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College Basketball Win Probability Model: In-Game Win Probability in hoopR Play-by-Play

Saiem Gilani

Source: vignettes/articles/college-basketball-win-probability-model.Rmd
college-basketball-win-probability-model.Rmd

Win probability (WP) is the chance the home team wins, given everything that has happened so far. Every play in load_mbb_pbp() carries two model columns: pregame_home_prob, the home team’s chance before tip-off, and home_win_prob, the in-game estimate after that play. Together they turn a play-by-play log into a story: when a game was decided, how unlikely a comeback was, which plays mattered most. This article explains how the columns are produced, measures how well calibrated they are on a full season, and draws a win probability chart.

The official model card is wp_enrich.md in the hoopR-mbb-data repository. Numbers below are computed in this article from the published play-by-play unless labeled “as reported in the model card”.

How is win probability estimated?

As described in the model card:

  • Model. A gradient-boosted classifier (XGBoost) over the game state: score margin, seconds remaining and its square root, the pregame logit (the pregame probability on the log-odds scale) and possession. It was fit on the 2023 season.
  • Pregame prior. pregame_home_prob comes from an as-of team-rating model over the season’s own results, so it reflects each team’s strength going into the game.
  • Applied in place. The model is applied to every published season of ESPN men’s college basketball play-by-play, adding the two columns with every original column preserved. There is no separate WP file to fall out of sync with the plays, and the publish step refuses a play-by-play file without finite WP columns.

Because the inputs are game state only, the model treats “down 6 with 4:00 left” the same way in every season. Whether that transfers across rule eras (the shot clock was 35 seconds before 2015-16, and the three-point line moved) is tested below.

Loading one season 

library(hoopR)
library(dplyr)
library(ggplot2)

season <- 2026
pbp <- load_mbb_pbp(seasons = season) |>
  select(game_id, period_number, start_period_seconds_remaining, home_score, away_score,
         home_team_abbrev, away_team_abbrev, home_win_prob, pregame_home_prob)

# realized outcome for each game, from the team box scores
outcomes <- load_mbb_team_box(seasons = season) |>
  filter(team_home_away == "home", team_score != opponent_team_score) |>
  transmute(game_id, home_win = as.numeric(team_score > opponent_team_score))

wp <- pbp |>
  filter(!is.na(home_win_prob)) |>
  inner_join(outcomes, by = "game_id")

tibble(
  plays = nrow(pbp),
  share_with_wp = round(mean(!is.na(pbp$home_win_prob)), 4),
  evaluated_plays = nrow(wp),
  games = n_distinct(wp$game_id),
  home_win_rate = round(mean(outcomes$home_win[outcomes$game_id %in% wp$game_id]), 3),
  mean_home_win_prob = round(mean(wp$home_win_prob), 3)
)
#> # A tibble: 1 × 6
#>     plays share_with_wp evaluated_plays games home_win_rate mean_home_win_prob
#>     <int>         <dbl>           <int> <int>         <dbl>              <dbl>
#> 1 2915731             1         2915210  6274         0.667              0.668

The mean predicted probability close to the realized home-win rate is the first, coarsest calibration check. College home-court advantage is large, and both numbers show it.

How well calibrated is it?

The Brier score is the mean squared difference between a probability and the 0/1 outcome; lower is better. A useful baseline predicts the season’s home-win rate on every play. Calibration error compares predicted and observed win rates within bins of predicted probability; here we use 20 bins and weight each bin by its plays.

brier <- function(p, y) mean((p - y)^2)

base_rate <- mean(wp$home_win)
bins <- wp |>
  mutate(bin = cut(home_win_prob, breaks = seq(0, 1, by = 0.05), include.lowest = TRUE)) |>
  group_by(bin) |>
  summarise(plays = n(), predicted = mean(home_win_prob), observed = mean(home_win))

pregame <- wp |> distinct(game_id, pregame_home_prob, home_win)

metrics <- tibble(
  brier_in_game = brier(wp$home_win_prob, wp$home_win),
  brier_baseline = brier(base_rate, wp$home_win),
  calibration_mae_20bin = weighted.mean(abs(bins$predicted - bins$observed), bins$plays),
  brier_pregame = brier(pregame$pregame_home_prob, pregame$home_win)
) |>
  mutate(skill_vs_baseline = 1 - brier_in_game / brier_baseline)

metrics |> mutate(across(everything(), \(x) round(x, 4))) |> as.data.frame()
#>   brier_in_game brier_baseline calibration_mae_20bin brier_pregame
#> 1        0.1212          0.221                0.0089        0.1872
#>   skill_vs_baseline
#> 1            0.4517
ggplot(bins, aes(predicted, observed)) +
  geom_abline(colour = "grey60", linetype = "dashed") +
  geom_line(colour = "#2C3D50") +
  geom_point(aes(size = plays), colour = "#2C3D50") +
  scale_size_area(max_size = 5, labels = scales::comma) +
  coord_equal(xlim = c(0, 1), ylim = c(0, 1)) +
  labs(
    title = "Calibration of in-game win probability, 2025-26",
    subtitle = "Observed home win rate vs predicted, 20 bins",
    x = "Predicted home win probability", y = "Observed home win rate",
    caption = "Data: hoopR::load_mbb_pbp()"
  ) +
  theme_minimal()

Reliability diagram for 2025-26 men's college basketball in-game win probability: observed home win rate against mean predicted probability in 20 bins, lying close to the diagonal.

Does it get sharper as the game goes on?

