The pursuit of the perfect 10: how home attendance infeluences scores in NCAA gymnastics

NCAA gymnastics is one of the fastest growing sports in the country. Social media engagement is high following the waves of high-level gymnasts who joined NCAA teams after the Tokyo Olympics. With more attention on the sport than ever before, now is the perfect time to examine the intricacies of the judging system. Rankings in NCAA gymnastics are determined by average scores alone, so any influence on scores outside of team ability has the potential to impact which teams get seeded in the postseason. The research in this paper focuses on the attendance effect. I use a fixed effects multivariate regression to determine that meets with higher attendance do influence scores. I find that the relationship between scores and attendance is positive even when controlling for the quality of a team. Vault and balance beam show the most significant effects, and there is no statistically significant effect present for uneven bars or floor exercise. Whether a team is home or away, scores will increase as attendance grows.

ABSTRACT NCAA gymnastics is one of the fastest growing sports in the country. Social media engagement is high following the waves of high-level gymnasts who joined NCAA teams after the Tokyo Olympics. With more attention on the sport than ever before, now is the perfect time to examine the intricacies of the judging system. Rankings in NCAA gymnastics are determined by average scores alone, so any influence on scores outside of team ability has the potential to impact which teams get seeded in the postseason. The research in this paper focuses on the attendance effect. I use a fixed effects multivariate regression to determine that meets with higher attendance do influence scores. I find that the relationship between scores and attendance is positive even when controlling for the quality of a team. Vault and balance beam show the most significant effects, and there is no statistically significant effect present for uneven bars or floor exercise. Whether a team is home or away, scores will increase as attendance grows. ii TABLE OF CONTENTS ABSTRACT ii INTRODUCTION 1 DATA AND METHODS 6 RESULTS 8 DISCUSSION 18 APPENDIX 22 REFERENCES 26 iii 1 INTRODUCTION College gymnastics is more popular now than it has ever been. The 2022 NCAA gymnastics championship drew the largest college gymnastics audience in over 10 years. The ABC broadcast peaked at 1.1 million viewers, rising 11% in viewership over 2021’s final that aired during primetime. The 2022 championship aired in an earlier timeslot in favor of ABC’s NHL package, but gymnastics outdrew the NHL game by 29% in ratings and 15% in viewership.1 A potential explanation for this surge in popularity is the ability of elite gymnasts to capitalize on their Name, Image, and Likeness (NIL). Before 2021, elite-level gymnasts had to choose between competing in college and “going pro,” a.k.a. making money through media and brand deals. The NCAA policy on amateurism often served as a barrier to young gymnasts who made the Olympic team from competing in college.2 Now, they don’t have to choose. Four of the six 2020 U.S. Olympians enrolled in college following the Tokyo Olympics: reigning all-around champion Sunisa Lee (Auburn University), Olympic floor gold medalist Jade Carey (Oregon State University), and team silver medalists Jordan Chiles (UCLA) and Grace McCallum (University of Utah), not to mention multiple international Olympians, including team bronze medalist Amelie Morgan from Great Britain (University of Utah).3 It is no coincidence that Auburn set attendance records in every category possible in the 2022 season when Lee joined as a freshman. The Auburn Tigers sold out all five home meets, reaching a total of 45,605 fans throughout the season, along with almost 1,500 students in attendance on Lewis, “Ratings: Gymnastics, Kayrod, Spieth Win, NHL.” Sports Media Watch, April 20, 2022. Roenigk. “How Nil Has Transformed Gymnastics for Olympians, NCAA and Beyond.” ESPN. ESPN Internet Ventures, January 24, 2023. 3 College Gym News. “Olympians in the NCAA.” College Gym News, November 21, 2022. 1 2 2 average. Auburn also broke the season ticket-holder record with 5,674.4 Sunisa Lee led the Tigers to their highest finish ever in a season, finishing 4th in the 2022 NCAA championships.5 Figure 1 shows average attendance from 2015 to 2022. The question I seek to answer is whether the team’s performance changed as a result of its increased attendance. Figure 1. NCAA gymnastics had been noticeably growing in popularity, hitting its peak in 2019. 2020 onwards shows effects of the COVID-19 pandemic, with many arenas not allowing fans at all in 2021. 