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tennisSetProbability.py
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tennisSetProbability.py
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## 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)
## some results:
## http://summerofjeff.wordpress.com/2010/12/02/single-set-win-expectancy-tables/
from tennisGameProbability import gameProb
from tennisTiebreakProbability import tiebreakProb
def fact(x):
if x in [0, 1]: return 1
r = 1
for a in range(1, (x+1)): r = r*a
return r
def ch(a, b):
return fact(a)/(fact(b)*fact(a-b))
def setOutcome(final, sGames, rGames, vw, g, h):
pOutcome = 0
for j in range((sGames+1)):
for k in range((rGames+1)):
if (j + k) == (6 - 1 - vw):
m = sGames - j
n = rGames - k
p = (g**j)*(h**k)*((1-g)**m)*((1-h)**n)*ch(sGames,j)*ch(rGames,k)*final
pOutcome += p
else: continue
return pOutcome
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