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Tip-Off in Basketball: Does it Matter Which Team Gets to Start the Game?

Andrew Scheiner, Barry Tesman, Eren Bilen

Dickinson College in Carlisle, Pennsylvania

MAA Mathfest August 2023

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OUTLINE

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Introductions

Tip-Off Data

Visualization

Purpose

Results

Conclusions

Future Work

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INTRODUCTIONS

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Andrew Scheiner ‘25

Computer Science &

Data Analytics

Barry Tesman

Professor of Mathematics

Eren Bilen

Assistant Professor

of Data Analytics

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Introductions

Tip-Off Data

Visualization

Purpose

Results

Conclusions

Future Work

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OUR ABSTRACT

What is the significance of the opening tipoff in National Basketball Association (NBA) games? Does it matter which team wins the opening tipoff and does it have any impact on the game outcome? In this study, we investigate whether the opening tipoff influences the game outcome by analyzing the play-by-play data of all NBA games (n=27,536) dating back to the 1999-2000 season up to the 2021-2022 season. In addition to the opening tipoff, we consider the importance of any jumpball event, the overtime tipoff, and the likelihood of scoring after securing a jumpball.

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OUR MOTIVATION AND INTEREST

Motivation

Wanted to show that the jumpballs in NBA were insignificant (i.e., little impact on game outcome)
Find other jumpball factors - best jumpers, chance of scoring next after winning jumpball, and more

Interest

Hope to shed light on the first event to occur in every basketball game
Could this impact sports betting?
Does the jumpball matter? Could coaches use our findings for new strategies?

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Introductions

Tip-Off Data

Visualization

Purpose

Results

Conclusions

Future Work

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THE STORY BEHIND THE DATA

Collection

Kaggle dataset which extends Sports Reference
Play-by-play data with on-court lineups for every NBA game starting from the 1999 season through the 2021 season

Processing

Jupyter Notebook
Pandas - Python package
R - programming language
Excel - organization, visual assistance

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The original dataset had over 13 million rows and was 3 Gigabytes in size!

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WHAT THE RAW DATA LOOKS LIKE

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To describe what the raw play-by-play data looked like and how we used it for our project, let’s take a look at the first time in which a jumpball occurs in our data.

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The row for this jumpball event is highlighted using the red boxes. In this case, this event is an opening tipoff between the San Antonio Spurs’ Tim Duncan and the Minnesota Timberwolves’ Darko Milicic.

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Next, as highlighted in yellow, Kevin Love receives the jumpball. My task as a data processor was to use this information and determine which team won the jumpball.

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So, by checking the rest of the data in the row, we can see that Love was on the home team because his player ID shows up in the H1 column in the same row, meaning the Timberwolves won the jumpball as they were the home team during the game this jumpball took place.

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WHAT THE PROCESSED JUMPBALL LIST LOOKS LIKE

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Our goal was to process the raw data enough to get a processed dataset with all of the jumpball and event information necessary to help investigate significance.

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Looking at our processed jumpball list let’s look at the same jumpball as before between Duncan and Milicic.

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First highlighted is the event itself which is critical to gathering the other variables.

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Then, we have basic info such as the teams, scores, period the game ended. These variables are crucial in determining the team which won the jumpball and a TRUE/FALSE variable recording: TRUE if the team who won the jumpball won the game and FALSE otherwise.

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Next, we wanted to classify types of jumpball events. By processing the time left and current period when the jumpball occurred, we could determine the type of jumpball. Time left needed to be numerical instead of in time format for easier processing.

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And last, we spent some time investigating jumpers. We found which jumpers won and lost each jumpball, gathered cumulative statistics and created ELO ratings.

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HOW THE DATA WAS PROCESSED

Impact on Game Outcome

Finding jump balls
Finding which side won each jump ball using player information
Finding final scores
Did the team that won the jumpball win the game?

Additional Findings

Jumpball types
Period that game ended
Time left in the game
Jumper information
Creating a jumper ELO score
Which team scored next after jumpball

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PROBLEMS ENCOUNTERED

Problems

Some jumpball events never recorded the receiver
Some player’s IDs were not found using regex
Some games do not have final scores
Shifted data

Solutions

Use next game event to determine who won possession
Find final scores externally and crosslist (ex. 2017-18 season)
Separately shift raw data manually before processing

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Introductions

Tip-Off Data

Visualization

Purpose

Results

Conclusions

Future Work

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SUMMARY STATISTICS

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“GameWinnerWonJB” has observations as follows: 0 = winner of jumpball lost the game. 1 = winner of jumpball won the game.

“ScoredNext” has observations as follows: 0 = the team that won the jumpball did not score next. 1 = the team that won the jumpball scored next.

Count and frequency here measure how often a team won the game after winning the jumpball.

