130: TRAM

broom
gtUtils
Published

February 7, 2025

Load game data

Code 
library(rlang)
library(cbbplotR)
# grab the raw ratings from kenpom 
# raw_ratings <- hoopR::kp_efficiency(min_year = 2025, max_year = 2025) |> 
#  dplyr::select(team, raw_o, raw_d) |> 
#  dplyr::mutate(raw_em = raw_o - raw_d)

# now grab the four factors from kenpom to compute tram 
# tram_data <- hoopR::kp_fourfactors(min_year = 2025, max_year = 2025) |> 
#  dplyr::mutate(
#    to_pct = off_to_pct / 100,
#    or_pct = off_or_pct / 100,
#    d_to_pct = def_to_pct / 100,
#    d_or_pct = def_or_pct / 100
#  ) |> 
#  dplyr::mutate(
#    off_svi = ((100 - (100 * to_pct)) + (or_pct * (0.561 * (100 - (100 * to_pct))))),
#    def_svi = ((100 - (100 * d_to_pct)) + (d_or_pct * (0.561 * (100 - (100 * d_to_pct))))),
#    tram = off_svi - def_svi,
#    old_svi_off = (100 + or_pct - to_pct),
#    old_svi_def = (100 + d_or_pct - d_to_pct),
#    old_svi_diff = old_svi_off - old_svi_def
#  ) |> 
#  dplyr::left_join(raw_ratings, by = c("team")) |> 
#  dplyr::mutate(adj_em = adj_o - adj_d) |> 
#  dplyr::select(team, conf, tram, raw_em, adj_em,
#                old_svi_diff, off_svi, def_svi, 
#                old_svi_off, old_svi_def,
#                to_pct, or_pct, d_to_pct, d_or_pct,
#                raw_o, raw_d, 
#                adj_o, adj_d, off_e_fg_pct, off_ft_rate,
#                def_e_fg_pct, def_ft_rate)

tram_data <- readr::read_csv("tram_data.csv")

# model based on raw efficiency margin 
# this is using the examples here: https://beanumber.github.io/abdwr3e/04-pythagoras.html
tram_raw <- lm(raw_em ~ tram, data = tram_data)
summary(tram_raw)

Call:
lm(formula = raw_em ~ tram, data = tram_data)

Residuals:
     Min       1Q   Median       3Q      Max 
-18.9928  -4.9364  -0.1968   4.8903  23.4395 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.01631    0.38851  -0.042    0.967    
tram         1.71733    0.08248  20.821   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 7.411 on 362 degrees of freedom
Multiple R-squared:  0.545, Adjusted R-squared:  0.5437 
F-statistic: 433.5 on 1 and 362 DF,  p-value: < 2.2e-16
Code 
r2_value <- summary(tram_raw)$r.squared
p_value <- summary(tram_raw)$coefficients[2,4]

preds <- predict(tram_raw, newdata = tram_data)
rmse_value <- sqrt(mean((tram_data$raw_em - preds)^2))

# plot the residuals 
aug <- broom::augment(tram_raw, data = tram_data)

highlight_teams <- aug |>
  # use power conferences
  dplyr::filter(conf %in% c("ACC", "MW", "BE", "B12", "B10", "SEC")) |> 
  dplyr::mutate(
    label = sprintf("%s\nActual Raw EM: %.1f\nPredicted: %.1f", 
                    team, 
                    raw_em, 
                    .fitted)
  ) |>
  dplyr::group_by(sign(.resid)) |>
  dplyr::slice_max(order_by = abs(.resid), n = 50) |>
  dplyr::ungroup() |> 
  dplyr::relocate(.fitted)  |> 
  # arbitrary selection of a few interesting teams to highlight
  dplyr::filter(team %in% c("Seton Hall", "Oklahoma St.",
                            "Creighton", "Alabama"))

Team plot for TRAM model

Code 
# limits for y-axis
max_abs_y <- max(abs(tram_data$raw_em))

