class EloRanker(TimeSeriesRanker):
"""
Elo Ranker is a traditional ranking algorithm adjusting player's rating by a series of gaming results.
All players starts from 1500 first, and after each paired contest, two player's ranking will be updated in such a way that the sum of their ranking does not change.
Parameters
----------
K: amount of weight to be applied to each update.
xi: somewhat related to "performance variance", the larger value assumes a more violent game performance and the ranking change will be more conservative.
baseline: the initial ranking of each player.
drawMargin: if the score difference is smaller or equal than drawMargin, this turn of game will be considered as draw. A draw will also effect player's rating.
"""
def __init__(self, K=10, xi=400, baseline=1500, drawMargin=0):
self.K = K
self.xi = xi
self.baseline = baseline
self.drawMargin = drawMargin
self.data = Table()
self.indexScoreLut = []
def setup(self, itemRatingLut=dict()):
"""
Setup the initial state of EloRanker with existing Rating.
This function is used in where prior information is given about competitiors, and one wants to continue ranking on that.
Parameters
----------
itemRatingLut: a dictionary working as player's name to rating look up table.
"""
if len(itemRatingLut) != 0:
# derive itemlut, indexlut and itemnum from itmScoreLut to setup self.data
itemnum = len(itemRatingLut)
itemlut = dict() # from item to index
indexlut = [] # from index to item
for i, itm in enumerate(itemRatingLut.items()):
k, v = itm
itemlut[i] = k
indexlut.append(k)
self.indexScoreLut.append(v)
self.data.setup(itemlut, indexlut, itemnum)
# TODO: should one infer baseline from itemscoreLut here?
elif self.data.itemnum == 0:
self.indexScoreLut = []
def update_single(self, host, visit, hscore, vscore, time=""):
"""
Update rating based on a single record.
Parameters
----------
host: name of host player
visit: name of visit player
hscore: score of host player
vscore: score of visit player
time: timestamp of the game. Should be numerical value. Default set to empty string.
Return
------
Tuple of (newHostRating, newVisitRating)
"""
self.data.update_single(host, visit, hscore, vscore, time=time)
ih = self.data.itemlut[host]
iv = self.data.itemlut[visit]
if ih >= len(self.indexScoreLut):
self.indexScoreLut.append(self.baseline)
if iv >= len(self.indexScoreLut):
self.indexScoreLut.append(self.baseline)
rh = self.indexScoreLut[ih]
rv = self.indexScoreLut[iv]
xi, K = self.xi, self.K
s = 0.5 if abs(hscore - vscore) <= self.drawMargin else (
1 if hscore > vscore else 0)
phwin = 1 / (1 + 10**((rv - rh) / xi))
alpha = (abs(hscore - vscore) + 3)**0.8 / (7.5 + 0.0006 * (rh - rv))
delta = K * alpha * (s - phwin)
self.indexScoreLut[ih] += delta
self.indexScoreLut[iv] -= delta
return (self.indexScoreLut[ih], self.indexScoreLut[iv])
def update(self, table):
"""
Update rating based on a table of record.
Parameters
----------
table: a Table object, consisting of new records that has never been previously feed to the ranker.
"""
self.data.update(table)
self.indexScoreLut = self.indexScoreLut[:] + [self.baseline] * (
self.data.itemnum - len(self.indexScoreLut))
xi, K = self.xi, self.K
for rec in table.iteritem():
ih, iv, hscore, vscore = rec.indexHost, rec.indexVisit, rec.hscore, rec.vscore
rh = self.indexScoreLut[ih]
rv = self.indexScoreLut[iv]
s = 0.5 if abs(hscore - vscore) <= self.drawMargin else (
1 if hscore > vscore else 0)
phwin = 1 / (1 + 10**((rv - rh) / xi))
alpha = (abs(hscore - vscore) + 3)**0.8 / (7.5 + 0.0006 *
(rh - rv))
delta = K * alpha * (s - phwin)
self.indexScoreLut[ih] += delta
self.indexScoreLut[iv] -= delta
def prob_win(self, host, visit):
"""
Probability of host player wins over visit player.
Parameters
----------
host: name of host player
visit: name of visit player
Return
------
float: probability of winning.
