Abstract
Every March a sample of the top Division I men’s basketball programs in the National Collegiate Athletic Association (NCAA) gather to compete in March Madness, a grueling single elimination tournament that captures the attention of millions of viewers and shines a prominent spotlight on the 68 teams that are competing for college basketball’s national championship. Interspersed amongst the numerous financial incentives that exist for each university, and the millions of dollars that are wagered on brackets and bets, are the suggestions of media members, coaches, and players as to which factors are important to teams in their quest for success. One common suggestion argues that player experience provides a benefit to teams as they attempt to handle the pressure and maintain their composure amidst one of the most hectic postseasons in all of sport. However, there have been few studies conducted to analyze the effects that the two primary categories of player experience (i.e., prior postseason experience and class rank) have on the performances of March Madness teams. Therefore, this study sought to test the validity of the assumption by using a series of empirical models to analyze player performance and experience data from the 693 games that took place during the 2007 to 2017 March Madness tournaments. The findings suggest that simply having a higher class rank than an opponent offers no discernible advantage at any stage of the competition, but that possessing more prior March Madness experience may significantly improve a team’s margin of victory in the later rounds.
Introduction
Each March, the top men’s basketball programs in the National Collegiate Athletic Association’s (NCAA) highest division (Division I) compete in the NCAA Men’s Basketball Championship, a six-stage, single elimination tournament known more commonly as
Indeed, March Madness games present teams with a variety of internal and external stressors that are far different from what they experience throughout the course of the regular season. On this stage, players must consistently perform at a high level while remaining cognizant of the fact that a loss signals the end of a season and potentially a career. They must also bear the emotional burdens of hundreds of thousands of stakeholders, some of whom may be supplying the program with financial benefits (e.g., increased donor contributions, improved ticket sales, and heightened media exposure) that are contingent on a successful showing in the tournament (Goff, 2000; Humphreys and Mondello, 2007). In addition, the NCAA incentivizes teams to perform well in March Madness games by placing a share of its media rights revenues in a fund that can award conferences and teams with as much as $1.7 million for every round of the tournament they advance to (Smith, 2017). All of these burdens and expectations are then further compounded by a national television spotlight that places these young athletes in front of media pundits who stand ready to dissect their performances on national television and professional scouts who will be determining whether or not they have what it takes to play at the next level. For the players who are not accustomed to it, the distractions and stresses supplied by these entities can add additional pressure to an already grueling tournament.
Given these added complexities, it should come as little surprise that March Madness regularly serves as a setting for one of the most oft-cited clichés in sport. Indeed, the assumption that
The frequent positioning of player experience as a key determinant in the outcome of March Madness games and other postseason sporting events would lead one to believe that this proposition has become a foundational pillar in the growing body of sports analytics literature. If pundits, coaches, and former participants are consistently propping up the experience narrative, then it stands to reason that this assumption is bolstered by a bevy of empirical evidence. However, a review of the extant literature on the subject reveals a surprising lack of studies that have sought to examine whether or not player experience affects the performances of teams competing in the postseason. In fact, a literature review on this topic discovered a small number of peer reviewed studies—one examining the NBA postseason (Tarlow, 2012), and the other looking at the NFL Playoffs (Pitts, 2016) —that have explicitly tested this assumption, and none were conducted within the contexts of March Madness or college sports in general.
Given that bracket predictions form a part of the essence of March Madness (Doty, 2017; Moyer, 2016), and that the tournament involves college athletes who may be encountering national spotlights and postseason pressures for the first time in their relatively young careers, this omission is perplexing. A review of the literature that does exist for the determinants of March Madness success instead reveals a plethora of models and metrics that have been developed for the sole purpose of forecasting game outcomes by using more traditional and tangible statistics. This only serves to further highlight the tendency for the research in this area to overlook variables such as experience that may help quantify some of a team’s more intangible qualities.
