def matchProb(s, t, gv=0, gw=0, sv=0, sw=0, mv=0, mw=0, sets=3):
## calculates probability of winning a match from any given score,
## given:
## s, t: p(server wins a service point), p(server wins return point)
## gv, gw: current score within the game. e.g. 30-15 is 2, 1
## sv, sw: current score within the set. e.g. 5, 4
## mv, mw: current score within the match (number of sets for each player)
## v's are serving player; w's are returning player
## sets: "best of", so default is best of 3
a = gameProb(s)
b = gameProb(t)
c = setGeneral(s, t)
#print 'set prob: ',c[0]
if gv == 0 and gw == 0: ## no point score
if sv == 0 and sw == 0: ## no game score
#print 'mwin: ', matchGeneral(c[0], v=mv, w=mw, s=sets)
return matchGeneral(c[0], v=mv, w=mw, s=sets)
else: ## we're in mid-set, no point score
sWin = setGeneral(s, t, v=sv, w=sw)[0]
sLoss = 1 - sWin
elif sv == 6 and sw == 6:
sWin = tiebreakProb(s, t, v=gv, w=gw)
sLoss = 1 - sWin
else:
gWin = gameProb(s, v=gv, w=gw)
gLoss = 1 - gWin
sWin = gWin*(1 - setGeneral(1-t, 1-s, v=sw, w=sv+1)[0])
sWin += gLoss*(1 - setGeneral(1-t, 1-s, v=sw+1, w=sv)[0])
sLoss = 1 - sWin
mWin = sWin*matchGeneral(c[0], v=mv+1, w=mw, s=sets)
mWin += sLoss*matchGeneral(c[0], v=mv, w=mw+1, s=sets)
#print 'mwin: ', mWin
return mWin
def matchProb(s, t, gv=0, gw=0, sv=0, sw=0, mv=0, mw=0, sets=3):
## calculates probability of winning a match from any given score,
## given:
## s, t: p(server wins a service point), p(server wins return point)
## gv, gw: current score within the game. e.g. 30-15 is 2, 1
## sv, sw: current score within the set. e.g. 5, 4
## mv, mw: current score within the match (number of sets for each player)
## v's are serving player; w's are returning player
## sets: "best of", so default is best of 3
a = gameProb(s)
b = gameProb(t)
c = setGeneral(s, t)
if gv == 0 and gw == 0: ## no point score
if sv == 0 and sw == 0: ## no game score
return matchGeneral(c, v=mv, w=mw, s=sets)
else: ## we're in mid-set, no point score
sWin = setGeneral(a, b, s, t, v=sv, w=sw)
sLoss = 1 - sWin
elif sv == 6 and sw == 6:
sWin = tiebreakProb(s, t, v=gv, w=gw)
sLoss = 1 - sWin
else:
gWin = gameProb(s, v=gv, w=gw)
gLoss = 1 - gWin
sWin = gWin*(1 - setGeneral((1-b), (1-a), (1-t), (1-s), v=sw, w=(sv+1)))
sWin += gLoss*(1 - setGeneral((1-b), (1-a), (1-t), (1-s), v=(sw+1), w=sv))
sLoss = 1 - sWin
mWin = sWin*matchGeneral(c, v=(mv+1), w=mw, s=sets)
mWin += sLoss*matchGeneral(c, v=mv, w=(mw+1), s=sets)
return mWin
def setGeneral(s, u, v=0, w=0, tb=1):
## calculate the probability of the current server winning
## a 6-game, tiebreak set, given prob. of server winning any
## given service point (s) or return point (u), and the current
## game score (v, w)
## get prob of current server winning a service game:
g = gameProb(s)
## and current server winning a return game:
h = gameProb(u)
## is set over?
if tb:
if v == 7: return 1
elif w == 7: return 0
elif v == 6 and (v-w) > 1: return 1
elif w == 6 and (w-v) > 1: return 0
else: pass
else:
if v >= 6 and (v-w) > 1: return 1
elif w >= 6 and (w-v) > 1: return 0
else: pass
## if not over, re-adjust down to no higher than 6-6
while True:
if (v+w) > 12:
v -= 1
w -= 1
else: break
## if no tiebreak, chance that server wins set is ratio of server's prob of winning
## two games in a row to returner's prob of winning two games in a row
if not tb: deuceprob = (g*h)/((g*h) + (1-g)*(1-h))
outcomes = {}
## special cases, 11 games or more already
if (v+w) == 12:
if tb:
tp = tiebreakProb(s, u)
outcomes['76'] = tp
outcomes['67'] = 1 - tp
else:
outcomes['75'] = deuceprob
outcomes['57'] = 1-deuceprob
elif (v+w) == 11:
if tb:
tp = tiebreakProb((1-u), (1-s))
if v == 6:
outcomes['75'] = g
x = (1-g)
outcomes['76'] = x*(1 - tp)
outcomes['67'] = x*tp
else:
outcomes['57'] = 1-g
x = g
outcomes['76'] = x*(1 - tp)
outcomes['67'] = x*tp
else:
if v == 6:
outcomes['75'] = g
outcomes['57'] = 0
f = 1 - g ## f is p(getting to 6-6)
else:
outcomes['57'] = 1-g
outcomes['75'] = 0
f = g ## f is p(getting to 6-6)
outcomes['75'] += f*deuceprob
outcomes['57'] += f*(1-deuceprob)
else:
## win probabilities
for i in range(5): ## i = 0
t = 6 + i - v - w ## total games remaining in set
if t < 1: continue
if t % 2 == 0:
final = h
sGames = t/2
rGames = sGames - 1
else:
final = g
sGames = (t-1)/2
