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

Basketball strategy leads to more complexity

In [31]:
fig
Out[31]:

The shot clock

Are we measuring a skill?

Future Work

In [ ]: