xT - Expected Threat tutorial¶

Expected threat is how we can quantify a players contributions independent of the outcome

Articles to read:¶

- https://karun.in/blog/expected-threat.html#visualizing-xt
- https://soccermatics.medium.com/explaining-expected-threat-cbc775d97935a
- https://theathletic.com/2751525/2021/08/06/introducing-expected-threat-or-xt-the-new-metric-on-the-block/
- https://sharmaabhishekk.github.io/projects/xt-derivation-julia (if you are interested in the Julia language)
- https://www.youtube.com/watch?v=RwVLUH4BFfA

In [156]:

import pandas as pd
import numpy as np

# import data
df = pd.read_csv("/Users/mckayjohns/Desktop/Soccer/europaFinal.csv")

# preprocess the dataframe so we only have the data we want
# We want to get it down to be only successful passes made by Bruno Penandes
# we can use pandas .loc method to achieve this with a bunch of & statements

df = df.loc[(df['teamId']=='Manchester United') & (df['playerId']==18) & (df['outcome']=='Successful') & (df['type']=='Pass')]

In [157]:

df.head()

Out[157]:

	minute	second	teamId	x	y	period	type	outcome	playerId	endX	endY
2	0	0.0	Manchester United	49.9	50.0	FirstHalf	Pass	Successful	18.0	31.5	59.6
119	6	11.0	Manchester United	65.4	96.8	FirstHalf	Pass	Successful	18.0	63.3	87.8
130	6	55.0	Manchester United	69.8	30.3	FirstHalf	Pass	Successful	18.0	74.4	18.8
133	7	1.0	Manchester United	84.3	23.3	FirstHalf	Pass	Successful	18.0	86.0	20.0
185	12	20.0	Manchester United	39.0	64.8	FirstHalf	Pass	Successful	18.0	32.8	72.9

In [158]:

#Import xT Grid, turn it into an array, and then get how many rows and columns it has
xT = pd.read_csv("/Users/mckayjohns/Desktop/Soccer/xT_grid.csv", header=None)
xT = np.array(xT)
xT_rows, xT_cols = xT.shape

In [159]:

xT # this is how our pitch is broken up

Out[159]:

array([[0.00638303, 0.00779616, 0.00844854, 0.00977659, 0.01126267,
        0.01248344, 0.01473596, 0.0174506 , 0.02122129, 0.02756312,
        0.03485072, 0.0379259 ],
       [0.00750072, 0.00878589, 0.00942382, 0.0105949 , 0.01214719,
        0.0138454 , 0.01611813, 0.01870347, 0.02401521, 0.02953272,
        0.04066992, 0.04647721],
       [0.0088799 , 0.00977745, 0.01001304, 0.01110462, 0.01269174,
        0.01429128, 0.01685596, 0.01935132, 0.0241224 , 0.02855202,
        0.05491138, 0.06442595],
       [0.00941056, 0.01082722, 0.01016549, 0.01132376, 0.01262646,
        0.01484598, 0.01689528, 0.0199707 , 0.02385149, 0.03511326,
        0.10805102, 0.25745362],
       [0.00941056, 0.01082722, 0.01016549, 0.01132376, 0.01262646,
        0.01484598, 0.01689528, 0.0199707 , 0.02385149, 0.03511326,
        0.10805102, 0.25745362],
       [0.0088799 , 0.00977745, 0.01001304, 0.01110462, 0.01269174,
        0.01429128, 0.01685596, 0.01935132, 0.0241224 , 0.02855202,
        0.05491138, 0.06442595],
       [0.00750072, 0.00878589, 0.00942382, 0.0105949 , 0.01214719,
        0.0138454 , 0.01611813, 0.01870347, 0.02401521, 0.02953272,
        0.04066992, 0.04647721],
       [0.00638303, 0.00779616, 0.00844854, 0.00977659, 0.01126267,
        0.01248344, 0.01473596, 0.0174506 , 0.02122129, 0.02756312,
        0.03485072, 0.0379259 ]])

In [160]:

print(xT_rows,xT_cols)

8 12

In [161]:

