NBA Foul Calls¶

Question: Is (not) committing and/or drawing fouls a measurable player skill?

In [11]:

orig_df.head(n=2).T

Out[11]:

play_id	20150301CLEHOU-0	20150301CLEHOU-1
period	Q4	Q4
seconds_left	112	103
call_type	Foul: Shooting	Foul: Shooting
committing_player	Josh Smith	J.R. Smith
disadvantaged_player	Kevin Love	James Harden
review_decision	CNC	CC
away	CLE	CLE
home	HOU	HOU
date	2015-03-01 00:00:00	2015-03-01 00:00:00
score_away	103	103
score_home	105	105
disadvantaged_team	CLE	HOU
committing_team	HOU	CLE

In [19]:

df.head()

Out[19]:

	seconds_left	foul_called	player_committing	player_disadvantaged	score_committing	score_disadvantaged	season
play_id
20151028INDTOR-1	89.0	1.0	162	98	99.0	106.0	0
20151028INDTOR-2	73.0	0.0	36	358	106.0	99.0	0
20151028INDTOR-3	38.0	1.0	229	222	99.0	106.0	0
20151028INDTOR-4	30.0	0.0	229	98	99.0	106.0	0
20151028INDTOR-6	24.0	0.0	229	100	99.0	106.0	0

Model outline¶

$$ \operatorname{log-odds}(\textrm{Foul}) \ \sim \textrm{Season factor} + \left(\textrm{Disadvantaged skill} - \textrm{Committing skill}\right) $$

In [22]:

with pm.Model() as irt_model:
    β_season = pm.Normal('β_season', 0., 2.5, shape=n_season)
    
    θ = hierarchical_normal('θ', n_player) # disadvantaged skill
    b = hierarchical_normal('b', n_player) # committing skill

    p = pm.math.sigmoid(
        β_season[season] + θ[player_disadvantaged] - b[player_committing]
    )
    
    obs = pm.Bernoulli(
        'obs', p,
        observed=df['foul_called'].values
    )

In [24]:

with irt_model:
    trace = pm.sample(500, **SAMPLE_KWARGS)

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (3 chains in 3 jobs)
NUTS: [σ_b, Δ_b, σ_θ, Δ_θ, β_season]
Sampling 3 chains: 100%|██████████| 3000/3000 [02:07<00:00, 23.58draws/s]

In [26]:

az.rhat(trace).max()

Out[26]:

<xarray.Dataset>
Dimensions:   ()
Data variables:
    β_season  float64 1.0
    Δ_θ       float64 1.01
    Δ_b       float64 1.0
    σ_θ       float64 1.01
    θ         float64 1.01
    σ_b       float64 1.0
    b         float64 1.0