NBA 2014–15 Shot Logs · 33,362 Three-Point Shots

Model Builder

Explore what predicted 3-point shot makes in the 2014–15 NBA season. Test whether adding different shot conditions improves the model — or build one from scratch.

Variable cards start empty. Click Load default model to load the published six-variable model as a starting point, then add or remove shot conditions to see how fit changes — or build one from scratch. Use the simulator at the bottom to test individual scenarios.

You can also open the Bayesian Network Analysis (BETA) directly — no prior model needed. It fits a constrained network on its own, mapping conditional dependencies among the selected shot conditions. It shows which conditions are connected to the make rate in the fitted network and whether those connections are represented as direct or indirect paths. Those paths do not establish causal or temporal direction.

How to Use This Tool

Not sure where to start? Variable cards begin empty — click Load default model to load the published six-variable model, then Run Analysis at the bottom to see how it performs and add or remove variables to explore. Or use Auto-Build to search automatically.

1. Pick an outcome

The outcome is 3-Point Shot Make — whether the shot went in (1 = made, 0 = missed). The case study uses this single outcome; all models predict it.

2. Pick predictors

Use the search box and category buttons to find shot-condition variables across Shot Mechanics, Shot Defense, and Game Context. Cards start empty — Load default model loads the six published-model predictors as a starting point; add or remove any. Run Analysis is capped at 20 predictors; Auto-Build searches the full set and isn't capped.

3. Fit and read

Click Run Analysis to fit the model with whatever variables you've checked. Or use Auto-Build Standard to let the algorithm search all variables automatically, or Auto-Build Actionable Predictors to weight selection toward variables coaches and players can influence (shot distance, defender distance) over fixed game context (period, game margin).

Optional: player

By default, the model is fit on all 33,362 shots from the 2014–15 season. Optionally pick a single player using the Showing dropdown to fit on just their attempts — useful for asking "what predicts this shooter's makes?" Players with fewer than 100 attempts are hidden.

Where to start. Variable cards start empty, so you are never anchored to one model. Three ways to begin: click Load default model to load the published six-variable three-point make-rate model, use Auto-Build to let the tool search the full set of shot conditions, or just check the variables you want.

Which conditions can you act on? BETA The Bayesian Network Analysis is a standalone tool — you don't need to build or Auto-Build a model here first. It resolves the factor set for you, fits a constrained Bayesian network, and ranks each shot condition by its model-implied do()-style projection on the make rate — separating conditions with a direct path to the make rate in the fitted network from those connected only indirectly or not at all. A what-if simulator lets you set a condition and read the projected change. These are conditional projections under the fitted structure, not causal effects; the arrows do not establish direction.

After you run — what to expect

Review results

Results show how well the model predicts shot makes and how much each condition contributes. The Other Conditions in This Data section lists every variable not yet in your model — each card shows whether adding it would likely improve fit.

Use the simulator

Click Launch in the Simulator panel to open an interactive tool. Set any combination of shot conditions — e.g. Defender Distance "Tight" and Shot Clock "Late" — and watch the predicted make probability update instantly.

Iterate and compare

Each run is saved in the Saved Analyses tray. Click Load to restore a run, or Pin two runs to view them side by side. Each card shows Tjur R², AUC, and Brier — higher Tjur R² and AUC, lower Brier means a better-performing model.

If you ran with a synthetic variable, results show three sections:

Full Model

Complete model including all selected predictors and the synthetic variable.

Base Model

Model performance without the synthetic variable.

Synthetic Variable Performance

How well the synthetic met its specifications and its impact on model fit.

What are you trying to predict?

Choose the outcome your model will try to explain.

Required

Loading outcomes…

Shot Conditions to Include in Your Model

Search variables

Filter by topic

View Group by category

Quick actions

Hide variable cards

Loading variables…

Outcome: …

0 of … predictor variables selected

Synthetic-Variable Sensitivity Module — optional vulnerability check using a hypothetical omitted factor

Enable the check — targets the selected outcome

What this checks. Adds a hypothetical omitted factor with a specified relationship to the outcome and a cap on its overlap with the model's predictors, then shows how much the model's fit diagnostics and predicted margins change. The exercise does not show that the factor exists or identify what it represents; it tests how vulnerable the published interpretation would be to a missing factor with those properties.

Target Correlation with Outcome

r =

-0.8 0.8

Max Correlation with Any Predictor

r =

0 0.8

# Response Categories

2 (Binary) 5 (Max)

The model you're about to fit

Predictors (X)

No predictors selected yet. Check variable cards above or click Auto-Build below.

Outcome (Y)

…

A logistic regression model uses the predictors on the left to estimate the probability of the outcome on the right. This summary updates as you change your selection — and shows exactly what gets submitted when you click Run Analysis. Auto-Build ignores this selection and chooses predictors for you.

Run Analysis

Build a model from exactly the predictors you've selected above. Full analyst control.

Returns: model fit, predictor strengths, calibration, and an interactive simulator.

Auto-Build

Ignores your selection above. Searches the full set of available predictors and chooses a subset under the selected rule. Standard prioritizes held-out predictive fit; Actionable Predictors applies an additional movability classification. That classification is a planning aid, not evidence of causal effect.

Prioritizes predictors classified as more movable — a planning filter, not causal evidence.