#Bin Data for xT

# We use a pandas method called .cut --> https://pandas.pydata.org/docs/reference/api/pandas.cut.html
# We say labels=False because we want the integer locator of the bin
df['x1_bin'] = pd.cut(df['x'], bins=xT_cols, labels=False)
df['y1_bin'] = pd.cut(df['y'], bins=xT_rows, labels=False)
df['x2_bin'] = pd.cut(df['endX'], bins=xT_cols, labels=False)
df['y2_bin'] = pd.cut(df['endY'], bins=xT_rows, labels=False)

In [162]:

df.head()

Out[162]:

	minute	second	teamId	x	y	period	type	outcome	playerId	endX	endY	x1_bin	y1_bin	x2_bin	y2_bin
2	0	0.0	Manchester United	49.9	50.0	FirstHalf	Pass	Successful	18.0	31.5	59.6	5	4	3	4
119	6	11.0	Manchester United	65.4	96.8	FirstHalf	Pass	Successful	18.0	63.3	87.8	7	7	7	7
130	6	55.0	Manchester United	69.8	30.3	FirstHalf	Pass	Successful	18.0	74.4	18.8	8	2	9	1
133	7	1.0	Manchester United	84.3	23.3	FirstHalf	Pass	Successful	18.0	86.0	20.0	10	1	10	1
185	12	20.0	Manchester United	39.0	64.8	FirstHalf	Pass	Successful	18.0	32.8	72.9	3	5	3	5

In [163]:

# Return Bin Values for xT
# We use a lambda function to assign the values from the bins to the x and y values with numpy array slicing
# it is going through each row and assigning the values based on where those numbers are in the numpy array
# kind of an advanced topic, so be sure to familiarize yourself with slicing and indexing
# its basically doing this: xT[4][5] where 4 is the fourth list and 5 is the fifth item in that list

df['start_zone_value'] = df[['x1_bin', 'y1_bin']].apply(lambda x: xT[x[1]][x[0]], axis=1)
df['end_zone_value'] = df[['x2_bin', 'y2_bin']].apply(lambda x: xT[x[1]][x[0]], axis=1)

In [164]:

df.head()

Out[164]:

	minute	second	teamId	x	y	period	type	outcome	playerId	endX	endY	x1_bin	y1_bin	x2_bin	y2_bin	start_zone_value	end_zone_value
2	0	0.0	Manchester United	49.9	50.0	FirstHalf	Pass	Successful	18.0	31.5	59.6	5	4	3	4	0.014846	0.011324
119	6	11.0	Manchester United	65.4	96.8	FirstHalf	Pass	Successful	18.0	63.3	87.8	7	7	7	7	0.017451	0.017451
130	6	55.0	Manchester United	69.8	30.3	FirstHalf	Pass	Successful	18.0	74.4	18.8	8	2	9	1	0.024122	0.029533
133	7	1.0	Manchester United	84.3	23.3	FirstHalf	Pass	Successful	18.0	86.0	20.0	10	1	10	1	0.040670	0.040670
185	12	20.0	Manchester United	39.0	64.8	FirstHalf	Pass	Successful	18.0	32.8	72.9	3	5	3	5	0.011105	0.011105

In [165]:

# now we find the difference between the start and end to get the xT value
df['xT'] = df['end_zone_value'] - df['start_zone_value']

In [166]:

df.head()

Out[166]:

	minute	second	teamId	x	y	period	type	outcome	playerId	endX	endY	x1_bin	y1_bin	x2_bin	y2_bin	start_zone_value	end_zone_value	xT
2	0	0.0	Manchester United	49.9	50.0	FirstHalf	Pass	Successful	18.0	31.5	59.6	5	4	3	4	0.014846	0.011324	-0.003522
119	6	11.0	Manchester United	65.4	96.8	FirstHalf	Pass	Successful	18.0	63.3	87.8	7	7	7	7	0.017451	0.017451	0.000000
130	6	55.0	Manchester United	69.8	30.3	FirstHalf	Pass	Successful	18.0	74.4	18.8	8	2	9	1	0.024122	0.029533	0.005410
133	7	1.0	Manchester United	84.3	23.3	FirstHalf	Pass	Successful	18.0	86.0	20.0	10	1	10	1	0.040670	0.040670	0.000000
185	12	20.0	Manchester United	39.0	64.8	FirstHalf	Pass	Successful	18.0	32.8	72.9	3	5	3	5	0.011105	0.011105	0.000000

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