"""
ih = self.data.itemlut.get(host, None)
iv = self.data.itemlut.get(visit, None)
rh = self.indexScoreLut[ih] if ih is not None else self.baseline
rv = self.indexScoreLut[iv] if iv is not None else self.baseline
return 1 / (1 + 10**((rv - rh) / self.xi))
def leaderboard(self, method="min"):
"""
Presenting current leaderboard.
Parameters
----------
method: method to process ranking value when rating is the same. See https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.Series.rank.html for more.
Return
------
pd.DataFrame: with column "name", "rating" and "rank".
"""
rtn = pd.DataFrame(
{
"name": self.data.indexlut,
"rating": self.indexScoreLut
},
columns=["name", "rating"])
rtn['rank'] = rtn.rating.rank(method=method,
ascending=False).astype(np.int32)
return rtn.sort_values(by=['rating', 'name'],
ascending=False).reset_index(drop=True)
class GlickoRanker(TimeSeriesRanker):
"""
Glicko 2 ranker. See more: http://www.glicko.net/glicko.html
Notice: different from previous rankers, Glicko algorithm involves a concept called "rating period". The update procedure is based on each rating period.
In order to specify rating period, one have to state clearly the timestamp in record. Records in the same timestamp will be updated as a batch.
If no timestamp is specified, the update algorithm will update the whole records in one batch.
Parameters
----------
baseline: the initial ranking value of new players. Default set to 1500.
rd: rating deviation, the possible deviation of a player. Default set to 350.
votality: this parameter is to measure the degree of expected fluctuation in a player's rating. Default set to 0.06.
tau: constrains the change of votality over time. The more enormous changes involved in your game, the lower tau should be. Default set to 0.5.
epsilon: parameter to control iteration. Default set to 1e-6.
darwMargin: if the score difference is smaller or equal than drawMargin, this turn of game will be considered as draw. Default set to 0.
"""
def __init__(self,
baseline=1500,
rd=350,
votality=0.06,
tau=0.5,
epsilon=0.000001,
drawMargin=0):
self.baseline = baseline
self.rd = rd
self.votality = votality
self.tau = tau
self.epsilon = epsilon
self.drawMargin = drawMargin
self.data = Table()
self.miu = [] # normalized rating
self.phi = [] # normalized rd
self.sigma = [] # votality
self.factor = 400 / math.log(10)
@staticmethod
def g(phi):
return 1 / (1 + 3 * phi**2 / PI**2)**(1 / 2)
@staticmethod
def E(miu, miut, phit):
g = GlickoRanker.g
return 1 / (1 + math.exp(g(phit) * (miut - miu)))
def volatility_iter(self, deltaSqr, phiSqr, sigma, votality):
epsilon, tau = self.epsilon, self.tau
f = lambda x: math.exp(x) * (deltaSqr - phiSqr - votality - math.exp(
x)) / 2 / (phiSqr + votality + math.exp(x))**2 - (x - math.log(
sigma**2)) / tau**2
A = 2 * math.log(sigma)
if deltaSqr > phiSqr + votality:
B = math.log(deltaSqr - phiSqr - votality)
else:
k = 1
while f(2 * math.log(sigma) - k * tau) < 0:
k += 1
B = 2 * math.log(sigma) - k * tau
fA = f(A)
fB = f(B)
while abs(B - A) > epsilon:
C = A + (A - B) * fA / (fB - fA)
fC = f(C)
if fC * fB < 0:
A = B
fA = fB
else:
fA = fA / 2
B = C
fB = fC
return math.exp(A / 2)
def setup(self,
itemRatingLut=dict(),
itemRDLut=dict(),
itemVolatilityLut=dict()):
"""
Setup the initial state of Glick 2 with existing rating and player deviation.
This function is used in where prior information is given about competitiors, and one wants to continue ranking on that.
Notice: one does not have to provide full look up table on every player: if a player exist in one look up table but doesn't in another one, corresponding parameter will be set to default value.
Parameters
----------
itemRatingLut: a dictionary working as player's name to rating look up table.
itemRDLut: a dictionary working as player's name to deviation look up table.
itemVolatilityLut: a dictionary working as player's name to volatility look up table.