Count and frequency here measure how often a team scored next after winning the jumpball.

variables

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SUMMARY STATISTICS

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All tipoffs

Beginning tipoffs

During regulation or overtime

During regulation

All overtime

Overtime tipoffs

During overtime

Beginning tipoffs

During regulation

During overtime

Overtime tipoffs

During overtime

Overtime tipoffs

During regulation

Beginning tipoffs

For example, this chart tells us that when looking at all overtime tipoffs, the winner of the overtime tipoff won the game 53.86% of the time.

For example, this chart tells us that when looking at all overtime tipoffs, the winner of the overtime tipoff was the team to score next 67.15% of the time.

This next slide contains some breakdowns we found on the distinct types of jumpballs.

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First we looked at jumpball type and frequency of occurrence throughout the entire scope of our dataset.

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We can see there were 27,434 opening tipoffs and 1,651 overtime jumpballs (overtime includes overtime tipoffs too). Frequency measures the percent of all jumpballs that each type made up. Please keep these totals in mind for when we look at regression later.

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We additionally looked at the frequency for when a jumpball winner would win the game based on type.

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For example, this chart tells us that when looking at all overtime tipoffs, the winner of the overtime tipoff won the game 53.86% of the time.

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And lastly here, we looked at the frequency for when a jumpball winner would score next based on type.

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For example, this chart tells us that when looking at all overtime tipoffs, the winner of the overtime tipoff was the team to score next 67.15% of the time.

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SUMMARY STATISTICS

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“Wj” stands for the winning jumper of a jumpball event while “Lj” stands for the losing jumper.

For this last summary statistics slide, I have the rest of the important variables we created and want to make some notes.

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First, we were able to find both the time left for all jumpball events and the period every jumpball occurred in.

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Next, I want to highlight the average final score for both the away and home teams for all games in our dataset. Home teams, on average, score more points than away teams and we will take a visual look at final scores based on the jumpball winning/losing teams later. In addition, the latest an NBA game ended was the 8th period, or quadruple overtime! I should also note there were 16 games we were unable to process final scores for.

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And last, I wanted to highlight some overall jumper statistics we found. For every jumpball event, info was divided into the winning jumper and the losing jumper. There were 82 jumpball events in which we were unable to uncover the jumpers.

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Call:

lm(formula = gamewinner_won_jb_B ~ beg_tipoff, data = jumpballs)

Residuals:

Min 1Q Median 3Q Max

-0.5298 -0.5265 0.4702 0.4735 0.4735

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 0.529818 0.003531 150.042 <2e-16 ***

beg_tipoff -0.003318 0.004643 -0.715 0.475

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.4992 on 47420 degrees of freedom

Multiple R-squared: 1.077e-05, Adjusted R-squared: -1.032e-05

F-statistic: 0.5108 on 1 and 47420 DF, p-value: 0.4748

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Even if a team wins an opening tipoff, this event does not have significance on the game outcome. The p-value of 0.475 is too high (above 0.05), so we can conclude that winning the opening tipoff will not give the winning team a greater chance at winning the game.

Equivalent to: -0.00001032, this extremely small R-squared value shows us that the percentage of the variation in the tipoff winner winning the game cannot be explained by the tipoff event alone.

This linear regression model (done in R) analyzes the relationship between a team winning the tipoff and potential ensuing impact on game outcome. We want evidence that a team winning the tipoff does not significantly impact game outcome in any way.

Response variable: 0 = winner of jumpball lost the game. 1 = winner of jumpball won the game.

Considering all opening tipoffs.

Data is the processed jumpball list.

Next, I would like to display and explain how we want to show significance through regression.

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This linear regression model (done in R) analyzes the relationship between a team winning the tipoff and potential ensuing impact on game outcome. We want evidence that a team winning the tipoff does not significantly impact game outcome in any way.

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Response variable: 0 = winner of jumpball lost the game. 1 = winner of jumpball won the game.
Considering all beginning tipoffs.
Data is the processed jumpball list.

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Even if a team wins an opening tipoff, this event does not have significance on the game outcome. The p-value of 0.475 is too high (above 0.05), so we can conclude that winning the opening tipoff will not give the winning team a greater chance at winning the game.

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Equivalent to: -0.00001032, this extremely small R-squared value shows us that the percentage of the variation in the tipoff winner winning the game cannot be explained by the tipoff event alone.

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Call:

lm(formula = gamewinner_won_jb_B ~ overtime, data = jumpballs)

Residuals:

Min 1Q Median 3Q Max

-0.5385 -0.5278 0.4722 0.4722 0.4722

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 0.527775 0.002336 225.934 <2e-16 ***

overtime 0.010780 0.012521 0.861 0.389

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.4992 on 47316 degrees of freedom

Multiple R-squared: 1.567e-05, Adjusted R-squared: -5.468e-06

F-statistic: 0.7413 on 1 and 47316 DF, p-value: 0.3893

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This linear regression model (done in R) analyzes the relationship between a team winning a jumpball in overtime (tipoff or not) and potential ensuing impact on game outcome. We want evidence that a team winning an overtime jumpball does not significantly impact game outcome in any way.