team_plot <- tram_data |> 
  ggplot2::ggplot(ggplot2::aes(x = tram, y = raw_em)) + 
  ggplot2::geom_point(alpha = 0.5) +
  ggplot2::geom_smooth(method = "lm", se = FALSE, color = "#56a0d3") +
  ggplot2::scale_y_continuous(limits = c(-max_abs_y, max_abs_y)) +
  ggplot2::geom_hline(yintercept = 0, color = "#333333", linetype = "dashed") +
  ggplot2::labs(
    title = "2024-25 Men's College Basketball\nRelationship Between TRAM and Raw Efficiency Margin",
    subtitle = "TRAM is Turnover-Rebound-Adjusted-Margin computed for D-I teams",
    x = "TRAM (Turnover-Rebound-Adjusted-Margin)",
    y = "Raw Efficiency Margin",  # Changed from "Raw EM"
    caption = "Viz and model by Chris at Bless your Chart | February 7, 2025"
  ) +
  ggplot2::theme_light() +
  ggplot2::annotate(
    "label", x = max(tram_data$tram), y = min(tram_data$raw_em), 
    label = sprintf("R² = %.2f\nRMSE = %.2f", r2_value, rmse_value),
    hjust = 1, vjust = 0, size = 3.5, color = "#333333", fill = "#56a0d3",
    alpha = .3
  ) +
  ggplot2::annotate(
    "label", x = min(tram_data$tram), y = max(tram_data$raw_em),
    label = "Higher TRAM correlates with \nhigher raw efficiency margin",  
    hjust = 0, vjust = 1, size = 4, color = "#333333", fill = "#56a0d3",
    alpha = .3
  )


ggplot2::ggsave(
  "team_plot.png",
  team_plot,
  w = 9.5,
  h = 7,
  dpi = 600,
  type = 'cairo'
)


team_plot

Residual plot

Code 
resid_plot <- aug |> 
  ggplot2::ggplot(ggplot2::aes(x = tram, y = .resid)) +
  ggplot2::geom_point(alpha = 0.3) + 
  ggplot2::geom_hline(yintercept = 0, linetype = 2, color = "#acacac") +
  ggplot2::annotate(
    "label", x = 14, y = -15,
    label = paste(
      "Highlighted Teams  \nActual Raw EM, Predicted Raw EM  \n",
      paste0(highlight_teams$team, 
             " ( ", round(highlight_teams$raw_em, 1), 
             ", ", round(highlight_teams$.fitted, 1), ")",
             collapse = "\n")
    ),
    hjust = 1, vjust = 0, color = "#333333", fill = "#56a0d3",
    alpha = .3, size = 2.5, fontface = "bold"
  ) +
  cbbplotR::geom_cbb_teams(
    data = highlight_teams,
    ggplot2::aes(
      team = team),
    width = .03,
    position = ggplot2::position_dodge2(width = 0.30, padding = 0.15)
  ) +
  ggplot2::labs(
    title = "TRAM Model Residuals: Actual and Predicted Raw Efficiency",
    subtitle = "Positive residuals: team performs better than TRAM predicts\nNegative residuals: team performs worse than TRAM predicts",
    x = "TRAM (Turnover-Rebound-Adjusted-Margin)",
    y = "Residual (Actual - Predicted Raw Efficiency Margin)",
    caption = "Viz and model by Chris at Bless your Chart | February 7, 2025"
  ) +
  ggplot2::theme_light()


ggplot2::ggsave(
  "resid_plot.png",
  resid_plot,
  w = 9.5,
  h = 7,
  dpi = 600,
  type = 'cairo'
)


resid_plot

Table for top TRAM teams

Code 
tram_header <- glue::glue(
  "<div style='display: flex; justify-content: space-between; align-items: center;'>
      <div>
       <img src='https://a.espncdn.com/combiner/i?img=/redesign/assets/img/icons/ESPN-icon-basketball.png'
       style='height: 40px; width: auto; vertical-align: middle;'>
     </div>
     <div style='flex-grow:1; margin-left: 30px; margin-right: 30px'>
       <span style='display: block; font-weight: bold; text-align: center; font-size: 24px;'>Teams with highest TRAM <br>Turnover-Rebound-Adjusted-Margin</span>
       <span style='font-size: 14px; font-weight: normal; display: block; text-align: center;'>Shows the teams with the highest TRAM along with the team's adjusted raw efficiency margin, raw efficiency margin, turnover and rebound rates for offense and defense.</span>
     </div>
     <div>
       <img src='https://a.espncdn.com/combiner/i?img=/redesign/assets/img/icons/ESPN-icon-basketball.png'
       style='height: 40px; width: auto; vertical-align: middle;'>
     </div>
   </div>
  <br>"
)

