def LastLeadChangeBias(sport):
if sport == 'NBA':
scope = 2880
bins = arcs.NBAbins()
else:
scope = 3600
if sport == 'NHL':
bins = arcs.NHLbins()
else:
bins = arcs.NFLbins()
data = lt.getData(sport)
lead = lt.Lead(data, sport)
top1, top2, maxLead = calcTertiles(lead)
lead1, lead2, lead3 = getTertiles(lead, top1, top2)
hcorr1, b1 = getLastLeadFreq(lead1, bins)
hcorr2, b2 = getLastLeadFreq(lead2, bins)
hcorr3, b3 = getLastLeadFreq(lead3, bins)
plt.scatter(b1[:len(b1)-1],hcorr1,facecolors='none', edgecolors='red',marker='s',\
label=sport+' data, final lead diff: 0-'+str(int(top1)))
plt.scatter(b2[:len(b2)-1], hcorr2, facecolors='none', edgecolors='blue', marker='o', \
label=sport+' data, final lead diff: '+str(int(top1))+"-"+str(int(top2)))
plt.scatter(b3[:len(b3)-1],hcorr3,facecolors='none', edgecolors='green',marker='D',\
label=sport+' data, final lead diff: '+str(int(top2))+'-'+str(int(maxLead)))
plt.xlim(xmin=0, xmax=scope)
plt.ylim(ymin=0, ymax=0.0025)
plt.xlabel('Clock time, seconds')
plt.ylabel('Probability of last lead change')
plt.legend()
plt.show()
def NumLeadChanges(sport):
scope, N = rw.getScope(sport)
data = lt.getData(sport)
lead = lt.Lead(data, sport)
hcorr, b = getNumFreq(lead)
maxc = b[-1]
rw_lead = rw.Lead(sport)
hcorr1, b1 = getNumFreq(rw_lead)
#(b[:b[-1]]).tofile('../Results/'+sport+'numLeadChangesX.csv', sep=',')
#hcorr.tofile('../Results/'+sport+'numLeadChangesY.csv', sep=',')
fontSize = 18
ax = plt.gca()
ax.tick_params(labelsize=fontSize)
plt.plot(b[:b[-1]], hcorr, 'r^-', lw=2, ms=8, label=sport + ' data')
plt.plot(b1[:b1[-1]], hcorr1, 'bo-', lw=2, ms=8, label='Poisson process')
#sqrt{2 / ( pi*N) }*exp(-(m^2) / (2N))
x = np.arange(0, maxc + 0.1, 0.1)
y = ((2 / (np.pi * N))**0.5) * np.exp(-(x**2) / (2 * N))
plt.plot(x, y, c='black', linewidth=2, label='Eq.(3)')
plt.xlim(xmin=0, xmax=maxc)
plt.ylim(ymin=0, ymax=0.5)
plt.xlabel('Number of lead changes', fontsize=fontSize)
plt.ylabel('Relative frequency', fontsize=fontSize)
plt.legend(prop={'size': fontSize})
plt.show()
def plotMaxLeadSmoothed(sport, step):
data = lt.getData(sport)
lead = lt.Lead(data, sport)
scope = len(lead[0])
m, t = lt.maxLeadTime(lead)
df = pd.DataFrame(m, index=t)
gr = df.groupby(df.index)
avgm = gr.aggregate(np.mean)
bins = np.arange(min(avgm.index), max(avgm.index) + 1, step)
groups = np.digitize(avgm.index.values.astype(int), bins)
grouped = avgm.groupby(groups)
groupAv = grouped.mean()
groupAv.dropna()
x = [bins[i - 1] for i in groupAv.index]
plt.scatter(x, groupAv)
plt.xlim(xmin=0, xmax=scope)
plt.ylim(ymin=0)
plt.xlabel('Elapsed time, t')
plt.ylabel('Maximum lead in a game')
plt.show()
def NumLeadChangesBias(sport):
data = lt.getData(sport)