Therefore, in light of the evidence suggesting that the experience assumption has gone untested in college sports and March Madness, the purpose of this study was to assess the extent to which prior postseason experience and class rank affected the performances of NCAA Division I men’s basketball teams. Using binary probit and ordinary least squares (OLS) regression models to test the commonly-held assumption that experience affects the outcomes of March Madness games, this analysis attempted to lend statistical power to an assumption in need of further support. Ultimately, this knowledge can benefit a number of parties, including the basketball programs, media pundits, and sports gamblers who must predict and prepare for March Madness games on a regular basis.
With this purpose in mind, the remainder of the study proceeds as follows: first, the background section gives a primer on the format, financial structure, and relevance of March Madness. Second, the literature review summarizes and discusses some of the most relevant studies, their results, and the theories that ground them. Third, the data, variables, and regression models are described in the method section. Fourth, the results of the empirical analyses are presented. Fifth, the results are discussed and recommendations for future research are made. Last, a conclusion section briefly summarizes the study.
Background
March Madness is the name given to the annual, season-ending tournament that decides which NCAA Division I men’s basketball team will be crowned as the national champion. Following conference tournaments and a series of play-in games known as the
The rewards for progressing through each stage of the tournament are rather lucrative due to the massive multimedia rights deal that was negotiated between the NCAA, Turner Broadcasting, and CBS Sports in 2011. The deal, which was extended in 2016, entitles the NCAA to an annual sum of $1.1 billion from the 2017 to 2032 postseasons (Osburn, Smeltz and Sabatelle, 2016). Traditionally, the NCAA takes anywhere from 25–30% of its March Madness media revenues and places the sum in an incentivized pool known as the
From a financial perspective, March Madness is also relevant to the millions of active observers who participate indirectly by attempting to predict match outcomes. Indeed, figures from the American Gaming Association (AGA) estimated that nearly $10.4 billion in wagers were placed on the 2017 edition of the tournament through office pools, Nevada sports books, offshore sites, and illegal bookies (Doty, 2017). Many of these bets were fueled by
Literature review
Throughout the years, academic investigators and basketball statisticians have attempted to predict the outcomes of March Madness games using a wide array of explanatory variables and empirical methods. Some of the earliest analyses used the seed assigned to each team as a rather intuitive means of predicting the likelihood that a team would win and the margin by which it would do so (Boulier and Stekler, 1999; Caudill, 2003; Schwertman, Schenk and Holbrook, 1996; Smith and Schwertman, 1999). The collective findings of these initial studies indicated that an obvious advantage exists for a team that possesses a higher seed than its regional opponents; however, subsequent analyses showed that the relationship between seed and performance breaks down as the tournament progresses (Baumann, Matheson and Howe, 2010; Jacobson and King, 2009).
To this end, additional studies have investigated a variety of predictors other than seed. These variables have ranged from simple measures such as regular season winning percentages, margins of victory in regular season games, records against tournament teams, and Vegas point spreads, to more complex ratings (e.g., NCAA RPI measures; KenPom, Sagarin, and Massey ratings) that are specific to an organization or website (Carlin, 1996; Harville, 2003; Hoegh et al., 2015; Kvam and Sokol, 2006). Many studies employ methods that simultaneously incorporate several of these variables in their models. Others compare the predictability of these measures and models in order to determine which ones are most accurate. The logit regression/Markov-chain model developed by Kvam and Sokol (2006), for example, incorporated variables such as margin of victory, game location, and strength of schedule into its metrics and was found to be more predictive than Vegas betting odds and other common ranking systems.
