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 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)