Returns: a chosen subset of predictors plus full model fit, strengths, and an interactive simulator.

Bayesian Network Analysis

Runs a Bayesian network on the predictors you've selected above — which are directly vs. indirectly connected to the outcome, and how those connections are represented in the fitted network.

Returns: direct vs. indirect connections, link confidence, and a what-if simulator.

Auto-Building Optimal Model… 0s

Initializing…
Screening candidate predictors
Running forward stepwise selection
Fitting final model
Computing diagnostics & margins

Full Model Performance

Complete model including all predictor variables and the synthetic variable

Model fit metrics Tap to view Predicted Probability, Pseudo R², Tjur R², AUC, Brier, AIC, LL, LR test

Predicted Probability

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Fit index — how it is built Scoring Details

The index averages the fit statistics available for this model: AUC, Brier, Tjur R², and pseudo R². The likelihood-ratio statistic and its nominal p-value are shown only as descriptive weighted-pseudolikelihood comparisons and are excluded from the index; under the analysis weight, the p-value is not interpreted as a significance test. The AIC improvement over the null model is also excluded because it measures distance from the null rather than predictive fit. On a binary outcome the four indexed measures describe closely related aspects of the same fit, so read the index as one summary rather than as four independent dimensions.

How the score is built

Each of the four measures is scored against the cut-offs below — the same ones its tile uses, plus an excellent mark above Strong. The score turns the four into a single number out of 100: Moderate on all four gives 60, Strong on all four gives 80, excellent on all four gives 100.

Discrimination (AUC)

Weak below 0.70 · Moderate 0.70 · Strong 0.80 · Excellent 0.90

Prediction error (Brier), lower is better

Weak above 0.18 · Moderate 0.18 · Strong 0.12 · Excellent 0.06

Separation (Tjur R²)

Weak below 0.10 · Moderate 0.10 · Strong 0.20 · Excellent 0.35

Pseudo R²

Weak below 0.20 · Moderate 0.20 · Strong 0.30 · Excellent 0.40

Values between two cut-offs score in between, in proportion; a measure past its excellent mark counts as excellent. Zero means chance or no better than a model with no predictors (AUC 0.50, Brier 0.25, Tjur and pseudo R² 0).

Aggregation Method

Clamp to [0,1], average equally over the metrics present, map to a 0–100 index. The cuts are the ones the metric tiles on this card already use for their Weak, Moderate and Strong chips, plus an excellent mark above Strong: each metric scores 0 at its floor, 0.6 at the Moderate cut, 0.8 at the Strong cut and 1 at the excellent mark. A model sitting on every Strong cut therefore scores 80, one on every Moderate cut scores 60, and the printed bands describe the tiles themselves, so the index cannot disagree with the chips beside it. The cuts and the bands are display conventions calibrated to this demonstration, not standards. The index summarizes fit only: it carries no information about whether the model contains the right predictors.

Display bands (fit only)

≥80

Strong

60–79

Moderate

<60

Weak

—

Model Fit

Pseudo R²

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Higher is better

Rating: —

Separation (Tjur R²)

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Higher is better

Rating: —

Discrimination (AUC)

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0.5 = random, 1 = perfect

Rating: —

Prediction Error (Brier)

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Lower is better

Rating: —

Information Criteria

AIC Comparison

Null Model

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Change

Final Model

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Lower is better

Log Likelihood Comparison

Null Model

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Change

Final Model

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Higher is better

LR χ²

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p-value

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Model triangulation check Cross-check a scenario against an independent propensity estimate

Set a scenario below and run it. The fitted model's scenario-implied change is then re-estimated through the same propensity-subclassification workflow used on the standalone triangulation page. Agreement is a robustness check on this scenario, not proof of a causal effect.

Modeling in this check is restricted to binary (yes/no) outcomes.

The number on each card is the variable's incremental contribution — the gain in Tjur R² it adds once the other variables are included, the same quantity reported elsewhere on this site. Bars and ordering use it too, largest first. Hover a number to see how much of the variable's one-at-a-time separation that represents.

Synthetic-variable impact Whether adding the synthetic variable improved fit, and how it shifted predicted margins

Synthetic variable impact analysis

A sensitivity analysis: how the model's diagnostics change when adding a synthetic variable — a hypothetical unmeasured factor built to the strength you specified, with its overlap with your predictors held under your cap — versus the base model.

Δ McFadden R²

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Δ Tjur R²

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Δ AIC

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Δ Log Likelihood

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Δ AUC

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Δ Brier

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Summary:

Adding the synthetic variable produces small changes across the displayed fit diagnostics, with the largest change in model fit as measured by AIC.

Model Builder

How to Use This Tool

1. Pick an outcome

2. Pick predictors

3. Fit and read

Optional: player

Review results

Use the simulator

Iterate and compare

If you ran with a synthetic variable, results show three sections:

What are you trying to predict?

Whose data?

Shot Conditions to Include in Your Model

Run a null model?

Full Model Performance

Predicted Probability

How the score is built

Aggregation Method

Display bands (fit only)

Model Fit

Information Criteria

Sample Completeness

Detailed Results

Predicted Margins (Table)

Predicted Margins (Chart)

Base Model — Detailed Results

Predicted Margins (Base Model)

Synthetic variable impact analysis

Synthetic-variable change in predicted margins: Full (less) Base