"""
# TODO: By using this function, users have to know exactly the existing user rating, RD and volatility, which implies that source of information comes from saved data.
# So there must be a model saving function.
# Description: we assume that the user list is obtained by the union of key of all luts given.
# That implies the provided Rating/RD/Volatility don't have to be of same length: the unfilled items will be given default value.
player = set(itemRatingLut.keys())
player.update(itemRDLut.keys())
player.update(itemVolatilityLut.keys())
if len(player) != 0:
# derive itemlut, indexlut and itemnum from itmScoreLut to setup self.data
itemnum = len(player)
itemlut = dict() # from item to index
indexlut = [] # from index to item
miu = []
phi = []
sigma = []
for i, itm in enumerate(player):
itemlut[itm] = i
indexlut.append(itm)
miu.append(
(itemRatingLut.get(itm, self.baseline) - self.baseline) /
self.factor)
phi.append(itemRDLut.get(itm, self.rd) / self.factor)
sigma.append(itemVolatilityLut.get(itm, self.votality))
self.data.setup(itemlut, indexlut, itemnum)
# Then setup self.miu, phi and sigma
self.miu = miu
self.phi = phi
self.sigma = sigma
elif self.data.itemnum == 0:
self.miu = []
self.phi = []
self.sigma = []
def update_single_batch(self, dataFrame):
# check time info
g, E, volatility_iter, drawMargin = GlickoRanker.g, GlickoRanker.E, self.volatility_iter, self.drawMargin
self.data.update_raw(dataFrame, weightcol='weight', timecol='time')
if self.data.itemnum > len(self.miu):
self.miu = self.miu[:] + [0] * (self.data.itemnum - len(self.miu))
self.phi = self.phi[:] + [self.rd / self.factor
] * (self.data.itemnum - len(self.phi))
self.sigma = self.sigma[:] + [self.votality] * (self.data.itemnum -
len(self.sigma))
mtx = pd.DataFrame(
data={
'host': pd.concat([dataFrame.host, dataFrame.visit]),
'visit': pd.concat([dataFrame.visit, dataFrame.host]),
'hscore': pd.concat([dataFrame.hscore, dataFrame.vscore]),
'vscore': pd.concat([dataFrame.vscore, dataFrame.hscore]),
'time': pd.concat([dataFrame.time, dataFrame.time])
},
columns=['host', 'visit', 'hscore', 'vscore', 'time'
]).reset_index(drop=True).sort_values(by=['time', 'host'])
gx = dict()
players = set(mtx.host)
for host in players:
hidx = self.data.itemlut[host]
gx[hidx] = g(self.phi[hidx])
for recs in mtx.groupby(by='host'):
host, results = recs
hidx = self.data.itemlut[host]
vt = []
dt = []
for rec in results.itertuples(index=False):
vidx = self.data.itemlut[rec.visit]
s = 0.5 if abs(rec.hscore - rec.vscore) <= drawMargin else (
0 if rec.hscore < rec.vscore else 1)
ex = E(self.miu[hidx], self.miu[vidx], self.phi[vidx])
vt.append(gx[vidx]**2 * ex * (1 - ex))
dt.append(gx[vidx] * (s - ex))
v = 1 / sum(vt)
delta = v * sum(dt)
sigma_ = volatility_iter(delta**2, self.phi[hidx]**2,
self.sigma[hidx], self.votality)
phiSqr_ = (self.phi[hidx]**2 + sigma_**2)
self.phi[hidx] = 1 / (1 / phiSqr_ + 1 / v)**(1 / 2)
self.miu[hidx] += self.phi[hidx]**2 * sum(dt)
# for players not attended, their RD will increase.
for kv in self.data.itemlut.items():
player, idx = kv
if player not in players:
self.phi[idx] = math.sqrt(self.phi[idx]**2 +
self.sigma[idx]**2)
return
def update(self, table):
"""
Update rating based on a table of record.
Parameters
----------
table: a Table object, consisting of new records that has never been previously feed to the ranker.
"""
# Check time info
if self.data.table.shape[0] > 0 and self.data.table.time.iloc[
-1] is not None:
if table.table.time.iloc[0] is None:
warnings.warn(
"The table to be updated misses time information. In that case, the whole table record will be updated in a single rating period."