lead = lt.Lead(data, sport)
top1, top2, maxLead = calcTertiles(lead)
lead1, lead2, lead3 = getTertiles(lead, top1, top2)
hcorr1, b1 = getNumFreq(lead1)
hcorr2, b2 = getNumFreq(lead2)
hcorr3, b3 = getNumFreq(lead3)
maxc = b1[-1]
plt.scatter(b1[:b1[-1]],hcorr1,facecolors='none', edgecolors='red',marker='s',\
label=sport+' data, final lead diff: 0-'+str(int(top1)))
plt.scatter(b2[:b2[-1]], hcorr2, facecolors='none', edgecolors='blue', marker='o', \
label=sport+' data, final lead diff: '+str(int(top1))+"-"+str(int(top2)))
plt.scatter(b3[:b3[-1]],hcorr3,facecolors='none', edgecolors='green',marker='D',\
label=sport+' data, final lead diff: '+str(int(top2))+'-'+str(int(maxLead)))
plt.xlim(xmin=0, xmax=maxc)
plt.ylim(ymin=0)
plt.xlabel('Number of lead changes')
plt.ylabel('Relative frequency')
plt.legend()
plt.show()
def ProbLeadSafe(sport):
data = lt.getData(sport)
lead = lt.Lead(data, sport)
z, ave_q = getSafeAvg(lead, sport)
sm_lead = sm.Lead(sport)
sm_z, sm_q = getSafeAvg(sm_lead, sport)
#BJsafe=lt.BJ(lead)
#BJz_tuples=lt.getZ(lead, BJsafe, sport)
#BJdf=pd.DataFrame(BJz_tuples)
#BJz,BJq=binAverage(BJdf)
plt.scatter(z, ave_q, color='red', marker='s', label=sport + ' data')
plt.plot(sm_z,
sm_q,
color='black',
linewidth=2.5,
label='theory (unbiased rw)')
#plt.plot(BJz, BJq, 'b--', linewidth=2.5,label='Bill James\' rule')
plt.legend()
plt.xlim(0, 2)
plt.ylim(0, 1)
plt.xlabel('Effective lead, z')
plt.ylabel('Probability that effective lead is safe')
plt.show()
def plotWScoringRate(sport):
if sport == 'NBA':
scope = 2880
seasons = '2002-2010'
bins = arcs.NBAbins()
else:
scope = 3600
seasons = '2000-2009'
if sport == 'NHL':
bins = arcs.NHLbins()
elif sport == 'CFB':
bins = arcs.NFLbins()
elif sport == 'NFL':
bins = arcs.NFLbins()
binw = arcs.getBinWidth(bins)
step = 120.0
data = lt.getData(sport)
lead = lt.Lead(data, sport)
inLead = lt.inLead(lead)
s = lt.lastChange(inLead)
#m,s=lt.maxLeadTime(lead)
'''rw_lead=rwk.Lead(sport)
rw_inLead=rwk.inLead(rw_lead)
rw=rwk.lastChange(rw_inLead)'''
sm_lead = sm.Lead(sport)
sm_inLead = sm.inLead(sm_lead)
sr = sm.lastChange(sm_inLead)
#msr,sr=lt.maxLeadTime(sm_lead)
ev_prob=pd.DataFrame.from_csv('/Users/Ish/Documents/SafeLeads/Results/'+sport+'_res/'+sport+'_eventProb.csv',\
header=None)
fontSize = 18
window = 10
#f, (ax1, ax2) = plt.subplots(2, sharex=True)
f = plt.figure()
gs = gridspec.GridSpec(2, 1, height_ratios=[2, 3]) #1 used to be 3
ax1 = plt.subplot(gs[0, :])
ax2 = plt.subplot(gs[1:, :], sharex=ax1)
smoothEvProb = movingaverage(ev_prob[1], window)
avg = np.mean(smoothEvProb)
#y_formatter = matplotlib.ticker.ScalarFormatter(useOffset=-100)
#ax1.yaxis.set_major_formatter(y_formatter)
ax1.plot(smoothEvProb, linewidth=1.3)
