Women’s March Madness

About the Data

This adapted data set contains historical records of every NCAA Division I Women’s Basketball Tournament appearance since the tournament began in 1982 up until 2018. Sourced from official NCAA, the adapted data set captures tournament results across more than four decades of collegiate women’s basketball. All data is sourced from the NCAA and contains the data behind the story The Rise and Fall Of Women’s NCAA Tournament Dynasties.

The rise in popularity of the NCAA Women’s March Madness, fueled by athletes like Caitlin Clark and Paige Bueckers, reflects a broader cultural shift in the recognition of women’s sports. Beyond entertainment and athletic achievement, women’s participation in sport has social and professional benefits.

As Beth A. Brooke notes in her article Here’s Why Women Who Play Sports Are More Successful, research from EY shows that 94% of women in executive leadership roles played sports, and over half competed at the university level. Participation in sports help develop skills such as resilience, teamwork, and competitiveness, traits that critical for career success.

Analyzing NCAA Women’s March Madness results and promoting visibility of women in sports, beyond exercising our data skills, supports advocation for equity, opportunity, and empowerment of women in leadership.

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Metadata

CSV Name

womensmarchmadness.csv

Data Set Characteristics

Multivariate

Subject Area

Women In Sports

Associated Tasks

Regression, Classification

Feature Type

Factor, Integer, Numeric

Instances

2092

Features

Has Missing Values?

Yes

Variables

Variable Name	Role	Type	Description	Units	Missing Values
year	Feature	integer	Year	-	No
school	Feature	nominal categorical	School	-	No
seed	Feature	ordinal categorical	Seed. The 0 seeding designation in 1983 notes the eight teams that played an opening-round game to become the No. 8 seed in each region.	-	No
conference	Feature	nominal categorical	Conference	-	No
conf_wins	Feature	numeric	Conference Wins	-	Yes
conf_losses	Feature	numeric	Conference Losses	-	Yes
conf_wins_pct	Feature	numeric	Conference Win Percentage	-	Yes
conf_rank	Feature	numeric	Place in Conference	-	Yes
division	Feature	nominal categorical	Conference Division	-	Yes
reg_wins	Feature	integer	Regional Wins	-	No
reg_losses	Feature	integer	Regional Losses	-	No
reg_wins_pct	Feature	numeric	Regional Win Percentage	%	No
bid	Feature	nominal categorical	Whether the school qualified with an automatic bid (by winning its conference or conference tournament) or an at-large bid. [‘at-large’, ‘auto’]	-	No
first_game_at_home	Feature	nominal categorical	Whether the school played its first-round tournament games on its home court. [‘Y’, ‘N’]	-	No
tourney_wins	Feature	integer	Tourney Wins	-	No
tourney_losses	Feature	integer	Tourney Losses	-	No
tourney_finish	Target	ordinal categorical	Ordered categories: [‘opening_round_loss’ < ‘first_round_loss’ < ‘second_round_loss’ < ‘top_16_loss’ < ‘top_8_loss’ < ‘top_4_loss’ < ‘top_2_loss’ < ‘champ’]	-	No
total_wins	Feature	integer	Total Wins	-	No
total_losses	Feature	integer	Total Losses	-	No
total_wins_pct	Feature	numeric	Total Win Percentage	%	No

Key Features of the Data Set

Each row represents a single team’s appearance in a specific tournament year and includes information such as:

Tournament Seed – Seed assigned to the team
Tournament Results – Number of wins, losses, and how far the team advanced
Bid Type – Whether the team received an automatic bid or was selected at-large.
Season Records – Regular season, conference, and total win/loss stats and percentages
Conference Information – Team’s conference name, record, and rank within the conference
Division – Regional placement in the tournament bracket (e.g., East, West)
Home Game Indication – Whether the team played its first game at home

Purpose and Use Cases

This data set is designed to support analysis of:

Team performance over time
Impact of seeding and bid types on tournament results
Conference strength
Emergence and decline of winning teams in women’s college basketball

Case Study

Objective

How much does a team’s tournament seed predict its success in the NCAA Division I Women’s Basketball Tournament?

