NBA Analysis
2026-09-07
Dataset
This report uses the attached games.csv dataset, It
contains historical NBA game results and team statistics. My research
question is whether a team’s rebounding advantage is related to its
point differential. I hypothesize that teams with a higher rebound
differential will also have a higher point differential.
https://www.kaggle.com/datasets/nathanlauga/nba-games?select=games.csv
nba <- read.csv("games.csv")
head(nba)## GAME_DATE_EST GAME_ID GAME_STATUS_TEXT HOME_TEAM_ID VISITOR_TEAM_ID SEASON
## 1 2022-12-22 22200477 Final 1610612740 1610612759 2022
## 2 2022-12-22 22200478 Final 1610612762 1610612764 2022
## 3 2022-12-21 22200466 Final 1610612739 1610612749 2022
## 4 2022-12-21 22200467 Final 1610612755 1610612765 2022
## 5 2022-12-21 22200468 Final 1610612737 1610612741 2022
## 6 2022-12-21 22200469 Final 1610612738 1610612754 2022
## TEAM_ID_home PTS_home FG_PCT_home FT_PCT_home FG3_PCT_home AST_home REB_home
## 1 1610612740 126 0.484 0.926 0.382 25 46
## 2 1610612762 120 0.488 0.952 0.457 16 40
## 3 1610612739 114 0.482 0.786 0.313 22 37
## 4 1610612755 113 0.441 0.909 0.297 27 49
## 5 1610612737 108 0.429 1.000 0.378 22 47
## 6 1610612738 112 0.386 0.840 0.317 26 62
## TEAM_ID_away PTS_away FG_PCT_away FT_PCT_away FG3_PCT_away AST_away REB_away
## 1 1610612759 117 0.478 0.815 0.321 23 44
## 2 1610612764 112 0.561 0.765 0.333 20 37
## 3 1610612749 106 0.470 0.682 0.433 20 46
## 4 1610612765 93 0.392 0.735 0.261 15 46
## 5 1610612741 110 0.500 0.773 0.292 20 47
## 6 1610612754 117 0.469 0.778 0.462 27 47
## HOME_TEAM_WINS
## 1 1
## 2 1
## 3 1
## 4 1
## 5 0
## 6 0Q1: Plotting a Graph
average_points <- c(
mean(nba$PTS_home, na.rm = TRUE),
mean(nba$PTS_away, na.rm = TRUE)
)
barplot(
average_points,
names.arg = c("Home Teams", "Away Teams"),
col = c("blue", "orange"),
main = "Average Points Scored by Home and Away Teams",
xlab = "Team Location",
ylab = "Average Points Scored",
ylim = c(0, 120)
)
This bar plot compares the average points scored by home and away teams. The home team scored approximately 103 points per game, while away teams scored 101 points. This suggest home teams score more on average than away teams.
Q2: Statistical Calculation
nba$REB_DIFF <- nba$REB_home - nba$REB_away
nba$POINT_DIFF <- nba$PTS_home - nba$PTS_away
rebound_statistics <- c(
Mean = mean(nba$REB_DIFF, na.rm = TRUE),
Median = median(nba$REB_DIFF, na.rm = TRUE),
Standard_Deviation = sd(nba$REB_DIFF, na.rm = TRUE)
)
round(rebound_statistics, 2)## Mean Median Standard_Deviation
## 1.26 1.00 8.98The mean rebound differential was 1.26, meaning home teams collected about 1.26 more rebounds than away teams per game on average. The median was 1 rebound, while the standard deviation was 8.98 rebounds. This shows that the typical rebound difference was small, but the amount of variation between games was much larger.
Q3: Correlation Between Rebound and Point Differential
analysis_data <- nba[
complete.cases(nba$REB_DIFF, nba$POINT_DIFF),
]
correlation_result <- cor.test(
analysis_data$REB_DIFF,
analysis_data$POINT_DIFF
)
correlation_result##
## Pearson's product-moment correlation
##
## data: analysis_data$REB_DIFF and analysis_data$POINT_DIFF
## t = 83.518, df = 26550, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4465560 0.4656079
## sample estimates:
## cor
## 0.4561342rebound_model <- lm(
POINT_DIFF ~ REB_DIFF,
data = analysis_data
)
summary(rebound_model)##
## Call:
## lm(formula = POINT_DIFF ~ REB_DIFF, data = analysis_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -58.970 -8.029 0.069 7.991 52.519
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.950574 0.074556 26.16 <2e-16 ***
## REB_DIFF 0.686300 0.008217 83.52 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.03 on 26550 degrees of freedom
## Multiple R-squared: 0.2081, Adjusted R-squared: 0.208
## F-statistic: 6975 on 1 and 26550 DF, p-value: < 2.2e-16plot(
analysis_data$REB_DIFF,
analysis_data$POINT_DIFF,
main = "Rebound Differential and Point Differential",
xlab = "Rebound Differential",
ylab = "Point Differential",
pch = 16,
col = rgb(0, 0, 1, 0.2)
)
abline(
rebound_model,
col = "orange",
lwd = 2
)
The correlation was 0.456, which denotes a moderates positive relationship between the rebound differential and the point differential. The R-squared was 0.208, meaning that the rebound differential could explain 20.8% of the differences in the scoring margin. The p-value is less than 2.2e-16, and hence the relationship is statistically significant. From the slope of the regression line above, one would conclude that the point differentials were higher where the team had higher rebounds compared to its opponent team.
Q4: Distribution of Point Differential
point_diff_data <- na.omit(nba$POINT_DIFF)
hist(
point_diff_data,
breaks = 30,
main = "Distribution of Home-Team Point Differential",
xlab = "Point Differential",
ylab = "Number of Games",
col = "steelblue",
border = "white"
)
abline(
v = mean(point_diff_data),
col = "red",
lwd = 2,
lty = 2
)
legend(
"topright",
legend = "Mean",
col = "red",
lwd = 2,
lty = 2
)
The histogram is roughly bell-shaped and centered slightly above zero. Most games had point differentials near the center, while very large wins or losses were less common. The red dashed line shows that the mean point differential was approximately 2.82 points, meaning home teams scored about 2.82 more points than away teams on average. Since the distribution is roughly symmetric and the dataset contains many observations, a t-test was used in the next analysis.
Q5: T-Test by Rebounding Advantage
nba$REB_GROUP <- ifelse(
nba$REB_DIFF > 0,
"Rebound Advantage",
"No Rebound Advantage"
)
t_test_result <- t.test(
POINT_DIFF ~ REB_GROUP,
data = nba
)
t_test_result##
## Welch Two Sample t-test
##
## data: POINT_DIFF by REB_GROUP
## t = -61.901, df = 25988, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group No Rebound Advantage and group Rebound Advantage is not equal to 0
## 95 percent confidence interval:
## -9.935803 -9.325898
## sample estimates:
## mean in group No Rebound Advantage mean in group Rebound Advantage
## -2.320045 7.310805In the case of the t-test, it indicated that there exists a significant difference between the two groups. In this case, the value of p was less than 2.2e-16. The mean of the point difference for home teams without a rebounding advantage was -2.32, while that of the home teams with rebounding advantage was 7.31. In this case, the difference was approximately 9.63 points. Since the value of p was less than 0.05, the results support my hypothesis.