ax1.hlines(avg, 0, scope, colors='red', linewidth=2)
yticks = ax1.yaxis.get_major_ticks()
yticks[0].label1.set_visible(False)
ax1.set_ylim(ymin=0, ymax=max(smoothEvProb) + 0.005)
ax1.set_ylabel('Pr(scoring event)', fontsize=fontSize,
labelpad=25) #25 for NBA
ax1.tick_params(labelsize=fontSize)
ax2.tick_params(labelsize=fontSize)
h, b = np.histogram(s, bins)
hcorr = h / (binw * len(s))
ax2.scatter(b[:len(bins) - 1],
hcorr,
c='blue',
marker='o',
label=sport + ' games')
hr, br = np.histogram(sr, bins)
hrcorr = hr / (binw * len(sr))
ax2.plot(br[:len(bins) - 1],
hrcorr,
color='DarkTurquoise',
linewidth=2,
label='Inhomogeneous Poisson process')
#ubiased RW
'''rwstep=20.0
rwbins=scope/rwstep
h,b=np.histogram(rw, rwbins)
hcorr=h/(rwstep*len(rw))
plt.plot(b[:rwbins], hcorr, c='purple',linewidth=2.5,label='Homogenous Poisson process') '''
x = np.array(range(scope)) #arcsine law
y = 1 / (np.pi * (x * (scope + 1 - x))**(0.5))
ax2.plot(x, y, color='FireBrick', linewidth=2, label='Arcsine law')
ax2.set_xlim(xmin=0, xmax=scope)
ax2.set_ylim(ymin=0, ymax=0.0027)
ax2.legend(prop={'size': fontSize})
ax2.set_xlabel('Game clock time, t (seconds)', fontsize=fontSize)
ax2.set_ylabel('Pr(last lead change)', fontsize=fontSize)
f.subplots_adjust(left=0.16,
right=0.95,
top=0.95,
bottom=0.11,
hspace=0.00001) #16,13
# Fine-tune figure; make subplots close to each other and hide x ticks for
# all but bottom plot.
plt.setp([a.get_xticklabels() for a in f.axes[:-1]], visible=False)
plt.show()
def PropInLead(sport):
#portion of time first team to score is in the lead
data = lt.getData(sport)
lead = lt.Lead(data, sport)
inLead = lt.inLead(lead)
rands = np.random.rand(len(inLead))
mult = -1 + 2 * (rands < 0.5)
matr = (np.tile(mult, (len(inLead[0]), 1))).T
rand_inLead = np.multiply(matr, inLead)
props = np.sum(rand_inLead < 0, axis=1)
sm_lead = sm.Lead(sport)
sm_inLead = sm.inLead(sm_lead)
rands = np.random.rand(len(sm_inLead))
mult = -1 + 2 * (rands < 0.5)
matr = (np.tile(mult, (len(sm_inLead[0]), 1))).T
sm_randInLead = np.multiply(matr, sm_inLead)
sm_props = np.sum(sm_randInLead < 0, axis=1)
rw_lead = rw.Lead(sport)
rw_inLead = rw.inLead(rw_lead)
rands = np.random.rand(len(rw_inLead))
mult = -1 + 2 * (rands < 0.5)
matr = (np.tile(mult, (len(rw_inLead[0]), 1))).T
rw_randInLead = np.multiply(matr, rw_inLead)
rw_props = np.sum(rw_randInLead < 0, axis=1)
if sport == 'NBA':
scope = 2880
bins = arcs.NBAbins()
else:
scope = 3600
if sport == 'NHL':
bins = arcs.NHLbins()
else:
bins = arcs.NFLbins()
binw = arcs.getBinWidth(bins)
fontSize = 18
ax = plt.gca()
ax.tick_params(labelsize=fontSize)
h, b = np.histogram(props, bins)
hcorr = h / (binw * len(props))
plt.scatter(b[:len(bins) - 1],