This analysis explores the relationship between a team’s seed and its results on a tournament to evaluate whether teams with lower seeds consistently outperform ones with higher seeds.

By examining historical data, we aim to:

Identify trends in tournament advancement by seed level

Seeding is intended to reflect a team’s regular-season performance. In theory, lower-numbered seeds (e.g., #1, #2) are given to the strongest teams, who should be more likely to advance. But upsets, bracket surprises, and standout performances from lower seeds raise questions like “How reliable is seeding as a predictor of success?”

Understanding these dynamics can inform fan expectations and bracket predictions.

Analysis

We should load the necessary libraries we will be using, including the diversedata package.

library(diversedata)
library(tidyverse)
library(AER)
library(broom)
library(knitr)
library(MASS)

1. Data Cleaning & Processing

First, let’s load our data (womensmarchmadness from diversedata package) and remove all NA values for our variables of interest seed and tourney_wins.

# Reading Data
marchmadness <- womensmarchmadness

# Review total rows
nrow(marchmadness)

[1] 2092

# Removing NA but only in selected columns
marchmadness <- marchmadness |> drop_na(seed, tourney_wins)

# Notice no rows were removed
nrow(marchmadness)

[1] 2092

Note that, the seed = 0 designation in 1983 notes the eight teams that played an opening-round game to become the No.8 seed in each region. For this exercise, we will not take them into consideration. Since seed is an ordinal categorical variable, we can set it as an ordered factor.

marchmadness <- marchmadness |> 
  filter(seed != 0)

2. Exploratory Data Analysis

We can see which seeds appear more often.

seed_count <- marchmadness |> 
  count(seed) |> 
  arrange(desc(n)) |>
  mutate(seed = factor(seed, levels = seed))

ggplot(
  seed_count, 
  aes(x = seed, y = n)
  ) +
  geom_col(fill = "skyblue2") +
  labs(
    title = "Distribution of Tournament Seeds",
    x = "Seed",
    y = "Number of Teams") +
  theme_minimal()

We can also take a look at the average tournament wins for each seed:

marchmadness |> 
  filter(!is.na(seed), seed != 0) |> 
  group_by(seed) |> 
  summarise(
    avg_tourney_wins = mean(tourney_wins, na.rm = TRUE)
    ) |>
  arrange(desc(avg_tourney_wins)) |>
  mutate(seed = factor(seed, levels = seed)) |>
  ggplot(
    aes(
      x = as.factor(seed),
      y = avg_tourney_wins)
    ) +
  geom_col(fill = "skyblue2") +
  labs(
    title = "Average Tournament Wins by Seed",
    x = "Seed",
    y = "Avg. Tourney Wins"
  ) +
  theme_minimal()

We can note that a teams with a higher seed tend to win more tournaments! We can also see the total amount of tourney wins for each seed.

seed_order <- marchmadness |> 
  filter(!is.na(seed), seed != 0) |> 
  group_by(seed) |> 
  summarise(avg_wins = mean(tourney_wins, na.rm = TRUE)) |> 
  arrange(desc(avg_wins)) |> 
  pull(seed)

marchmadness |> 
  filter(!is.na(seed), seed != 0) |> 
  mutate(seed = factor(seed, levels = seed_order)) |> 
  ggplot(
    aes(x = seed, y = tourney_wins)
  ) +
  geom_jitter(alpha = 0.25, color = "skyblue2") +
  geom_violin(fill = "skyblue2") +
  labs(
    title = "Distribution of Tournament Wins by Seed",
    x = "Seed",
    y = "Tournament Wins"
  ) +
  theme_minimal()

3. Seed Treatment: Numeric vs Factor

An important decision on this analysis is whether to use seed as a numeric or an ordered categorical predictor. Treating seed as a numeric explanatory variable assumes that the effect of seed is linear on the log scaled of the amount of tourney_wins.

To test if this assumption is appropriate, we can compare models that make different assumptions about seed. We’ll create models using seed as both a numeric variable and a factor.