Absent from many of these models, though, are variables incorporating the intangible qualities of teams and their opponents. In this regard, the more discrete benefits afforded by an attribute like experience have gone largely ignored in the existing body of sports analytics literature. This gap is perplexing considering that a number of studies in areas outside of sport have highlighted the various advantages that experience can provide to people performing tasks in specialized scenarios. In the criminal justice realm, for example, studies have shown that experience can help police officers appraise and respond to stressful situations more appropriately (Anshel, Robertson and Caputi, 1997; Larsson, Kempe and Starrin, 1988). Likewise, natural disaster victims and musical performers who are accustomed to the stresses of a flood or audition are less likely to experience feelings of distress and anxiety during future occurrences of an event (Norris and Murrell, 1988; Van Kemenade, Van Son and Van Heesch, 1995). There even exists a theory,
The fields of economics and business management also contain a variety of studies that have categorized experience as an asset. A meta-analysis performed by Quińones, Ford, and Teachout (1995) in this area condensed the findings of over 40 studies and revealed that experience and job performance were positively related across a variety of industries, job positions, and performance measures. Seeing as experience can offer a number of general and specific benefits to individuals and organizations across a variety of disciplines, it remains surprising that so few studies have analyzed this concept as it relates to the postseason performances of collegiate sports teams. After all, studies have shown that athletes are susceptible to choking under pressure (Baumeister, 1984; Baumeister and Showers, 1986; Beilock and Carr, 2001; Goldman and Rao, 2012; Wallace, Baumeister and Vohs, 2005), and a theory like the inoculation hypothesis shows why prior experience could be valuable to teams competing in postseason scenarios where the pressure is high. If experience is advantageous to people and organizations in so many other high-pressure settings, then it stands to reason that this asset will carry over to the performances of players and teams competing in March Madness and other postseason sporting events.
However, in the context of sport, at any level, there is a rather limited selection of studies that have focused primarily on the impact that player experience has on teams competing in the postseason. One study attempted to forecast the number of playoff games an NBA team would win using multiple least squares regression and experience variables that represented the number of years a player had played in the NBA, the number of prior postseason games a player had played, and the number of years of shared experience that existed between any two starters on a team (Tarlow, 2012). Including these measures alongside a host of control variables, only the shared experience measure, as a proxy of team chemistry, was found to be a significant determinant of postseason wins.2 Another study that examined this phenomenon used binary probit regression models to analyze NFL playoff games and how the comparative levels of prior postseason experience held by each team and its key players affected the likelihood of a game being won (Pitts, 2016). The relevant prior experience variables in this analysis were coded as the advantage or disadvantage that a team held compared to its opponent in the areas of quarterback postseason experience (i.e., the number of previous playoff games started by a quarterback minus the number of previous playoff games started by his opponent) and team postseason experience (i.e., the number of playoff games a team had competed in minus the number of playoff games its opponent had competed in). Ultimately, neither form of experience was found to afford NFL teams with any significant advantage. Simply possessing players with more postseason experience than an opponent did not improve a team’s chances of winning.3
Taken together, the primary findings of these aforementioned studies seem to imply that the experience narrative being preached by members of the media each postseason is overstated and unfounded. Pitts (2016) notes that the results “are not consistent with the purported importance of previous playoff experience by many fans and media” (p. 105). Similarly, Tarlow (2012) makes reference to the media and states that “the most common criticism is of the inexperience of younger teams and this study does not support this conclusion, regardless of whether their NBA experience or playoff experience is the topic of discussion” (p. 8). If taken verbatim, these conclusions would suggest that researchers do not need to map out the intangible qualities of a team because raw measures of performance, alone, are more capable of predicting success. However, a possible explanation for the insignificance of these findings is that most professional athletes are already accustomed to dealing with the pressures of a big game. Even those players who have little to no postseason experience at the professional level have already participated in college and regular season games where the stakes were high and the scrutiny was intense. Thus, it is not unreasonable to assume that professional athletes have developed effective coping strategies to ensure that they are not unprepared or overwhelmed in future postseason games. A further explanation for why these findings may not hold weight is that both analyses used very general measures of experience (games played) and performance (wins) that may not fully capture the intangible benefits that experience can offer. As noted by Quińones et al. (1995), the more specific measures of experience and performance tend to display the most powerful effects. Therefore, this review of literature and the abundance of theories that naturally support the experience assumption make it clear that further analyses are needed to test this phenomenon at the collegiate level of play.