team_tbl <- tram_data |>
  dplyr::filter(tram > 9.5) |> 
  dplyr::arrange(-tram) |> 
  dplyr::select(team, tram, raw_em, adj_em, to_pct, or_pct, d_to_pct, d_or_pct) |> 
  dplyr::mutate(tram = round(tram, 1)) |> 
  cbbplotR::gt_cbb_teams(team, team) |>
  gt::gt() |>
  gtUtils::gt_theme_gtutils() |>
  gt::fmt_markdown(team) |>
  gt::cols_align(team, align = "left") |> 
  gt::fmt(
    columns = c(tram, raw_em, adj_em),
    fns = function(x) {
      ifelse(x > 0, paste0("+", x), x)
    }
  ) |>
  gt::cols_label(
    team = "",
    tram = "TRAM",
    raw_em = "Raw", 
    adj_em = "Adjusted",
    to_pct = "TO%",
    or_pct = "OR%",
    d_to_pct = "TO%",
    d_or_pct = "DR%"
  ) |> 
  gt::tab_header(title = gt::html(tram_header)) |>
  gt::tab_source_note(
    source_note =
      gt::html(
        "<hr>These are teams that increase their efficiency through rebounds and turnovers. None of this data includes shooting performances.<hr>Data via hoopR and kenpom.com, theme via {gtUtils} and logos from ESPN.<hr><b>Table by Chris at Bless your chart | data through February 6 games</b>"
      )
  ) |>
  gt::tab_spanner(label = "Offense", columns = c(to_pct, or_pct)) |>
  gt::tab_spanner(label = "Defense", columns = c(d_to_pct, d_or_pct)) |>
  gt::tab_spanner(label = "Efficiency Margin", columns = c(raw_em, adj_em)) |>
  gt::data_color(
    columns = c(tram, adj_em, raw_em),
    direction = c("column"),
    method = c("numeric"),
    palette = "Greens"
  ) |> 
  gtUtils::gt_color_pills(to_pct,
    domain = c(.1, .20), format_type = "percent", digits = 1,
    palette = c("#FFFACD", "#B0E57C")
  ) |> 
  gtUtils::gt_color_pills(or_pct,
    domain = c(.25, .45), format_type = "percent", digits = 1,
    palette = c("#FFFACD", "#B0E57C")
  ) |> 
  gtUtils::gt_color_pills(d_to_pct,
    domain = c(.15, .25), format_type = "percent", digits = 1,
    palette = c("#FFB6B6", "#D8BFD8"),
    reverse = TRUE
  ) |> 
  gtUtils::gt_color_pills(d_or_pct,
    domain = c(.25, .33), format_type = "percent", digits = 1,
    palette = c("#FFB6B6", "#D8BFD8"),
    reverse = TRUE
  ) |> 
  gtUtils::gt_border_bars_bottom(c("#636363", "#969696", "#cccccc")) |> 
  gt::tab_options(table.width = gt::px(675)) |>
  gtUtils::gt_border_grid(color = "black",
                          weight = 0.5,
                          include_labels = FALSE) |>
  gtExtras::gt_add_divider(columns = team,
                           sides = "right",
                           color = "black") |>
  gt::tab_style(
    locations = gt::cells_source_notes(),
    style = gt::cell_text(
      font = gt::google_font("Signika Negative"),
      size = gt::px(11.5),
      weight = 250
    )
  ) |>
  gt::tab_style(
    style = list(gt::cell_text(font = gt::google_font("Signika Negative"))),
    locations = gt::cells_body(columns = everything())
  ) |>
  gt::tab_style(
    locations = gt::cells_column_spanners(),
    style = gt::cell_text(
      font = gt::google_font("Signika Negative"),
      weight = 850,
      size = gt::px(15)
    )
  ) 

gtUtils::gt_save_crop(team_tbl,
                      file = "team_tbl.png",
                      whitespace = 60,
                      bg = "#FFFDF5")

team_tbl
Teams with highest TRAM
Turnover-Rebound-Adjusted-Margin Shows the teams with the highest TRAM along with the team's adjusted raw efficiency margin, raw efficiency margin, turnover and rebound rates for offense and defense.

TRAM Efficiency Margin Offense Defense
Raw Adjusted TO% OR% TO% DR%

Houston

 +14.2 +30.3 +34.8 14.3% 38.5% 22.5% 28.8%

Marquette

 +12 +15.2 +23.7 12.9% 30.0% 23.7% 31.5%

St. John’s

 +11.3 +19.4 +24.4 16.0% 37.5% 21.9% 28.1%

Iowa St.

 +10.5 +19.4 +26.3 15.5% 33.8% 22.1% 27.8%

UCLA

 +10.4 +16.7 +21.4 16.3% 32.2% 24.0% 29.2%

Texas A&M

 +10.4 +13.8 +24.7 17.8% 42.8% 20.9% 28.1%

UC San Diego

 +10.4 +18.7 +14.5 14.5% 26.7% 23.7% 27.2%

Saint Mary’s

 +10.4 +20.4 +22.4 15.0% 40.9% 17.8% 25.9%

Vanderbilt

 +9.9 +13.2 +15.1 14.4% 31.6% 22.1% 29.7%

Maryland

 +9.7 +22.8 +24 14.8% 32.4% 20.8% 26.6%
These are teams that increase their efficiency through rebounds and turnovers. None of this data includes shooting performances.
Data via hoopR and kenpom.com, theme via {gtUtils} and logos from ESPN.
Table by Chris at Bless your chart | data through February 6 games