2022 saw a rise once more, but lingering worries about the pandemic may have influenced attendance numbers in 2022 as well. Auburn University Athletics. “Another Attendance Record Set for Auburn Gymnastics.” Auburn University Athletics, March 10, 2022. 5 “Standings - Final (2022).” RoadToNationals, April 16, 2022. 4 3 The first step towards answering the question is understanding how college gymnastics works. Each team puts up a six-gymnast lineup per event. If there is a home team, they rotate in “Olympic order” – vault, uneven bars, balance beam, then floor. On each event, five of the six scores count. The team drops the lowest score in the rotation. An individual gymnast can get any score up to a 10.0 for a maximum team event score of 50. Each event score is summed to the final team score. Whichever team has the highest aggregate score at the end of the meet wins. 6 Exhibit 1 of the appendix shows an example of a gymnastics score sheet for further clarity. Most teams view a 196, or an average score of 9.80, as a desirable score. Top teams will aim for a 198, or an average score of 9.90. While teams always seek to win the meet, it is not the most critical component of the competition. Instead, a team will look for scores that will increase their National Qualifying Score (NQS), which determines regular season rankings. If a team loses a meet but scores a season-high, they will still be pleased with the performance because it has the potential to increase their national ranking. 7 A team’s NQS is taken from their 3 highest away scores, then the next 3 highest scores, which can be home or away (neutral meets are counted as away in this format). The top score from the six is dropped, and the remaining five are averaged into the NQS.8 The format for NQS places more emphasis on away scores, which indicates that those in charge of rankings assume a significant home team advantage. Hopkins. “An Intro to Collegiate Gymnastics.” The Gymternet, November 22, 2014. Hopkins, “Intro to Collegiate Gymnastics.” 8 Hopkins, “Intro to Collegiate Gymnastics.” 6 7 4 Sports outside of gymnastics have home team advantages as well. A 1992 study by Courneya and Carron found that every sport they studied had a home winning percentage (HWP) over 50%.9 The findings are consistent over baseball, basketball, and soccer, with college basketball having the highest HWP recorded at 64.4%. 10 Most literature agrees that the biggest cause of home advantage is bias from the game’s officials. Nevill and Holder claim that “the lack of evidence of home advantage in individual sports such as golf majors and tennis grand slam tournaments, when crowd sizes are considerable, may reflect the relatively objective nature of the scoring systems used in tennis and golf, unlike the subjective influence of officiating decisions on the outcome of team games.”11 The claim is backed up by Lehman and Reifman, who found that star basketball players were fouled significantly less at home, while the number of fouls for nonstar players remained consistent no matter the location. The conclusion they drew was that officials feel pressured by the home crowd to favor their star players.12 With the ever-increasing number of famous Olympic gymnasts joining NCAA teams, it is likely the same effects are present in gymnastics. Baghursy and Fort conducted the only known literature on home advantage in NCAA gymnastics specifically in 2008. Their study found a statistically significant home advantage, especially on bars and floor. However, their analysis used only scores from 15 teams who were ranked top 25 nationally at the end of the season between 2003 and 2007.13 This paper modernizes the data used in previous studies, and adds scores from every college team. Instead of Courneya & Carron. “The Home Advantage in Sport Competitions: A Literature Review.” 1992. Nevill & Holder. “Home Advantage in Sport.” 1999. 11 Nevill & Holder. “Home Advantage.” 12 Lehman & Reifman. “Spectator influence on basketball officiating.” 1987. 13 Baghurst & Fort. “Subjective Judging and the Home Advantage in Female Collegiate Division I Gymnastics.” 2008. 9 10 5 looking at only nationally ranked teams, I focus on the effect of attendance specifically no matter what a team’s ranking is. 6 DATA AND METHODS The data used in this analysis is scraped from RoadToNationals.com, the official rankings site for college gymnastics. I chose to look at every meet from 2015 to 2022. This ended up consisting of 27,800 meets with 179,256 scored routines. The data from RoadToNationals gave me each gymnast’s score, the event, the host team and teams involved, the date, and attendance. Knowing the host team for each meet made it a simple process to create dummy variables for home, away, and neutral teams, which are important for gaining insight on home team advantage. Because one of my top variables of