A healthy WP model becomes more certain, and so more accurate, as time runs out:

wp |>
  group_by(period_number) |>
  summarise(plays = n(), brier = round(brier(home_win_prob, home_win), 4))
#> # A tibble: 5 × 3
#>   period_number   plays  brier
#>           <int>   <int>  <dbl>
#> 1             1 1394943 0.154 
#> 2             2 1496074 0.0901
#> 3             3   20509 0.148 
#> 4             4    3119 0.136 
#> 5             5     565 0.157

Period 3 and beyond are overtimes, which start from a tie and are inherently uncertain.

Does it transfer to an older era?

The model was fit on 2023. Applying it to 2012, under the 35-second shot clock and the old three-point line, tests whether game state meant the same thing then:

old <- load_mbb_pbp(seasons = 2012) |>
  select(game_id, home_win_prob, pregame_home_prob)

old_outcomes <- load_mbb_team_box(seasons = 2012) |>
  filter(team_home_away == "home", team_score != opponent_team_score) |>
  transmute(game_id, home_win = as.numeric(team_score > opponent_team_score))

old_wp <- old |>
  filter(!is.na(home_win_prob)) |>
  inner_join(old_outcomes, by = "game_id")

if (nrow(old_wp) > 0) {
  old_bins <- old_wp |>
    mutate(bin = cut(home_win_prob, breaks = seq(0, 1, by = 0.05), include.lowest = TRUE)) |>
    group_by(bin) |>
    summarise(plays = n(), predicted = mean(home_win_prob), observed = mean(home_win))
  bind_rows(
    metrics |> transmute(era = "2026 (in era)", plays = nrow(wp), brier = brier_in_game,
                         skill_vs_baseline, calibration_mae_20bin),
    tibble(
      era = "2012 (35-second shot clock)", plays = nrow(old_wp),
      brier = brier(old_wp$home_win_prob, old_wp$home_win),
      skill_vs_baseline = 1 - brier / brier(mean(old_wp$home_win), old_wp$home_win),
      calibration_mae_20bin = weighted.mean(abs(old_bins$predicted - old_bins$observed), old_bins$plays)
    )
  ) |>
    mutate(across(where(is.double), \(x) round(x, 4))) |>
    as.data.frame()
} else {
  message("The 2012 asset does not carry the WP columns.")
}
#>                           era   plays  brier skill_vs_baseline
#> 1               2026 (in era) 2915210 0.1212            0.4517
#> 2 2012 (35-second shot clock) 1118161 0.1259            0.4151
#>   calibration_mae_20bin
#> 1                0.0089
#> 2                0.0237

As reported in the model card (computed on its own render), 2012 scored a Brier of 0.1242 with 42.3% skill over the baseline and a 20-bin calibration error of 0.0255, against 0.1212, 45.1% and 0.0106 in 2026: a real but small era-transfer cost.

Drawing a win probability chart

Pick the game whose home win probability fell lowest before the home team came back to win:

comeback <- wp |>
  filter(home_win == 1) |>
  group_by(game_id, home_team_abbrev, away_team_abbrev) |>
  summarise(min_wp = min(home_win_prob), .groups = "drop") |>
  arrange(min_wp) |>
  slice_head(n = 1)
comeback
#> # A tibble: 1 × 4
#>     game_id home_team_abbrev away_team_abbrev  min_wp
#>       <int> <chr>            <chr>              <dbl>
#> 1 401824361 UNH              BU               0.00126
# elapsed time from the period clock: two 20-minute halves, then 5-minute overtimes
game <- wp |>
  filter(game_id == comeback$game_id) |>
  mutate(elapsed_min = if_else(
    period_number <= 2,
    (period_number - 1) * 20 + (1200 - start_period_seconds_remaining) / 60,
    40 + (period_number - 3) * 5 + (300 - start_period_seconds_remaining) / 60
  ))

ggplot(game, aes(elapsed_min, home_win_prob)) +
  geom_hline(yintercept = 0.5, colour = "grey70") +
  geom_vline(xintercept = c(20, 40), colour = "grey85", linetype = "dashed") +
  geom_step(colour = "#2C3D50", linewidth = 0.8) +
  scale_y_continuous(labels = scales::percent, limits = c(0, 1)) +
  labs(
    title = sprintf("%s comeback vs %s, 2025-26", comeback$home_team_abbrev, comeback$away_team_abbrev),
    subtitle = sprintf("Home win probability bottomed out at %.1f%%", 100 * comeback$min_wp),
    x = "Minutes elapsed", y = "Home win probability",
    caption = "Data: hoopR::load_mbb_pbp() (home_win_prob)"
  ) +
  theme_minimal()

Line chart of home win probability over game time for the biggest comeback by a home team in 2025-26 men's college basketball.

The change in home_win_prob from one play to the next is win probability added (WPA), a natural way to rank the most important plays of a game: mutate(wpa = home_win_prob - lag(home_win_prob)) within a game.

Limitations

  • Game state only. Foul counts, bonus situations and timeouts remaining are not inputs, so late-game estimates in fouling situations are rougher.
  • One training season. The model was fit on 2023; the holdout above bounds the era-transfer error rather than assuming it away.
  • The pregame prior moves. It is an as-of team-rating model, so early-season priors rest on few games.
  • Calibration is not causation. A well-calibrated WP says how often teams in a state win, not what a coach should do in it.
  • Coverage. The model card recorded a period when seasons 2003-2023 temporarily lacked the WP columns after a republish; check mean(!is.na(pbp$home_win_prob)) on the seasons you load.

Where to go next