Even if a team wins an overtime jumpball, this event does not have significance on the game outcome. The p-value of 0.389 is too high (above 0.05), so we can conclude that winning an overtime jumpball will not give the winning team a greater chance at winning the game.

Equivalent to: -0.000005468, this extremely small R-squared value shows us that the percentage of the variation in an overtime jumpball winner winning the game cannot be explained by an overtime jumpball event alone.

Response variable: 0 = winner of jumpball lost the game. 1 = winner of jumpball won the game.

Considering all overtime jumpballs.

Data is the processed jumpball list.

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	Response Variable = Did jumpball winner win game?		Response Variable = Did jumpball winner score next?
Explanatory Variable	Point Estimate	P-Value	Point Estimate	P-Value
All overtime jumpballs	0.010780	0.3893	0.025556	0.0330
Overtime tipoffs	0.010856	0.4152	0.025896	0.0424
All tipoffs to start the game	-0.003318	0.4748	-0.009367	0.0353
Any tipoff event	-0.001983	0.6733	-0.006366	0.1574
Jumpballs during regulation or overtime	0.001983	0.6733	0.006366	0.1574
Jumpballs only during regulation	0.001821	0.6991	0.006011	0.1828
Jumpballs only during overtime (not overtime tipoffs)	0.009579	0.7871	0.021575	0.5251

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ADDITIONAL REGRESSION FINDINGS

Selection models were unable to show us significant results.
We accounted for any team differences via team fixed effects and the results are insignificant.
While variables might have shown significance through low p-values, it’s tough to conclude correlation because of small, varying coefficients and low R-squared values.

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Introductions

Tip-Off Data

Visualization

Purpose

Results

Conclusions

Future Work

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WANT BIG IMPACT?

USE BIG IMAGE.

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The boxed cells show the correlation between two variables. The constant variable always being compared here is if a team that won the jumpball won the game. Each highlighted cell is comparing this constant variable with all other numerical variables in the processed jumpball dataset.

The correlation values in all of the red highlighted cells are extremely small and insignificant. While the correlation for a team winning the game after winning the jumpball and scoring next is higher than 0.05, this still likely shows very slight significance and importance on game outcome.

The constant variable always being compared in these boxed cells is if a team that won the jumpball scored next. Each highlighted cell is comparing this constant variable with all other numerical variables in the processed jumpball dataset.

This correlation plot helps visualize the findings from our regression models by showing point estimates when comparing all numerical variables with each other

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The boxed cells show the correlation between two variables. The constant variable always being compared here is if a team that won the jumpball won the game. Each highlighted cell is comparing this constant variable with all other numerical variables in the processed jumpball dataset.

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The correlation values in all of the red highlighted cells are extremely small and insignificant. While the correlation for a team winning the game after winning the jumpball and scoring next is higher than 0.05, this still likely shows very slight significance and importance on game outcome.

[Click] [Click]

The constant variable always being compared in these boxed cells is if a team that won the jumpball scored next. Each highlighted cell is comparing this constant variable with all other numerical variables in the processed jumpball dataset.

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WANT BIG IMPACT?

USE BIG IMAGE.

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There were multiple Charlotte teams in the scope of this dataset; CHH stands for the 1999-2002 Charlotte Hornets.

VAN stands for the Vancouver Grizzlies who were active from 1999-2001.

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WANT BIG IMPACT?

USE BIG IMAGE.

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WANT BIG IMPACT?

USE BIG IMAGE.

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WANT BIG IMPACT?

USE BIG IMAGE.

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Introductions

Tip-Off Data

Visualization

Purpose

Results

Conclusions

Future Work

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WHAT WE CAN TAKEAWAY

We do not have enough statistical evidence that the opening tipoff (and rather, any jumpball for the matter) has an impact on game outcome.
So, why start the game with a tip off, if it is inconsequential to the game result? Maybe for “excitement”?
However, we found some statistical significance in the relationship between winning the jumpball and scoring next. (considering jumpball type)

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Introductions

Tip-Off Data

Visualization

Purpose

Results

Conclusions

Future Work

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WHAT’S NEXT?

Does it matter which team won the first quarter?
Does it matter if a team starts with the ball in a given quarter or period?
These results could be broken down more into team splits, home/away team splits - which could impact betting, strategy, jumpball success, and more.
What other events in basketball seem out-of-place? (e.g. the free throw, inbound, etc.) Are they significant to the game?

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THANK YOU TO

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My research supporters,

Professor Barry Tesman and Professor Eren Bilen for their guidance and support throughout this whole process.

MAA, MathFest, and Rick Cleary for accepting our abstract and organizing an amazing conference.

My grandfather, Richard Holtzman for accompanying me on my trip.

Everyone in attendance for listening! Please let me know if you have any questions.

Dickinson College’s Kenderdine Travel Fund for helping with travel costs.