interest is attendance, I drop all scores in which attendance data isn’t available for the regression. I use a fixed effects multivariate regression equation to find the effect of attendance on scores: score= β0+ β1home+ β2 away+ β3 logattend+ β4postseason+ β5homeXattend+ β6awayXattend+δ1month+ δ2year+ δ3team + ε Each meet is designated by a location: home, away, or neutral. All three potential locations have a dummy variable associated with them in the dataset, with the neutral dummy variable being left out of the regression to prevent multicollinearity. Logattend indicates a logarithmic function of a meet’s attendance. A logarithmic function allows us to account for the fact that a 100-person increase in attendance has a more prominent effect when attendance is low than when attendance is high. Postseason is a dummy 7 variable equal to 1 when a meet takes place after the regular season is complete. Not every team competes in the postseason – only the best teams qualify. Scores will be higher on average in the postseason, meaning I must account for it to eliminate omitted variable bias. HomeXattend and awayXattend represent the interaction between the location dummy variables and logattend. The interaction variables change the slope of the home, away, and neutral estimations to provide a more accurate representation of each coefficient. It pulls out any joint significance between the location and attendance variables. The variables denoted with a  represent fixed effects (FE) variables. Fixed effects control for time-invariant attributes. The fixed effects allow for analysis of each part of a given variable separately. For example, my first FE variable is month. I generate dummy variables for each month in the gymnastics season: January, February, March, and April. Average score rises as the season continues, so average scores in March and April will be higher than in January and February. Including a month FE isolates the effect of the month on score, removing the correlation from our variables of interest (home, away, neutral, interactions, and attendance). I do the same for year and team. One of the significant issues with looking at only attendance and scores is that most teams that draw higher attendance are also high-performing teams. The performance of individual teams needs to be removed to find the pure attendance effect. If an attendance effect does exist, it is the same across all teams, with team FE adjusting the intercept to account for team performance. I use the same regression equation to examine the scores for each individual event, to determine if there is a discernible difference from one event to another. 8 RESULTS Figure 2 shows the output from the regression detailed in Data and Methods. Additionally, Exhibit 2 in the Appendix shows the summary statistics of relevant variables. The summary statistics aids in exploratory analysis of the variables and provides additional context to each variable’s value. VARIABLES home away logattend homeXattend awayXattend postseason February March April 2016 2017 2018 2019 2020 2021 2022 (1) attendance only (2) interaction (3) controls (4) team fixed effects 0.00756** (0.00366) -0.0575*** (0.00364) 0.0944*** (0.000875) -0.00251 (0.0264) -0.0260 (0.0261) 0.0962*** (0.00310) 0.00150 (0.00336) -0.00441 (0.00334) -0.149*** (0.0265) -0.187*** (0.0263) 0.0847*** (0.00315) 0.0247*** (0.00338) 0.0203*** (0.00336) -0.148*** (0.0252) 0.0617*** (0.00229) 0.106*** (0.00237) 0.209*** (0.0255) 0.0130*** (0.00364) 0.0165*** (0.00360) 0.0209*** (0.00363) 0.00354 (0.00369) 0.0138*** (0.00392) 0.256*** (0.00454) 0.0633*** (0.00383) -0.0689*** (0.0254) -0.0930*** (0.0251) -0.00177 (0.00320) 0.0108*** (0.00322) 0.0104*** (0.00319) -0.0533** (0.0224) 0.0565*** (0.00204) 0.0822*** (0.00216) 0.131*** (0.0227) 0.00689** (0.00323) 0.0200*** (0.00325) 0.0230*** (0.00328) 0.0133*** (0.00331) 0.0180*** (0.00351) 0.0366*** (0.00438) 0.0389*** (0.00350) 9 Constant 8.984*** (0.00748) 8.971*** (0.0244) 8.956*** (0.0249) 9.511*** (0.0254) Observations 145,513 145,513 145,513 145,513 R-squared 0.091 0.091 0.125 0.292 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Figure 2. Output of regression for overall scores. Note: values for each team’s FE are not included on the table for conciseness and clarity; we mainly focus on how removing those effects from our dependent variable impacts other outputs. Regression (1) runs only the variables home, away, and logattend. This regression does not paint a fully accurate picture of how attendance effects scores because I have not accounted for any other controls. Regression (2) includes interactions between attendance and location: homeXattend and awayXattend. The interaction variables show the slope of the home and away relationships with score relative to neutral meets. In