hcorr,
c='blue',
marker='o',
label=sport + ' games')
hr, br = np.histogram(sm_props, bins)
hrcorr = hr / (binw * len(sm_props))
plt.plot(br[:len(bins) - 1],
hrcorr,
color='DarkTurquoise',
linewidth=2,
label='Inhomogeneous Poisson process')
#Unbiased rw
#rwstep=20.0
#rwbins=scope/rwstep
#hw,bw=np.histogram(rw_props,rwbins)
#hwcorr=hw/(rwstep*len(rw_props))
#plt.plot(bw[:rwbins],hwcorr,color='DarkSalmon', linewidth=2,label='Homogeneous Poisson process')
#arcsine law
x = np.array(range(scope))
y = 1 / (np.pi * (x * (scope + 1 - x))**(0.5))
plt.plot(x, y, color='FireBrick', linewidth=2, label='Arcsine law')
plt.xlim(xmin=0, xmax=scope)
plt.ylim(ymin=0, ymax=0.0027)
plt.legend(prop={'size': fontSize})
plt.xlabel('Number of seconds a team is in the lead', fontsize=fontSize)
plt.ylabel('Relative frequency', fontsize=fontSize)
plt.subplots_adjust(left=0.16, right=0.95, top=0.95, bottom=0.13)
#plt.savefig(sport+'varBinnedUpdate.pdf')
#plt.close()
plt.show()
def plotBathtub(sport):
if sport == 'NBA':
scope = 2880
seasons = '2002-2010'
bins = NBAbins()
else:
scope = 3600
seasons = '2000-2009'
if sport == 'NHL':
bins = NHLbins()
elif sport == 'CFB':
bins = NFLbins()
elif sport == 'NFL':
bins = NFLbins()
binw = getBinWidth(bins)
step = 120.0
data = lt.getData(sport)
lead = lt.Lead(data, sport)
inLead = lt.inLead(lead)
s = lt.lastChange(inLead)
#m,s=lt.maxLeadTime(lead)
'''rw_lead=rwk.Lead(sport)
rw_inLead=rwk.inLead(rw_lead)
rw=rwk.lastChange(rw_inLead)'''
sm_lead = sm.Lead(sport)
sm_inLead = sm.inLead(sm_lead)
sr = sm.lastChange(sm_inLead)
msr, sr = lt.maxLeadTime(sm_lead)
fontSize = 18
ax = plt.gca()
ax.tick_params(labelsize=fontSize)
h, b = np.histogram(s, bins)
hcorr = h / (binw * len(s))
plt.scatter(b[:len(bins) - 1],
hcorr,
c='blue',
marker='o',
label=sport + ' games')
hr, br = np.histogram(sr, bins)
hrcorr = hr / (binw * len(sr))
plt.plot(br[:len(bins) - 1],
hrcorr,
color='DarkTurquoise',
linewidth=2,
label='Inhomogeneous Poisson process')
#ubiased RW
'''rwstep=20.0
rwbins=scope/rwstep
h,b=np.histogram(rw, rwbins)
hcorr=h/(rwstep*len(rw))
plt.plot(b[:rwbins], hcorr, c='purple',linewidth=2.5,label='Homogenous Poisson process') '''
x = np.array(range(scope)) #arcsine law
y = 1 / (np.pi * (x * (scope + 1 - x))**(0.5))
plt.plot(x, y, color='FireBrick', linewidth=2, label='Arcsine law')
plt.xlim(xmin=0, xmax=scope)
plt.ylim(ymin=0, ymax=0.0027)
plt.legend(prop={'size': fontSize})
plt.xlabel('Game clock time, t (seconds)', fontsize=fontSize)
plt.ylabel('Probability of maximum lead change', fontsize=fontSize)
plt.subplots_adjust(left=0.16, right=0.95, top=0.95, bottom=0.13)
#plt.savefig(sport+'varBinnedUpdate.pdf')
#plt.close()
plt.show()