)
elif table.table.time.iloc[0] <= self.data.table.time.iloc[-1]:
warnings.warn(
"The table to be updated is recorded in a time before or equal to existing period. We could not update players' info in a delayed manner. The time sequence will be discarded."
)
for grp in table.table.groupby(by='time'):
cur_time, gp = grp
self.update_single_batch(gp)
def update_single(self, *args, **kwargs):
raise Exception(
"Update single is not allowed in Glicko 2 ranking algorithm. You must specify the rating period explicitly in time column wrapped in Table."
)
def prob_win(self, host, visit):
"""
Probability of host player wins over visit player.
Parameters
----------
host: name of host player
visit: name of visit player
Return
------
float: probability of winning.
"""
E = GlickoRanker.E
hidx = self.data.itemlut.get(host, None)
vidx = self.data.itemlut.get(visit, None)
hmiu = self.miu[hidx] if hidx is not None else 0
vmiu = self.miu[vidx] if vidx is not None else 0
hphi = self.phi[hidx] if hidx is not None else self.rd / self.factor
vphi = self.phi[vidx] if vidx is not None else self.rd / self.factor
return E(hmiu, vmiu, math.sqrt(hphi**2 + vphi**2))
def leaderboard(self, method="min"):
"""
Presenting current leaderboard.
Parameters
----------
method: method to process ranking value when rating is the same. See https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.Series.rank.html for more.
Return
------
pd.DataFrame: with column "name", "rating" and "rank".
"""
rtn = pd.DataFrame(
{
"name":
self.data.indexlut,
"rating": [
self.factor * (i - 1.96 * j) + self.baseline
for (i, j) in zip(self.miu, self.phi)
]
},
columns=["name", "rating"])
rtn['rank'] = rtn.rating.rank(method=method,
ascending=False).astype(np.int32)
return rtn.sort_values(by=['rating', 'name'],
ascending=False).reset_index(drop=True)
class TrueSkillRanker(TimeSeriesRanker):
"""
Pairwise TrueSkill Ranker is subset of real TrueSkill ranker. See more: https://www.microsoft.com/en-us/research/project/trueskill-ranking-system/
Unlike original TrueSkill ranker, this ranker only process pairwise gaming records.
Parameters
----------
baseline: the initial ranking value of new players. Default set to 1500.
rd: rating deviation, the possible deviation of a player. Default set to 500.
performanceRd: the possible deviation of each game. Default set to 250.
drawProbability: the probability of draw. Default set to 0.1 and cannot be set to 0.
darwMargin: if the score difference is smaller or equal than drawMargin, this turn of game will be considered as draw.
Even if drawMargin is set to 0, drawProbability should never be set to 0.
"""
def __init__(self,
baseline=1500,
rd=500,
performanceRd=250,
drawProbability=0.1,
drawMargin=0):
self.miu = baseline / rd
self.sigma = 1
self.baseline = baseline
self.rd = rd
self.performanceRd = performanceRd
self.drawMargin = drawMargin
self.drawProbability = drawProbability
self.data = Table()
self.indexMiuLut = []
self.indexSigmaSqrLut = []
@property
def drawProbability(self):
return self._draw_probability
@drawProbability.setter
def drawProbability(self, p):
if p <= 0:
warnings.warn(
"Probability of draw must be set above 0. Set to default value 0.1."
)
self._draw_probability = 0.1
else:
self._draw_probability = p
@property
def realDrawMargin(self):
return math.sqrt(2) * self.beta * ppf((1 + self.drawProbability) / 2)
@property
def beta(self):
return self.performanceRd / self.rd
@staticmethod
def v(t, a):
return pdf(t - a) / cdf(t - a)
@staticmethod
def w(t, a):
return TrueSkillRanker.v(t, a) * (TrueSkillRanker.v(t, a) + t - a)
@staticmethod
def vt(t, a):
return (pdf(-a - t) - pdf(a - t)) / (cdf(a - t) - cdf(-a - t))
@staticmethod
def wt(t, a):
return TrueSkillRanker.vt(t, a)**2 + (
(a - t) * pdf(a - t) +
(a + t) * pdf(a + t)) / (cdf(a - t) - cdf(-a - t))
def setup(self, itemRatingLut=dict(), itemRDLut=dict()):
"""
Setup the initial state of TrueSkill with existing rating and player deviation.
