Simple Logistic Regression on Games Won and Interceptions Thrown by Jacksonville Jaguars, 2018-2024
“DUUUVAL”
Background:
In American football, an average game features 10 to 12 offensive possessions per team. When a team has offensive possession of the ball and loses their possession of the ball to the opposing team due to a forward pass that was caught by the opposing team, this is categorized as an interception. This results in the opposing team gaining possession of the ball, or a turnover. For each interception thrown, the team that had possession of the ball loses time to complete plays that earn points, such as touchdowns.
This analysis assess the impact of interceptions thrown on games won for the Jacksonville Jaguars for the seasons of 2018-2024. The seven seasons for the Jaguars have been organized by game, interceptions thrown, and whether each game was won or lost. It is important to not that this data only includes regular season data and 116 games total were collected.
Data Table:
datatable(jags)Logistic Regression Model:
With this analysis, the change of probability of winning a game given the observed interceptions thrown will be studied using the follwing Logistic Regression model:
\[ P(Y_i = 1|\, x_i) = \frac{e^{\beta_0 + \beta_1 x_i}}{1+e^{\beta_0 + \beta_1 x_i}} = \pi_i \]
Where for observation i:
\[ Y_i = 1 \text{ denotes a game won by the Jacksonville Jaguars} \]
\[ Y_i = 0 \text{ denotes a game lost by the Jacksonville Jaguars} \]
\[ x_i\text{ denotes the number of interceptions thrown during a game} \]
Hypotheses:
The hypotheses for this analysis are as follows:
\[ \begin{aligned} H_0&: \beta_1 = 0 \\ H_a&: \beta_1 \neq 0 \\ \alpha &= 0.05 \end{aligned} \]
The null hypothesis is that beta one is equal to zero, meaning that the number of thrown interceptions gives no insight about the outcome of the game as far as winning or losing for the Jaguars.
The alternative hypothesis is suggests that the number of interceptions thrown during a game can help calculate the probability of winning that given game.
The significance level used for this analysis will be observed at 0.05.
Analysis:
ggplot(jags, aes(x= interceptions, y=win)) +
geom_jitter(height = 0.03, width = 0.15, alpha = 0.05, color = "#008080", size =2.5) +
geom_smooth(method = "glm",
method.args = list(family= "binomial"),
se = TRUE,
color = "#BDB76B",
linewidth=1.2) +
scale_y_continuous(labels = scales::percent, breaks = seq(0, 1, 0.2)) +
scale_x_continuous(breaks = 0:4) +
labs(
title = "Jacksonville Jaguars Win Probability vs. Interceptions Thrown",
subtitle = "Logistic Regression Curve (Regular Season Games, 2018-2024)",
x = "Interceptions Thrown by Jaguars (X)",
y = "Probability of Winning the Game (Y)",
caption = "Data Source: Official NFL Box Scores"
) +theme_minimal(base_size = 12) +
theme(
plot.title = element_text(face = "bold", size = 14, color = "#008080"),
panel.grid.minor = element_blank()
)
Observations from the Graph:
From the graph, it can be observed that the points on the top of the y-axis (Wins) are heavily concentrated around the values 0 and 1 for Interceptions Thrown. Conversely, the points on the bottom of the y-axis (Losses) show a wider spread, capturing almost all of the games where 2, 3, or 4 interceptions were thrown
Test:
model <- glm(win ~ interceptions, data=jags, family=binomial)
pander(model)| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | -0.1336 | 0.2561 | -0.5217 | 0.6019 |
| interceptions | -1.069 | 0.3348 | -3.192 | 0.001415 |
Statistical Model:
Using the findings from the logistic regression, the model for the data is as shown:
\[ P(Y_i = 1|\, x_i) = \frac{e^{-0.1336+ -1.069x_i}}{1+e^{-0.1336 + -1.069x_i}} = \pi_i \]
Observations from Test:
Since the p-value from the test is 0.001415, lower than the alpha of 0.05, it is safe to reject the null hypothesis. This means that there is sufficient evidence that there is certain association between the probability of winning a game and the number of interceptions thrown by the Jacksonville Jaguars during the seasons from 2018-2024.
The estimated slope for the dataset is -1.069, representing the change in log-odds per interception. Converting this to probabilities shows that for the first interception thrown the probability of the Jaguars winning the game decreases from 46.7% at zero interceptions to 23.1% with one interception thrown.
Limitations:
Because the data that was observed was solely from turnovers that were counted as interceptions, this means that other means of turnovers such as fumbles, could have also resulted in losses for the Jaguars, even through not represented with this data.
Also to be noted is the change in play of losing versus winning teams. Riskier passes and plays are made often when a team is already losing, such as passing into an area with deep coverage in an attempt for scoring. These riskier passes can result in interceptions, even though the team is losing before the interception is thrown.
Conclusion:
In conclusion, after running a logistic regression test, there is significant evidence to conclude that the number of interceptions thrown and be used to help calculate the probability of the Jacksonville Jaguars winning a game. The odds of winning a game for the Jaguars decreases by 65.7% for every interception thrown according to the data observed. It can also be said that interceptions significantly decrease the likely hood of winning a game for the Jaguars.