Import data.
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import pandas as pd
import numpy as np
away_data = pd.read_csv('https://raw.githubusercontent.com/metrica-sports/sample-data/master/data/Sample_Game_1/Sample_Game_1_RawTrackingData_Away_Team.csv', skiprows=2)
home_data = pd.read_csv('https://raw.githubusercontent.com/metrica-sports/sample-data/master/data/Sample_Game_1/Sample_Game_1_RawTrackingData_Home_Team.csv', skiprows=2)
Reformat into lists indexed by player, e.g. locs_home[0] contains locations for player 0 on home team.
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locs_home = [np.asarray(home_data.iloc[:,range(3 + j*2,3 + j*2 +2)]) * np.array([105,68]) for j in range(14)]
locs_away = [np.asarray(away_data.iloc[:,range(3 + j*2,3 + j*2 +2)]) * np.array([105,68]) for j in range(14)]
locs_ball = [np.asarray(home_data.iloc[:,range(31,33)]) * np.array([105,68])]
t = home_data['Time [s]']
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np.all(np.isfinite(locs_home[0][24000:25000,:]))
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True
Influence function as defined in appendix of the paper (I've tried to keep their notation as much as possible).
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def influence_function(player_index, location, time_index, home_or_away):
from scipy.stats import multivariate_normal as mvn
if home_or_away == 'h':
data = locs_home.copy()
elif home_or_away == 'a':
data = locs_away.copy()
else:
raise ValueError("Enter either 'h' or 'a'.")
return
if np.all(np.isfinite(data[player_index][[time_index,time_index + 1],:])) & np.all(np.isfinite(locs_ball[0][time_index,:])):
jitter = 1e-10 ## to prevent identically zero covariance matrices when velocity is zero
## compute velocity by fwd difference
s = np.linalg.norm(data[player_index][time_index + 1,:] - data[player_index][time_index,:] + jitter) / (t[time_index + 1] - t[time_index])
## velocities in x,y directions
sxy = (data[player_index][time_index + 1,:] - data[player_index][time_index,:] + jitter) / (t[time_index + 1] - t[time_index])
## angle between velocity vector & x-axis
theta = np.arccos(sxy[0] / np.linalg.norm(sxy))
## rotation matrix
R = np.array([[np.cos(theta), -np.sin(theta)],[np.sin(theta),np.cos(theta)]])
mu = data[player_index][time_index,:] + sxy * 0.5
Srat = (s / 13) ** 2
Ri = np.linalg.norm(locs_ball[0][time_index,:] - data[player_index][time_index,:])
Ri = np.minimum(4 + Ri**3/ (18**3/6),10) ## don't think this function is specified in the paper but looks close enough to fig 9
S = np.array([[(1 + Srat) * Ri / 2, 0], [0, (1 - Srat) * Ri / 2]])
Sigma = np.matmul(R,S)
Sigma = np.matmul(Sigma,S)
Sigma = np.matmul(Sigma,np.linalg.inv(R)) ## this is not efficient, forgive me.
out = mvn.pdf(location,mu,Sigma) / mvn.pdf(data[player_index][time_index,:],mu,Sigma)
else:
out = np.zeros(location.shape[0])
return out
Here's a plot of the pitch control at the 24000th timepoint.
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import matplotlib.pyplot as plt
xx,yy = np.meshgrid(np.linspace(0,105,200),np.linspace(0,68,200))
Zh = np.zeros(40000)
Za = np.zeros(40000)
for k in range(11):
Zh += influence_function(k,np.c_[xx.flatten(),yy.flatten()],24000,'h')
Za += influence_function(k,np.c_[xx.flatten(),yy.flatten()],24000,'a')
Zh = Zh.reshape((200,200))
Za = Za.reshape((200,200))
plt.contourf(xx,yy,1 / (1 + np.exp(-Za + Zh)))
for k in range(11):
plt.scatter(locs_home[k][24000,0],locs_home[k][24000,1],color='darkgray')
plt.scatter(locs_away[k][24000,0],locs_away[k][24000,1],color='black')
plt.scatter(locs_ball[0][24000,0],locs_ball[0][24000,1],color = 'red')
plt.colorbar()
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<matplotlib.colorbar.Colorbar at 0x7f4f476c2358>
And, for reference, the locations of the home players (grey), away players (black) & the ball (red).
Seems sensible, I think, but quite possibly some mistakes on my end. Guess we'll see what Javi produces over next few days :)
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from IPython.display import HTML
import matplotlib.animation as animation
fig,ax = plt.subplots()
ims= []
xx,yy = np.meshgrid(np.linspace(0,105,200),np.linspace(0,68,200))
def animate(i):
fr = 23000 + i
Zh = np.zeros(40000)
Za = np.zeros(40000)
for k in range(11):
Zh += influence_function(k,np.c_[xx.flatten(),yy.flatten()],fr,'h')
Za += influence_function(k,np.c_[xx.flatten(),yy.flatten()],fr,'a')
Zh = Zh.reshape((200,200))
Za = Za.reshape((200,200))
im = plt.contourf(xx,yy,1 / (1 + np.exp(-Za + Zh)))
for k in range(11):
plt.scatter(locs_home[k][fr,0],locs_home[k][fr,1],color='darkgray')
plt.scatter(locs_away[k][fr,0],locs_away[k][fr,1],color='black')
plt.scatter(locs_ball[0][fr,0],locs_ball[0][fr,1],color = 'red')
HTML(animation.FuncAnimation(fig, animate, frames=1000, interval = 40,repeat=False).to_html5_video())
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