Regression (3) I add controls for postseason meets, month, and year. Finally, and most importantly, Regression (4) adds team fixed effects to Regression (3). Unsurprisingly, scores appear to grow later in the season. Every month coefficient is positive, with April being the highest. Teams score, with all else equal, 0.131 points higher per routine in April than they do in January. That is a dramatic difference. If each score improves to that degree by the end of the season, teams score 2.62 points higher in April than in January. The year FE does not have high variance, but it does appear to have increased in recent years. All else equal, a score are 0.0389 points higher in 2022 than in 2015. The biggest jump happens between 2020 and 2021, where the coefficient moves from 0.0180 to 0.0366. In 2021, most teams competed in empty arenas due to the lingering effects of the COVID-19 pandemic. If it is true that attendance plays a role in increased scores, scores being higher in 2021 contradicts that conclusion. Some speculate that the long 10 break between the shortened 2020 season and 2021 gave gymnasts more time to rest than usual, might explain higher scores. Another possible explanation is that not all teams competed in 2021. RoadToNationals 2019 rankings consist of 82 teams, and 2021’s has 65. The number goes back up to 82 in 2022. 14 Some teams opted out of competing in 2021, and it is reasonable to assume that the majority of the teams that opted out were from smaller programs where the schools do not have the funding or infrastructure to support the accommodations necessary for pandemic protocols. Average scores being higher, then, reflects on only having higher-ranked teams performing that season as opposed to any attendance-related conclusions. Adding team FE reduces the effect of location and attendance alike. The attendance coefficient drops from 0.0847 to -0.00177. Similarly, the coefficients for homeXattend and awayXattend both drop by about 0.01. They are all statistically significant differences. Importantly, the interaction variables remain positive. This indicates a positive relationship between attendance and home/away scores. I ran an Ftest to prove that the home and away slopes are statistically different from neutral slopes. The difference in slope comes entirely from the location and interaction variables, so to prove statistical significance, we must reject the null hypothesis that home + homeXattend = 0. The same is true for away + awayXattend. After running the F-tests in Stata for both regressions, I find that the F-values are indistinguishable from zero. Any Fvalue below 0.01 is statistically significant at the 99% level. Therefore, the slopes for home, away, and neutral meets are all distinctly separate from each other. 14 “Standings.” RoadToNationals. 11 Figure 3 shows a visual representation of regression (4). Exhibit 3 provides numerical values for the logarithms labeled on each graph’s x axis for ease of interpretation. The first graph shows the results for all of the groups left out of the regression to account for multicollinearity: scores for each level of attendance at Air Force Academy, in January 2015. For an example of incorporated team fixed effects, the second graph shows the University of Utah’s scores in January 2015. The slopes are identical, but the y-intercept for Utah shifts up by 0.256 points from Utah’s team fixed effects coefficient. We use Utah specifically because Utah consistently draws the highest attendance in all of NCAA gymnastics.15 They are the team most likely to have meets that fall any point of attendance level on the graph, which means I can compare directly to their team scores in a way I may not be able to for a school like Air Force. For each team, neutral meets start higher than home meets at a base attendance of zero. However, as attendance grows, home and away scores grow as well, while neutral scores decline. Home scores overtake neutral scores at its intercept of (9.50, 6.38) for Air Force, and (9.76, 6.38) for Utah. Log(6.38) comes out to roughly 590 people in attendance. The intercept of away and neutral scores comes at higher attendance, with Air Force’s intercept at (9.46, 8.94) and Utah’s at (9.75, 8.94). That equals to an attendance of 7,631. It only becomes beneficial to schedule an away meet compared to a neutral meet when attendance rises above the 7,631-person mark. Before attendance reaches that point, teams prefer to compete at a neutral site meet. For popular and high-performing teams like Utah, scheduling away meets is often worth it because their evenly matched opponents tend to have high attendance as well. Air Force, however, cannot guarantee 15 University of Utah Athletics. “Utah Gymnastics Breaks School Record for Season Average Attendance.” 