This function is used in where prior information is given about competitiors, and one wants to continue ranking on that.
Parameters
----------
itemRatingLut: a dictionary working as player's name to rating look up table.
itemRDLut: a dictionary working as player's name to deviation look up table.
"""
player = set(itemRatingLut.keys())
player.update(itemRDLut.keys())
if len(player) != 0:
# derive itemlut, indexlut and itemnum from itmScoreLut to setup self.data
itemnum = len(player)
itemlut = dict() # from item to index
indexlut = [] # from index to item
miu = []
sigmasqr = []
for i, itm in enumerate(player):
itemlut[itm] = i
indexlut.append(itm)
miu.append((itemRatingLut.get(itm, self.baseline)) / self.rd)
sigmasqr.append((itemRDLut.get(itm, self.rd) / self.rd)**2)
self.data.setup(itemlut, indexlut, itemnum)
self.indexMiuLut = miu
self.indexSigmaSqrLut = sigmasqr
elif self.data.itemnum == 0:
self.indexMiuLut = []
self.indexSigmaSqrLut = []
def update_single(self, host, visit, hscore, vscore, time=""):
"""
Update rating based on a single record.
Parameters
----------
host: name of host player
visit: name of visit player
hscore: score of host player
vscore: score of visit player
time: timestamp of the game. Should be numerical value. Default set to empty string.
Return
------
Tuple of (newHostRating, newVisitRating)
"""
v, w, vt, wt, beta, drawMargin, realDrawMargin = TrueSkillRanker.v, TrueSkillRanker.w, TrueSkillRanker.vt, TrueSkillRanker.wt, self.beta, self.drawMargin, self.realDrawMargin
self.data.update_single(host, visit, hscore, vscore, time=time)
ih = self.data.itemlut[host]
iv = self.data.itemlut[visit]
if ih >= len(self.indexMiuLut) or iv >= len(self.indexMiuLut):
self.indexMiuLut = self.indexMiuLut[:] + [self.miu] * (
self.data.itemnum - len(self.indexMiuLut))
self.indexSigmaSqrLut = self.indexSigmaSqrLut[:] + [1] * (
self.data.itemnum - len(self.indexSigmaSqrLut))
mh = self.indexMiuLut[ih]
mv = self.indexMiuLut[iv]
sh = self.indexSigmaSqrLut[ih]
sv = self.indexSigmaSqrLut[iv]
cs = sh + sv + 2 * beta * beta
if abs(hscore - vscore) <= drawMargin:
self.indexMiuLut[ih] += sh * vt(
0, realDrawMargin / cs**(1 / 2)) / cs**(1 / 2)
self.indexMiuLut[iv] += sv * vt(
0, realDrawMargin / cs**(1 / 2)) / cs**(1 / 2)
self.indexSigmaSqrLut[ih] *= (
1 - sh / cs * wt(0, realDrawMargin / cs**(1 / 2)))
self.indexSigmaSqrLut[iv] *= (
1 - sv / cs * wt(0, realDrawMargin / cs**(1 / 2)))
else:
b = 1 if hscore > vscore + drawMargin else -1
self.indexMiuLut[ih] += b * sh * v(
b * (mh - mv) / cs**(1 / 2),
realDrawMargin / cs**(1 / 2)) / cs**(1 / 2)
self.indexMiuLut[iv] -= b * sv * v(
b * (mv - mh) / cs**(1 / 2),
realDrawMargin / cs**(1 / 2)) / cs**(1 / 2)
self.indexSigmaSqrLut[ih] *= (
1 - sh *
w(b *
(mh - mv) / cs**(1 / 2), realDrawMargin / cs**(1 / 2)) / cs)
self.indexSigmaSqrLut[iv] *= (
1 - sv *
w(b *
(mv - mh) / cs**(1 / 2), realDrawMargin / cs**(1 / 2)) / cs)
return (
self.rd *
(self.indexMiuLut[ih] - 1.96 * self.indexSigmaSqrLut[ih]**(1 / 2))
+ (self.baseline - 3 * self.rd), self.rd *
(self.indexMiuLut[iv] - 1.96 * self.indexSigmaSqrLut[iv]**(1 / 2))
+ (self.baseline - 3 * self.rd))
def update(self, table):
"""
Update rating based on a table of record.