Methodology
Data
The majority of the data in this study were derived from www.sports-reference.com/cbb and www.teamrankings.com, two reliable online archives for historical college basketball statistics. These websites contain the postseason box scores, team roster pages, and team statistics that were used to compile a dataset consisting of all 693 March Madness games (excluding play-in games) that were played from 2007 to 2017. In addition, www.kenpom.com was used to obtain data pertaining to the effective heights of each team. All data were manually pulled from their respective sources, recorded, and then analyzed using a combination of procedures in the R 3.3.1 and IBM SPSS Statistics 20 software packages.
The timeframe used in this sample was chosen because of its recency and because all seasons were played with the “one-and-done” rule in effect (i.e., as of the 2006 NBA draft, all high school players from the United States were required to attend one year of college before entering the NBA). Each observation in the eleven-season sample corresponds to a single March Madness game. This format was chosen per the recommendations set forth by Robst, VanGilder, Berri, and Vance (2011), and Pitts (2016), which highlighted the issues of independence that can arise when the outcome of a single game is treated as two separate events.4 In order to avoid this dilemma, one participating team was randomly (alphabetically) assigned to be the team,
Summary of the Explanatory and Outcome Variables
awww.teamrankings.com; bwww.sports-reference.com; www.kenpom.com.
Summary of the Explanatory and Outcome Variables
awww.teamrankings.com; bwww.sports-reference.com; www.kenpom.com.
In an effort to more clearly depict the effects that experience may have on the outcome variables, two different measures of experience were employed in this study. The first fell within the
To this end, the
The
The remaining explanatory variables were primarily included to control for factors outside of experience that may be related to the relative quality of a team. The win-loss percentage (
It further needs to be mentioned that each of the explanatory variables were interacted with a binary categorical variable indicating whether the observed game was taking place in the Sweet 16 or beyond (
Empirical specifications
Two regression models were developed in an attempt to assess the impact that experience has on
where
For
Descriptive statistics
Before examining the results of the model estimations, a look at the descriptive statistics in Table 2 helps to shed some light on the differences that may exist between winning and losing teams in the early and late stages of the tournament. Looking first at the prior experience variables (
Descriptive Statistics of the Variables Grouped by Tournament Phase and Team Result
Notes. The variables are represented in this table as the individual mean values for the winning and losing teams while in the models they are analyzed as the differences between the two teams in the observed game; standard deviations are in parentheses.
Descriptive Statistics of the Variables Grouped by Tournament Phase and Team Result
In terms of class rank among the starting five, it appears as though the winning teams were actually marginally younger than their opposition in both samples. Winning teams in the Round of 64 and Round of 32 also had younger substitutes, while winning teams in the later stages of the tournament actually had substitutes who were slightly older. Even so, the mean difference between winning and losing teams across all players in terms of class rank was negligible. Though further analysis is needed, the descriptive statistics seem to suggest that class rank, alone, is not a variable that offers a discernable advantage at any stage of the tournament.
Looking lastly at the variables that were included to control for basic aspects of team quality, it is interesting to note how the gap closes between teams in terms of
The results of the binary probit regression model8 estimating the probability of a team winning its March Madness game are presented in Table 3. These results are presented as marginal effects in order to show the percentage increase in a team’s likelihood of winning for every one-unit increase in the explanatory variable being examined while holding all other variables constant at their means. Marginal effects offer a more interpretable value than the standard coefficients of a probit model, which are presented as
Results for Binary Probit Model with WIN as the Outcome Variable
Notes. ***p < 0.01; **p < 0.05; *p < 0.10.
Results for Binary Probit Model with WIN as the Outcome Variable
Shifting focus to the late round interaction terms, the interaction between
Lastly, it merits a mention that the interaction between
After analyzing the effects that the explanatory variables had on a team’s probability of winning, the focus was shifted to the OLS models analyzing the effects that each variable had on a team’s margin of victory or defeat. The
Results for OLS Model with MARGIN as the Outcome Variable
Notes. ***p < 0.01; **p < 0.05; *p < 0.10.
