Model
Predictive question
This project asks a predictive question: how much of the variation in NHL player height can be explained by position, body size, draft history, and performance-related variables? The analysis uses a multivariable model built from thousands of player records and more than 10 covariates.
Model specification
We fit an ordinary least squares regression model with height as the outcome:
\[ \text{Height}_i = \beta_0 + \beta_1(\text{Defense}_i) + \beta_2(\text{WeightKg}_i) + \beta_3(\text{Drafted}_i) + \beta_4(\text{DraftRound}_i) + \beta_5(\text{DraftOverall}_i) + \beta_6(\text{Goals}_i) + \beta_7(\text{Assists}_i) + \beta_8(\text{GamesPlayed}_i) + \beta_9(\text{Points}_i) + \beta_{10}(\text{PIM}_i) + \beta_{11}(\text{PPG}_i) + \beta_{12}(\text{Age}_i) + \varepsilon_i \]
Covariates
- Position-group indicator for Defense
- Weight in kilograms
- Draft status, draft round, and draft overall pick
- Goals, assists, games played, points, penalty minutes, and points per game
- Age in years
Outcome
- Player height in centimeters
Interpretation
- \(\beta_0\) is the baseline height for the reference case
- \(\beta_1\) captures the height difference associated with being a defenseman relative to the reference category
- the remaining coefficients describe how height changes with each additional covariate, holding the others fixed
Estimated model results
The model uses 4,997 player observations and 12 covariates. It explains about 53% of the variation in height, suggesting that body size and career variables are meaningfully associated with player height.
| Term | Estimate | 95% CI | Interpretation |
|---|---|---|---|
| Baseline / intercept | 138.1 cm | 136.5 to 139.7 | Baseline height for the reference case |
| Defense indicator | +0.99 cm | +0.76 to +1.22 | Defensemen are about 1.0 cm taller than the reference group after adjusting for the other covariates |
| Weight (kg) | +0.52 cm per kg | +0.50 to +0.53 | Heavier players tend to be taller |
| Drafted | +1.85 cm | +1.10 to +2.60 | Drafted players are taller on average in this model |
| Age | -0.01 cm per year | -0.02 to +0.00 | Older players are slightly shorter on average, though the effect is small |
The table reports 95% confidence intervals for each estimate, giving a sense of the range of plausible values around the fitted effects.
What this means
This is a richer statistical model than a simple position comparison because it uses many observed player characteristics at once. It is useful for prediction and for understanding which factors are most strongly associated with height after adjusting for the others.