExp[k]['b'])
                         }
            for r in range(1, 11):
                runExp[k][r] = ((1 - runExp[k][0])*tangoRunExp[k][r])
    return runExp

def getInnWinexp(runExp):
    ## Chance of home team winning with zero
    ## outs at the beg. of each inning

    innWinexp = {'101': {0: 0.5
                      }
              }

    for i in range(-25, 0):
        innWinexp['101'][i] = 0
    for i in range(1, 26):
        innWinexp['101'][i] = 1

    for i in range(9, 0, -1):
        for j in range(2, 0, -1):
            if j == 2:  next = str(i+1) + '1'
            else:   next = str(i) + '2'
            this = str(i) + str(j)
            innWinexp[this] = {}
            if j == 2:
                for k in range(-25, 26):
                    p = 0
                    if i == 9 and k > 0:
                        innWinexp[this][k] = 1
                        continue
                    else:   pass
                    for m in range(0, 11):
                        if k+m > 25:    iw = 1
                        else:   iw = innWinexp[next][k+m]
                        p += runExp['10'][m]*iw
                    innWinexp[this][k] = p
            else:
                for k in range(-25, 26):
                    p = 0
                    for m in range(0, 11):
                        if k-m < -25:   iw = 0
                        else:   iw = innWinexp[next][k-m]
                        p += runExp['10'][m]*iw
                    innWinexp[this][k] = p
    return innWinexp


def getWinexp(innWinexp, runExp, inn, half, base, outs, rdiff):    
    if inn > 9: inn = 9
    innkey = str(inn) + str(half)
    if outs > 2:    outs = 2
    sitkey = str(base) + str(outs)
    if half == 2:  next = str(inn+1) + '1'
    else:   next = str(inn) + '2'
    if sitkey == '10':  ## beginning of half inning
        if rdiff > 25:  rdiff = 25
        elif rdiff < -25:   rdiff = -25
        else:   pass
        Winexp = innWinexp[innkey][rdiff]
    elif half == 1:
        Winexp = 0
        for i in range(10, -1, -1):
            if rdiff-i < -25:   iw = 0
            elif rdiff-i > 25:  iw = 1
            else:   iw = innWinexp[next][rdiff-i]
            Winexp += runExp[sitkey][i]*iw
    else:
        Winexp = 0
        for i in range(0, 11):
            if rdiff-i < -25:   iw = 0
            elif rdiff+i > 25:   iw = 1
            else:   iw = innWinexp[next][rdiff+i]
            Winexp += runExp[sitkey][i]*iw
    return Winexp

def getVol(innWinexp, runExp, inn, half, base, outs, rdiff):
    ## changes if strikeout:
    if outs == 2:
        outsK = 0
        baseK = 1
        if half == 1:
            halfK = 2
            innK = inn
        else:
            halfK = 1
            innK = inn + 1
    else:
        outsK = outs + 1
        baseK, halfK, innK = base, half, inn
    WinexpK = getWinexp(innWinexp, runExp, innK, halfK, baseK, outsK, rdiff)
    ## changes if homerun
    if half == 1:
        rdiff -= baseHr[base]
    else:
        rdiff += baseHr[base]
    base = 1
    WinexpHr = getWinexp(innWinexp, runExp, inn, half, base, outs, rdiff)
    return (abs(WinexpHr - WinexpK))/0.133

def rpgToInnWinexp(rpg):
    rpinn = float(rpg)/9 ## r/inn
    runsinn = getRunsInn(rpinn)
    runExp = getRunExp(rpinn, runsinn)
    innWinexp = getInnWinexp(runExp)
    return innWinexp, runExp

####sample usage
##inn = 2
##half = 1 ## 1 = top, 2 = bottom
##base = 1 ## base situation: 1 through 8
##outs = 2
##rdiff = 2 ## run differential from home team perspective
##
##rpg = 4.5 ## runs per team-game
##innWinexp, runExp = rpgToInnWinexp(rpg)
##
##winexp = getWinexp(innWinexp, runExp, inn, half, base, outs, rdiff)
##
##vol = getVol(innWinexp, runExp, inn, half, base, outs, rdiff)
##
##print winexp, lev

In the very unlikely event anything further happens with this, it lives in this repo:
https://github.com/JeffSackmann/baseball_misc