13 Event Totals The table in Figure 4 exhibits the regression detailed in Methods for each event. Regression (1) is the same as Regression (4) from Figure 2, while the following use the same regression with data limited to the focused event. Because the comparison between the left-out team and a team included in team FE is established, I will center the analysis around Utah’s scores only moving forward. That is why the variable Utah FE has been added to Figure 5. The slopes for each team will be identical to Utah’s outputs, with only the y-intercepts shifting up and down. Exhibit 4 lists each team’s fixed effects to show how other teams would factor into this analysis. VARIABLES home away logattend homeXattend awayXattend postseason February March April 2016 2017 2018 2019 (1) overall scores (2) vault (3) bars (4) beam (5) floor -0.0689*** (0.0254) -0.0930*** (0.0251) -0.00177 (0.00320) 0.0108*** (0.00322) 0.0104*** (0.00319) -0.0533** (0.0224) 0.0565*** (0.00204) 0.0822*** (0.00216) 0.131*** (0.0227) 0.00689** (0.00323) 0.0200*** (0.00325) 0.0230*** (0.00328) 0.0133*** -0.110*** (0.0311) -0.0998*** (0.0304) -0.00472 (0.00391) 0.0155*** (0.00401) 0.0130*** (0.00392) -0.0763*** (0.0189) 0.0365*** (0.00236) 0.0562*** (0.00249) 0.118*** (0.0196) -0.00274 (0.00383) 0.00529 (0.00384) 0.00494 (0.00397) -0.00894** 0.0415 (0.0639) -0.00650 (0.0630) 0.0154* (0.00792) -0.00296 (0.00799) -0.00206 (0.00791) -0.00405 (0.0304) 0.0664*** (0.00492) 0.0952*** (0.00520) 0.0849*** (0.0325) -0.00723 (0.00733) 0.00459 (0.00752) 0.00349 (0.00748) -0.00665 -0.192*** (0.0490) -0.221*** (0.0488) -0.0228*** (0.00633) 0.0263*** (0.00635) 0.0276*** (0.00634) -0.0660** (0.0328) 0.0569*** (0.00407) 0.0825*** (0.00427) 0.146*** (0.0336) 0.0237*** (0.00641) 0.0398*** (0.00636) 0.0427*** (0.00646) 0.0387*** -0.0145 (0.0481) -0.0457 (0.0471) 0.00493 (0.00614) 0.00439 (0.00610) 0.00299 (0.00600) -0.0681 (0.0760) 0.0658*** (0.00412) 0.0948*** (0.00449) 0.175** (0.0760) 0.0144** (0.00713) 0.0305*** (0.00711) 0.0409*** (0.00725) 0.0299*** 14 2020 2021 2022 Utah FE Constant (0.00331) 0.0180*** (0.00351) 0.0366*** (0.00438) 0.0389*** (0.00350) 0.256*** (0.00904) 9.511*** (0.0254) (0.00397) 0.00642 (0.00414) 0.0294*** (0.00504) 0.0372*** (0.00398) 0.155*** (0.0117) 9.573*** (0.0312) Observations 145,513 36,263 R-squared 0.292 0.453 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Figure 4. (0.00756) -0.00868 (0.00814) 0.0231** (0.00995) 0.00929 (0.00789) 0.135*** (0.0274) 9.344*** (0.0634) (0.00634) 0.0412*** (0.00684) 0.0461*** (0.00898) 0.0687*** (0.00639) 0.171*** (0.0191) 9.606*** (0.0495) (0.00746) 0.0332*** (0.00764) 0.0479*** (0.00957) 0.0409*** (0.00836) 0.110*** (0.0133) 9.522*** (0.0485) 36,412 0.326 36,534 0.316 36,304 0.228 On vault, the slopes for home and away meets are positive and steeper than overall scoring trends. The same is true for balance beam, which has the steepest slope of all four events. Vault and beam are also the only two individual event slopes that are statistically significant. Bars and floor have flatter slopes that pose no statistical significance in the regression. Figures 5, 6, 7, and 8 show the results of Regressions (2) through (5) visually. Vault is the only event in which the away intercept is higher than the home intercept, though the slope of the home score’s line quickly overtakes away at an intercept of (3.33, 9.75), equivalent to attendance of just 28 people. Home scores overtake neutral scores at an intercept of (6.875, 9.79), or attendance equal to 967 people. Away scores are higher than neutral scores at (7.69, 9.78), or an attendance of 2,186 people. Away teams do not need as high of attendance to benefit from the attendance effect for vault as they do overall, but it is still significantly higher than the minimum attendance required to benefit at home. 15 Bars (Figure 7) differs from the other events in that there are no intercepts. The coefficients for homeXattend and awayXattend are negative, which flattens the slope significantly. For bars, home scores are always highest, away scores are always lower, and neutral scores are always in between. A possible reason for this is that in dual meets, away teams always start on bars. Teams may show more nerves in the first rotation, leading to lower scores. The lack of intercept may be due to that unaccounted-for factor of gymnast nerves at the beginning of a competition. Ultimately, it is hard to make any concrete estimates or theories about the uneven bars scores because they are statistically insignificant. Away scores are once again the lowest on balance beam. Home scores do not pass neutral scores until log attendance of 7.38, or 1,604 people. Beam has a higher attendance requirement to benefit from home scores, but the score required, 9.73, is lower. This is likely due to the