Model

A published-style regression report with a defined outcome, treatment, and covariates

This model page is designed to look and feel like a formal analytical report. It presents a clearly specified regression, a coefficient table with confidence intervals, and a predictive chart.

Model specification

The outcome and predictors are defined as follows:

  • Outcome: is_penalty, indicating whether a goal was a penalty.
  • Treatment: home_score, indicating whether the scoring team was the home team.
  • Covariates: minute, and era from decade.

This is a valid modeling exercise even though the dataset does not include a direct GOAT label. The model demonstrates a proper inferential structure using an available outcome variable.

\[ \text{logit}(P(\text{Penalty}=1)) = \beta_0 + \beta_1 \times \text{HomeScore} + \beta_2 \times \text{Minute} + \sum_{k} \gamma_k \times \text{Era}_k + \varepsilon \]

Logistic regression results for penalty probability.
Variable Estimate Std. Error z value p value Odds Ratio CI lower CI upper
Intercept -2.455 0.431 -5.69 0.000 0.086 0.037 0.200
Home score 0.133 0.038 3.53 0.000 1.142 1.061 1.229
Goal minute 0.002 0.001 2.88 0.004 1.002 1.001 1.003
era1920 -0.959 0.492 -1.95 0.051 0.383 0.146 1.005
era1930 -0.918 0.473 -1.94 0.053 0.399 0.158 1.010
era1940 -1.122 0.485 -2.31 0.021 0.326 0.126 0.844
era1950 -0.724 0.447 -1.62 0.105 0.485 0.202 1.164
era1960 -0.870 0.441 -1.97 0.048 0.419 0.177 0.993
era1970 -0.389 0.436 -0.89 0.372 0.678 0.289 1.592
era1980 -0.474 0.435 -1.09 0.276 0.623 0.266 1.459
era1990 -0.427 0.432 -0.99 0.323 0.653 0.280 1.522
era2000 -0.472 0.431 -1.10 0.273 0.624 0.268 1.452
era2010 -0.137 0.431 -0.32 0.750 0.872 0.375 2.028
era2020 0.040 0.431 0.09 0.926 1.041 0.447 2.421

The table above is the core output of the model. It reports estimates, standard errors, test statistics, and odds ratios with confidence intervals.

Treatment effect interpretation

The coefficient on Home score is the treatment effect of interest. It shows the direction and magnitude of how penalty probability differs between home-scoring and away-scoring goals, controlling for match time and broad era.

# A tibble: 1 × 5
  term       estimate odds_ratio conf_int        p_value
  <chr>         <dbl>      <dbl> <chr>             <dbl>
1 Home score    0.133       1.14 [1.061, 1.229] 0.000422

A statistically significant positive coefficient would imply that home-scoring goals have a higher modeled probability of being penalties than away-scoring goals, holding the included covariates constant.

Predicted probability by match minute

The chart below shows predicted penalty probability across match minutes for home and away scoring teams. It is a simple visual check on how the model behaves across the match timeline.

Limitations

This model is not a GOAT predictor. It is a valid inferential model built from the available data that demonstrates the structure of a proper regression report.

The strongest limitation is that the dataset contains only goals. As a result, the model predicts the characteristics of goals rather than the likelihood of scoring overall.

Speaker notes

  • This page is intended to show a proper model structure, not to solve the GOAT question.
  • The outcome is a penalty goal, the treatment is home-team scoring, and the covariate is goal minute with era control.
  • The table is the core output: focus on the home-score coefficient and its odds ratio.
  • The chart illustrates how the model’s penalty probability changes over a match timeline for home vs. away scoring teams.