However, first, we need to encode seed as an ordered factor.

marchmadness_factor <- marchmadness |> 
  mutate(seed = as.ordered(seed)) |> 
  mutate(seed = fct_relevel
         (seed, 
           c("1", "2", "3", "4", "5", 
             "6", "7", "8", "9", "10", 
             "11", "12", "13", "14", "15", 
             "16")))

Given that we’re setting tourney_wins as a response, our linear regression model may output negative values at high seed values. Therefore, a Poisson Regression model is better suited, considering that tourney wins is a count variable and is always non-negative.

options(contrasts = c("contr.treatment", "contr.sdif"))

poisson_model <- glm(tourney_wins ~ seed, family = "poisson", data = marchmadness)

poisson_model_factor <- glm(tourney_wins ~ seed, family = "poisson", data = marchmadness_factor)

We can visualize how the two models fit the data to evaluate if treating seed as numeric or factor would have a significant impact on our modelling process.

marchmadness <- marchmadness |> 
  mutate(
    Numeric_Seed = predict(poisson_model, type = "response"),
    Factor_Seed = predict(poisson_model_factor, type = "response")
  )

plot_data <- marchmadness |> 
  dplyr::select(seed, tourney_wins, Numeric_Seed, Factor_Seed) |> 
  pivot_longer(cols = c("Numeric_Seed","Factor_Seed"), names_to = "model", values_to = "predicted")

ggplot(plot_data, aes(x = seed, y = predicted, color = model)) +
  geom_point(aes(y = tourney_wins), alpha = 0.3, color = "black") +
  geom_line(stat = "smooth", method = "loess", se = FALSE, linewidth = 1.2) +
  labs(title = "Predicted Tournament Wins by Seed",
       x = "Seed",
       y = "Predicted Wins",
       color = "Model") +
  theme_minimal()

Visually, both models don’t appear to be significantly different from each other. Now, if we wanted to formally evaluate which is the better approach we could use likelihood-based model selection tools.

kable(glance(poisson_model), digits = 2)

null.deviance	df.null	logLik	AIC	BIC	deviance	df.residual	nobs
3438.76	2083	-2117.42	4238.84	4250.12	1610.34	2082	2084

kable(glance(poisson_model_factor), digits = 2)

null.deviance	df.null	logLik	AIC	BIC	deviance	df.residual	nobs
3438.76	2083	-2079.52	4191.04	4281.31	1534.54	2068	2084

Based on lower residual deviance, higher log-likelihood, and a lower AIC, the model that treats seed as a factor fits the data better. This would suggest that the relationship between tournament seed and number of wins is not linear, and would support using an approach that does not assume a constant effect per unit change in seed.

However, before deciding on using a more complex model, we can evaluate if this complexity offers a significantly better modeling approach. To do this, we can perform a likelihood ratio test.

\(H_0\): Model poisson_model fits the data better than model poisson_model_factor

\(H_a\): Model poisson_model_factor fits the data better than model poisson_model

anova_result <- tidy(anova(poisson_model, poisson_model_factor, test = "Chisq"))

kable(anova_result, digits = 2)

term	df.residual	residual.deviance	df	deviance	p.value
tourney_wins ~ seed	2082	1610.34	NA	NA	NA
tourney_wins ~ seed	2068	1534.54	14	75.79	0

These results indicate strong evidence that the model with seed treated as a factor fits the data significantly better than treating it as a numeric predictor. Therefore, we will proceed by using seed as a factor.

4. Overdispersion Testing

It is noteworthy that Poisson assumes that the mean is equal to the variance of the count variable. If the variance is much greater, we might need a Negative Binomial model. We can do an dispersion test to evaluate this matter.