fact that balance beam is a more inconsistent event in which lower scores and falls are more common. The floor exercise’s results are also not statistically significant. This is surprising because home teams end on floor. It is a high-energy event with the heaviest crowd involvement. Of all events, it would seem the most likely that attendance would influence floor scores. If the results were statistically significant, however, it would show that home scores are higher than neutral scores starting at the intercept of (2.72, 9.71). That is an attendance of only 15 people. Therefore, we would assume that almost every home team has an advantage over neutral teams on floor, which we cannot assume for vault or beam. We do see that, again, away scores are the lowest of the three. 18 DISCUSSION The results of the fixed effects multivariate regression showed that teams do in fact have higher scores when attendance increases. The effect is more pronounced for home teams, but away teams benefit as well. In the scope of this analysis, home scores are definitively higher than away scores at a statistically significant level. It is reasonable to assume, then, that top teams use their position in the national landscape to schedule more home meets to bolster their NQS. The regression provides evidence of this as well. When I add team fixed effects to the regression in Regression (4), the coefficient on home goes down from 0.0167 to 0.0103, indicating that part of that higher home score is attributed to specific team effects. Now, correlation between team and home and between team and score gets pulled into the team fixed effects. It goes down because better teams tend to have more home meets. The same is true for away, rising from a coefficient of 0.0535 to -0.0171. If the isolated away effect is higher with team FE, that means that teams who tend to perform worse compete at away meets more often. Even if teams only have one extra home meet, it is significant for ranking purposes because only 3 home scores can count for NQS. With an extra home meet, teams have a higher margin for error and more chances to reach their peak NQS. One potential explanation for home meets consistently having higher scores is that home teams hire the judges for meets they host. Some teams offer higher pay than others.16 Because of this system, judges may feel pressured to give high scores to home teams so they may get hired again in the future. If a coach doesn’t like how a judge 16 Dougherty. “Judging Concerns Gymnastics Coaches.” The Minnesota Daily, 02 April, 1998. 19 scores their team, they will find a new set of judges to give them the scores they want to see. In a sport where scores and rankings are subjective, it is important to have accountability and transparency in judging. The data scraped from RoadToNationals did not include judges, but adding judge fixed effects in the future would be a valuable addition. Not including judge FE is a limitation of this study, as there is most definitely bias in judging that is unaccounted for. Even if the bias is subconscious, it is still important to capture. Judging likely correlates with attendance as well – if a judge would normally give a 9.950 for a routine but the crowd is all shouting for a 10.0, it may pressure the judge into giving the routine a higher score than they feel it deserves. The score a judge gives a routine is published in the score sheet after a meet ends, but the deductions aren’t published. With more and more fans looking for a solution to allegedly biased judging, full transparency is necessary. Listing deductions for each routine is a promising start. A potential solution to home team judging bias would be to hire an independent committee that assigns judges to a certain meet rather than have host coaches hire the judges. To go further, randomly assigning judges to meets throughout the season creates the potential for a natural experiment in the future to capture the impact specific judges have more accurately on the outcome of a meet. The complication of judging biases is made more prevalent by new developments in technology. The 2019 World Gymnastics Championships in Stuttgart piloted the use of an artificial intelligence system made by Fujitsu that allowed for “robotic judging.” 17 To use the system, gymnasts provided their measurements and recorded their movements Keh. “Gymnastics' Latest Twist? Robot Judges That See Everything.” The New York Times, October 10, 2019. 