Parameters
----------
table: a Table object, consisting of new records that has never been previously feed to the ranker.
"""
v, w, vt, wt, beta, drawMargin, realDrawMargin = TrueSkillRanker.v, TrueSkillRanker.w, TrueSkillRanker.vt, TrueSkillRanker.wt, self.beta, self.drawMargin, self.realDrawMargin
self.data.update(table)
if self.data.itemnum > len(self.indexMiuLut):
self.indexMiuLut = self.indexMiuLut[:] + [self.miu] * (
self.data.itemnum - len(self.indexMiuLut))
self.indexSigmaSqrLut = self.indexSigmaSqrLut[:] + [1] * (
self.data.itemnum - len(self.indexSigmaSqrLut))
for rec in table.iteritem():
ih, iv, hscore, vscore = rec.indexHost, rec.indexVisit, rec.hscore, rec.vscore
mh = self.indexMiuLut[ih]
mv = self.indexMiuLut[iv]
sh = self.indexSigmaSqrLut[ih]
sv = self.indexSigmaSqrLut[iv]
cs = sh + sv + 2 * beta * beta
if abs(hscore - vscore) <= drawMargin:
self.indexMiuLut[ih] += sh * vt(
0, realDrawMargin / cs**(1 / 2)) / cs**(1 / 2)
self.indexMiuLut[iv] += sv * vt(
0, realDrawMargin / cs**(1 / 2)) / cs**(1 / 2)
self.indexSigmaSqrLut[ih] *= (
1 - sh / cs * wt(0, realDrawMargin / cs**(1 / 2)))
self.indexSigmaSqrLut[iv] *= (
1 - sv / cs * wt(0, realDrawMargin / cs**(1 / 2)))
else:
b = 1 if hscore > vscore + drawMargin else -1
self.indexMiuLut[ih] += b * sh * v(
b * (mh - mv) / cs**(1 / 2),
realDrawMargin / cs**(1 / 2)) / cs**(1 / 2)
self.indexMiuLut[iv] -= b * sv * v(
b * (mv - mh) / cs**(1 / 2),
realDrawMargin / cs**(1 / 2)) / cs**(1 / 2)
self.indexSigmaSqrLut[ih] *= (
1 - sh * w(b * (mh - mv) / cs**
(1 / 2), realDrawMargin / cs**(1 / 2)) / cs)
self.indexSigmaSqrLut[iv] *= (
1 - sv * w(b * (mv - mh) / cs**
(1 / 2), realDrawMargin / cs**(1 / 2)) / cs)
def prob_win(self, host, visit):
"""
Probability of host player wins over visit player.
Parameters
----------
host: name of host player
visit: name of visit player
Return
------
float: probability of winning.
"""
beta = self.beta
ih = self.data.itemlut.get(host, None)
iv = self.data.itemlut.get(visit, None)
mh = self.indexMiuLut[ih] if ih is not None else self.miu
mv = self.indexMiuLut[iv] if iv is not None else self.miu
sh = self.indexSigmaSqrLut[ih] if ih is not None else 1
sv = self.indexSigmaSqrLut[iv] if iv is not None else 1
cs = sh + sv + 2 * beta * beta
return cdf((mh - mv) / cs**(1 / 2))
def leaderboard(self, method="min"):
"""
Presenting current leaderboard.
Parameters
----------
method: method to process ranking value when rating is the same. See https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.Series.rank.html for more.
Return
------
pd.DataFrame: with column "name", "rating" and "rank".
"""
rtn = pd.DataFrame(
{
"name":
self.data.indexlut,
"rating": [
self.rd * (i - 1.96 * j**(1 / 2) - 3) + self.baseline
for (i, j) in zip(self.indexMiuLut, self.indexSigmaSqrLut)
]
},
columns=["name", "rating"])
rtn['rank'] = rtn.rating.rank(method=method,
ascending=False).astype(np.int32)
return rtn.sort_values(by=['rating', 'name'],
ascending=False).reset_index(drop=True)