Letting \(Y_i\) be the \(ith\) Poisson response in the count regression model, in the presence of equidispersion, \(Y_i\) has the following parameters:

\(E(Y_i)=\lambda_i, Var(Y_i)=\lambda_i\)

The test uses the following mathematical expression (using a \(1+\gamma\) dispersion factor):

\(Var(Y_i)=(1+\gamma)\times\lambda_i\)

with the hypotheses:

\(H_0:1 + \gamma = 1\)

\(H_a: 1 + \gamma > 1\)

When there is evidence of overdispersion in our data, we will reject \(H_0\).

kable(tidy(dispersiontest(poisson_model_factor)), digits = 2)

estimate	statistic	p.value	method	alternative
0.96	-0.56	0.71	Overdispersion test	greater

Since the P-value (0.71) is much greater than 0.05, we fail to reject the null hypothesis. This suggests that there is no significant evidence of overdispersion in the Poisson model.

5. Hypothesis Testing: Are Seed and Wins Associated?

summary_model <- tidy(poisson_model_factor) |> 
  mutate(exp_estimate = exp(estimate)) |> 
  mutate_if(is.numeric, round, 3) |> 
  filter(p.value <= 0.05)
  
kable(summary_model, digits = 2)

term	estimate	std.error	statistic	p.value	exp_estimate
seed2-1	-0.34	0.07	-4.96	0.00	0.71
seed3-2	-0.33	0.08	-4.05	0.00	0.72
seed5-4	-0.46	0.10	-4.34	0.00	0.63
seed8-7	-0.34	0.15	-2.22	0.03	0.71
seed12-11	-0.64	0.23	-2.75	0.01	0.52
seed13-12	-0.92	0.38	-2.40	0.02	0.40

Based on these results, we can see that seed is significantly associated with tourney_wins, particularly in changes in levels between lower seeds. These results can be interpreted as:

Seed 2 teams are expected to win 29% fewer games than Seed 1 teams

Seed 2 teams are expected to win 29% (1-0.71) fewer games than Seed 1 teams.
Seed 3 teams are expected to win 28% fewer games than Seed 2 teams.
Seed 5 teams are expected to win 37% fewer games than Seed 4 teams.
Seed 8 teams are expected to win 29% fewer games than Seed 7 teams.
Seed 12 teams are expected to win 48% fewer games than Seed 11 teams.
Seed 13 teams are expected to win 60% fewer games than Seed 12 teams.

This conclusion is easier to interpret visually, so, let’s plot our Poisson regression model to view the impact of seed on tourney_wins:

marchmadness$predicted_wins <- predict(poisson_model_factor, type = "response")

model_plot <- ggplot(marchmadness, aes(x = seed, y = tourney_wins)) +
  geom_jitter(width = 0.3, alpha = 0.5) +
  geom_line(aes(y = predicted_wins), color = "skyblue2", linewidth = 1.2) +
  labs(title = "Poisson Regression: Predicted Tournament Wins by Seed",
       x = "Seed",
       y = "Tournament Wins") +
  theme_minimal()

model_plot

Discussion

This analysis examined the relationship between a team’s tournament seed and its performance in the NCAA Division 1 Women’s Basketball Tournament. The results suggest that:

Poisson regression supports seeding as a predictor: The Poisson regression model indicates that seed is a significant predictor of tournament wins, suggesting that higher-ranked teams tend to win more, even between closely ranked seeds.
Proper variable coding is essential: Treating seed as a numeric variable would assume a linear relationship on the log scale of expected tournament wins, meaning each one-unit increase in seed (e.g., from 1 to 2, or 10 to 11) would be associated with the same proportional decrease in wins. This oversimplifies the real pattern. By encoding seed as an ordered factor, the model can estimate distinct effects for each seed level, allowing for more accurate and nuanced interpretation.
There is a lot of variation around the prediction: While seeding generally reflects team strength, upsets and unexpected performances do occur, showing that other factors also influence tournament outcomes.

Seeding is an important predictor of success, but clearly other factors influence the results. Unexpected performances are common in March Madness, so investigating additional variables could provide a fuller picture of what drives tournament outcomes.

Attribution

Data sourced from FiveThirtyEight’s NCAA Women’s Basketball Tournament data set, available under a Creative Commons Attribution 4.0 International License. Original data set: FiveThirtyEight GitHub Repository. Story: Louisiana Tech Was the UConn of the ’80s.

Brooke-Marciniak, B. A. (2016, February 7). Here’s why women who play sports are more successful. LinkedIn article.