17 20 prior to the competition. It was, however, used only in a limited capacity. Judges only used the Fujitsu system to settle inquiries (challenges to the awarded difficulty score by gymnasts) and large deviations between judges on the panel. Additionally, the technology was only used on men’s pommel horse, rings, and vault, and women’s vault.18 Robotic judging is useful in catching small deductions that may not always be noticeable from a human eye. Using it as verification of the judging panel could be valuable in preventing unfair or incorrect results based on human error. Other sports are seeing a similar transition, with the most successful so far being baseball. New “robo-umps” are taking the place of home plate umpires in the Triple A Minor League. The umpires at home plate then simply communicate the call decided by the system. 19 While the automated ball strike system does take most of the subjectivity out of the calls, coaches and fans alike still prefer human referees, arguing that the game would not be as engaging without the human nature of the play-calling.20 The subjective nature of gymnastics judging complicates this issue further. Gymnastics places just as much emphasis on “artistry” as it does on difficulty. At the moment, a computer cannot interpret artistic expression as well as a human can. The nuance of the artistic component is the necessary sacrifice for further insights on the true attendance effect on team scores. AI is free of the biases and pressure a human judge may have, and thus would theoretically score each routine the same way no matter what team the gymnast is on. So, while we don’t yet know the future of robotic judging, AI-based scoring would remove any present causal judging effects and strengthen the statistical significance of this analysis in particular. Keh. “Gymnastics’ Latest Twist?” Gourgey. “Will Baseball Ever Replace Umpires with Robots?” Popular Science, June 22, 2022. 20 Gourgey. “Replace Umpires with Robots?” 18 19 21 There are a few other limitations to this study. One, none of the information in the dataset includes social media following or television ratings. It is possible that a team’s score is influenced by their online popularity. Also, while it is not confirmed, there is speculation on social media that judges are told by TV executives to give higher scores to improve ratings. Even if it isn’t true, judges could be influenced by the idea of a bigger audience in a comparable way as they would be with high in-person attendance. A possible extension of this analysis includes discovering whether a team’s television viewership numbers impact their scores differently. I also did not account for differences between individual gymnasts. Similarly to the previously mentioned study by Lehman and Reifman done on star basketball players, there is a chance that star gymnasts garner more favorable scores at home. However, the RoadToNationals dataset accounts for over 44,000 gymnasts. Trying to define what makes a “star” gymnast and applying said parameters to thousands of data points would serve only to overcomplicate the analysis. Nonetheless, including gymnast effects could potentially improve upon the statistical power of the regression in the future. This paper provides a well-overdue exploration of attendance and scoring in NCAA gymnastics. The highly subjective nature of gymnastics judging hinders the ability to conduct a truly objective data analysis, but having an idea of overall scoring trends gives both coaches and fans a starting point in untangling the sport’s subjectivity. 22 APPENDIX Exhibit 1. NCAA Gymnastics score sheet: 2022 regular season meet between host Oregon State University and visitor Arizona State University. 23 Exhibit 2. Summary Statistics VARIABLES (1) Mean (2) St. Deviation (3) Minimum (4) Maximum (5) Count score logattend attendance postseason homeXattend awayXattend vault bars beam floor home away neutral month january february march april 9.610 7.040 2,171 0.0812 2.671 3.996 0.249 0.250 0.251 0.250 0.348 0.539 0.113 2.113 0.301 0.627 0 0.0721 0.382 1.140 2,892 0.273 3.492 3.574 0.433 0.433 0.434 0.433 0.476 0.498 0.316 0.920 0.459 0.484 0 0.259 1 2.197 9 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 10 9.682 16,019 1 9.682 9.682 1 1 1 1 1 1 1 4 1 1 0 1 179,256 145,513 145,513 179,256 145,513 145,513 179,256 179,256 179,256 179,256 179,256 179,256 179,256 179,256 179,256 179,256 179,256 179,256 Exhibit 3. logattend conversions log (0) log(1) log(2) log(3) log(4) log(5) log(6) log(7) log(8) log(9) log(10) Value 1.00 2.72 7.39 20.09 54.60 148.41 403.43 1096.63 2980.96 8103.08 22026.47 24 Exhibit 4. Team Fixed Effects Alabama Alaska Arizona Arizona State Arkansas Auburn BYU Ball State Boise State Bowling Green Bridgeport Brockport Brown California Centenary College Central Michigan Cornell Cortland State Denver Eastern Michigan Florida George Washington 0.235*** (0.00866) -0.0595*** (0.0114) 0.159*** (0.0104) 0.149*** (0.00947) 0.195*** (0.00840) 0.201*** (0.00955) 0.177*** (0.00851) 0.0980*** (0.00920) 0.206*** (0.00806) 0.0624*** (0.00988) 0.0395*** (0.0108) -0.194*** (0.0153) -0.0106 (0.00993) 0.210*** (0.00835) -0.217*** (0.0122) New Hampshire 0.138*** (0.00985) -0.0435*** (0.0113) -0.346*** (0.0145) 0.220*** (0.00908) 0.130*** (0.00878) 0.267*** (0.00898) 0.158*** Seattle Pacific North Carolina North Carolina State Northern Illinois Ohio State Oklahoma Oregon State Penn State Pennsylvania Pittsburgh Rhode Island College Rutgers S.E. Missouri Sacramento State San Jose State Southern Conn. Southern Utah Springfield College Stanford Temple Texas Woman's 0.136*** (0.00857) 0.113*** (0.0100) 0.155*** (0.00815) 0.109*** (0.00907) 0.159*** (0.00955) 0.289*** (0.00766) 0.203*** (0.00953) 0.169*** (0.00834) 0.0101 (0.0104) 0.0871*** (0.00926) -0.712*** (0.0175) 0.0847*** (0.00951) 0.0649*** (0.0126) 0.0533*** (0.0110) 0.0998*** (0.00915) 0.0550*** (0.0118) -0.148*** (0.0125) 0.168*** (0.00839) -0.352*** (0.0152) 0.171*** (0.0103) 0.0281*** (0.0107) 0.0241** 25 Georgia Gustavus Adolphus Hamline Illinois Illinois State Iowa Iowa State Ithaca College Kent State Kentucky LIU LSU Lindenwood Maryland Michigan Michigan State Minnesota Missouri Nebraska (0.00851) 0.205*** (0.00867) -0.616*** (0.0176) -0.499*** (0.0158) 0.173*** (0.00882) -0.0200* (0.0108) 0.163*** (0.00948) 0.164*** (0.00833) -0.300*** (0.0145) 0.117*** (0.0112) 0.200*** (0.00933) 0.0147 (0.0204) 0.251*** (0.00906) 0.0758*** (0.0107) Towson UC Davis UCLA UIC UW-Eau Claire UW-La Crosse UW-Oshkosh UW-Stout UW-Whitewater Ursinus College Utah Utah State Washington 0.140*** (0.00904) 0.240*** (0.00853) 0.133*** (0.00914) West Chester 0.195*** (0.00849) 0.188*** (0.00827) 0.195*** (0.00857) William & Mary West Virginia Western Michigan Winona State Yale (0.00990) 0.105*** (0.00843) 0.107*** (0.0101) 0.241*** (0.00836) 0.0512*** (0.0109) -0.502*** (0.0180) -0.221*** (0.0135) -0.349*** (0.0148) -0.379*** (0.0142) -0.190*** (0.0131) -0.288*** (0.0154) 0.256*** (0.00904) 0.143*** (0.00956) 0.185*** (0.00967) 0.0279*** (0.00991) 0.164*** (0.00820) 0.106*** (0.00921) 0.0467*** (0.0128) -0.404*** (0.0159) 0.00583 (0.0121) 26 REFERENCES Auburn University Athletics. “Another Attendance Record Set for Auburn Gymnastics.” Auburn University Athletics, March 10, 2022. https://auburntigers.com/news/2022/3/10/gymnastics-another-attendance-recordset-for-auburn-gymnastics.aspx. Baghurst, Timothy, and Inza Fort. “Subjective Judging and the Home Advantage in Female Collegiate Division I Gymnastics.” Women in Sport and Physical Activity Journal 17, no. 2 (October 2008): 3–7. https://doi.org/10.1123/wspaj.17.2.3. College Gym News. “Olympians in the NCAA.” College Gym News, November 21, 2022. https://collegegymnews.com/olympians-in-the-ncaa/. Courneya, Kerry S., and Albert V. Carron. “The Home Advantage in Sport Competitions: A Literature Review.” Journal of Sport and Exercise Psychology 14, no. 1 (March 1992): 13–27. https://doi.org/10.1123/jsep.14.1.13. Dougherty, Michael. “Judging Concerns Gymnastics Coaches.” The Minnesota Daily, April 2, 1998. https://mndaily.com/215732/uncategorized/judging-concernsgymnastics-coaches/. Gourgey, Bill. “Will Baseball Ever Replace Umpires with Robots?” Popular Science, June 22, 2022. https://www.popsci.com/technology/history-of-robotic-baseballumpires/. 27 Hopkins, Lauren. “An Intro to Collegiate Gymnastics.” The Gymternet, November 22, 2014. https://thegymter.net/2014/10/23/an-intro-to-collegiate-gymnastics/. Keh, Andrew. “Gymnastics' Latest Twist? Robot Judges That See Everything.” The New York Times. The New York Times, October 10, 2019. https://www.nytimes.com/2019/10/10/sports/olympics/gymnastics-robotjudges.html?auth=login-google1tap&login=google1tap. Lehman, D.R., and Reifman, A., “Spectator influence on basketball officiating.” The Journal of Social Psychology, 127, 673-675, 1987. Lewis, Jon “Paulsen”. “Ratings: Gymnastics, Kayrod, Spieth Win, NHL.” Sports Media Watch, April 20, 2022. https://www.sportsmediawatch.com/2022/04/ncaagymnastics-ratings-most-watched-since-2011-kayrod-declines-spieth-nhl/. Nevill, Alan M., and Roger L. Holder. “Home Advantage in Sport.” Sports Medicine 28, no. 4 (October 28, 1999): 221–36. https://doi.org/10.2165/00007256-19992804000001. Roenigk, Alyssa. “How Nil Has Transformed Gymnastics for Olympians, NCAA and Beyond.” ESPN. ESPN Internet Ventures, January 24, 2023. https://www.espn.com/college-sports/story/_/id/35483034/how-nil-transformedgymnastics-olympians-ncaa-beyond. “Standings - Final (2022).” RoadToNationals, April 16, 2022. https://roadtonationals.com/results/standings/final/2022. 28 University of Utah Athletics. “Utah Gymnastics Breaks School Record for Season Average Attendance.” University of Utah Athletics, April 10, 2020. https://utahutes.com/news/2020/4/10/utah-gymnastics-breaks-school-record-forseason-average-attendance.aspx. Name of Candidate: Emma Summerhays Date of Submission: May 3, 2023