rGames = (t-1)/2
pOutcome = setOutcome(final, sGames, rGames, v, g, h)
key = '6' + str(i)
outcomes[key] = pOutcome
## loss probabilities
## this section isn't necessary, but I wrote it for informal
## testing purposes
for i in range(5):
t = 6 + i - v - w ## total games in set; here it's 6
if t < 1: continue
if t % 2 == 0:
final = 1-h
sGames = t/2
rGames = sGames - 1
else:
final = 1-g
sGames = (t-1)/2
rGames = (t-1)/2
pOutcome = setOutcome(final, sGames, rGames, w, (1-g), (1-h))
key = str(i) + '6'
outcomes[key] = pOutcome
## prob of getting to 5-5
t = 10 - v - w
if t % 2 == 0:
sGames = t/2
rGames = t/2
else:
sGames = (t-1)/2 + 1
rGames = (t-1)/2
f = setOutcome(1, sGames, rGames, v, g, h)
if tb == 1:
outcomes['75'] = f*g*h
outcomes['57'] = f*(1-g)*(1-h)
x = f*g*(1-h) + f*(1-g)*h ## p(getting to 6-6)
if (v+w) % 2 == 0:
tp = tiebreakProb(s, u)
else:
tp = tiebreakProb(u, s)
outcomes['76'] = x*tp
outcomes['67'] = x - x*tp
else:
outcomes['75'] = f*deuceprob
outcomes['57'] = f*(1-deuceprob)
win = 0
for o in outcomes:
if o in ['60', '61', '62', '63', '64', '75', '76']:
win += outcomes[o]
else: pass
return win, outcomes
def setGeneral(s, u, v=0, w=0, tb=1):
## calculate the probability of the current server winning
## a 6-game, tiebreak set, given prob. of server winning any
## given service point (s) or return point (u), and the current
## game score (v, w)
## get prob of current server winning a service game:
__ = '' # dummy variable to address type issues
g = gameProb(s)
## and current server winning a return game:
h = gameProb(u)
## is set over?
if tb:
if v == 7: return 1, __
elif w == 7: return 0, __
elif v == 6 and (v - w) > 1: return 1, __
elif w == 6 and (w - v) > 1: return 0, __
else: pass
else:
if v >= 6 and (v - w) > 1: return 1, __
elif w >= 6 and (w - v) > 1: return 0, __init__
else: pass
## if not over, re-adjust down to no higher than 6-6
while True:
if (v + w) > 12:
v -= 1
w -= 1
else:
break
## if no tiebreak, chance that server wins set is ratio of server's prob of winning
## two games in a row to returner's prob of winning two games in a row
if not tb: deuceprob = (g * h) / ((g * h) + (1 - g) * (1 - h))
outcomes = {}
## special cases, 11 games or more already
if (v + w) == 12:
if tb:
tp = tiebreakProb(s, u)
outcomes['76'] = tp
outcomes['67'] = 1 - tp
else:
outcomes['75'] = deuceprob
outcomes['57'] = 1 - deuceprob
elif (v + w) == 11:
if tb:
tp = tiebreakProb((1 - u), (1 - s))
if v == 6:
outcomes['75'] = g
x = (1 - g)
outcomes['76'] = x * (1 - tp)
outcomes['67'] = x * tp
else:
outcomes['57'] = 1 - g
x = g
outcomes['76'] = x * (1 - tp)
outcomes['67'] = x * tp
else:
if v == 6:
outcomes['75'] = g
outcomes['57'] = 0
f = 1 - g ## f is p(getting to 6-6)
else:
outcomes['57'] = 1 - g
outcomes['75'] = 0
f = g ## f is p(getting to 6-6)
outcomes['75'] += f * deuceprob
outcomes['57'] += f * (1 - deuceprob)
else:
## win probabilities
for i in range(5): ## i = 0
t = 6 + i - v - w ## total games remaining in set
if t < 1: continue
if t % 2 == 0:
final = h
sGames = t / 2
rGames = sGames - 1
else:
final = g
sGames = (t - 1) / 2
rGames = (t - 1) / 2
pOutcome = setOutcome(final, sGames, rGames, v, g, h)
key = '6' + str(i)
outcomes[key] = pOutcome
## loss probabilities
## this section isn't necessary, but I wrote it for informal
## testing purposes
for i in range(5):
t = 6 + i - v - w ## total games in set; here it's 6
if t < 1: continue
if t % 2 == 0:
final = 1 - h
sGames = t / 2
rGames = sGames - 1
else:
final = 1 - g
sGames = (t - 1) / 2
rGames = (t - 1) / 2
pOutcome = setOutcome(final, sGames, rGames, w, (1 - g), (1 - h))
key = str(i) + '6'
outcomes[key] = pOutcome
## prob of getting to 5-5
t = 10 - v - w
if t % 2 == 0:
sGames = t / 2
rGames = t / 2
else:
sGames = (t - 1) / 2 + 1
rGames = (t - 1) / 2
f = setOutcome(1, sGames, rGames, v, g, h)
if tb == 1:
outcomes['75'] = f * g * h
outcomes['57'] = f * (1 - g) * (1 - h)
x = f * g * (1 - h) + f * (1 - g) * h ## p(getting to 6-6)
if (v + w) % 2 == 0:
tp = tiebreakProb(s, u)
else:
tp = tiebreakProb(u, s)
outcomes['76'] = x * tp
outcomes['67'] = x - x * tp
else:
outcomes['75'] = f * deuceprob
outcomes['57'] = f * (1 - deuceprob)
win = 0
for o in outcomes:
if o in ['60', '61', '62', '63', '64', '75', '76']:
win += outcomes[o]
else:
pass
return win, outcomes