Results for OLS Model with MARGIN as the Outcome Variable
However, when looking at the interaction terms, it is seen that prior March Madness experience among a team’s starters (
The interaction terms also reaffirmed what was seen in the probit model, with
Discussion of results
This study conducted its analyses in an attempt to answer some of the questions that have been left unanswered by prior studies in the field; namely, does player experience have an effect on the performances of college basketball teams whose players may be less familiar with the high stress scenarios of the postseason than professional athletes? While the regularity with which this assumption is made in television studios and press conferences around the nation may lead one to believe that this question has long been answered, research exploring this phenomenon at the professional level has argued quite the opposite. Indeed, attempts to quantify the advantages of player experience in the NBA and NFL postseasons have found few discernible links between the amount of player experience a team has and its ability to win or perform at a higher level (Pitts, 2016; Tarlow, 2012).
Aside from the inherent limitations of the previous studies, one plausible explanation for these findings is that professional athletes have already been inoculated to stressful scenarios and have developed effective coping mechanisms for dealing with the pressure. This certainly fits with the inoculation hypothesis mentioned earlier, a theory which states that prior exposure to a stressor can increase one’s ability to tolerate that stressor in the future (Eysenck, 1983). Professional athletes have been through the stress of making it to, and remaining in, the highest level of the game. They are also getting paid millions of dollars regardless of whether they win or lose. On the contrary, college athletes may be experiencing a number of stressors for the first time if they have never appeared in a major tournament. The additional media obligations and scrutiny of the national spotlight may weigh heavier on the uninitiated. As amateurs, their future income as a professional may be contingent on a successful showing in the tournament. Seeing the stark differences between collegiate and professional athletes, this study set out to examine a phenomenon that has been frequently overlooked by prior studies in the field.
While the term “experience” often carries with it a sense of ambiguity as announcers, coaches, and analysts fail to differentiate between a player’s class ranking and his previous postseason experience, the empirical analyses conducted in this study defined the parameters more clearly by analyzing two forms of experience (i.e., class rank and prior March Madness experience) and their differential effects on performance in the later rounds of the tournament. One of the key findings of this study is that experience can have an impact, but perhaps not in the ways one might expect. Indeed, class rank, a variable assumed by many to be positively predictive of performance, appears to have a negative effect on both point margins and a team’s probability of winning in the later stages of the tournament; that is, older teams actually perform significantly worse than younger teams when the pressure is highest. This stands in contrast to prior March Madness experience, which was seen in both the descriptive statistics and the OLS model to have a positive impact on team performance in the later rounds of the competition.
Clearly, though, these results cannot be considered in a vacuum, as some amount of class rank is needed in order to obtain prior experience in March Madness tournaments. A player could not simply have a greater amount of playing time in previous postseasons without having used up at least one year of eligibility. According to the descriptive statistics, the average winning team in the Sweet 16 and beyond boasted a
Taken together, these findings raise a number of interesting talking points: (1) being more experienced to the extent that a team is simply older or more mature in terms of class rank is not advantageous; rather, it is what a team has been able to do with its yearly experience (e.g., reach previous March Madness tournaments) that matters; (2) in an era full of talented, one-and-done freshmen, it might not be wholly surprising that both brands of experience have less of a positive impact than what is commonly presented; (3) keeping in line with the draft theme, one reason for why teams with a higher class rank might fare slightly worse is because their upperclassmen are not good enough to get drafted to the NBA at a younger age and may now be facing-off against teams with younger players who are more talented prospects; (4) lastly, perhaps the teams with higher class rankings fare worse because they contain a higher-than-average number of seniors who succumb to the pressures of career-ending scenarios. Moving forward, researchers could delve deeper into the impacts of one-and-done players and career-ending scenarios since these are both unique facets of the college game.
It is further worth discussing how these experience variables were not significant until the later stages of the tournament when they were interacted with the
Nonetheless, while winning teams appear to have more prior March Madness experience, and advantages in the
Furthermore, even though multicollinearity issues between the explanatory variables were taken into consideration when developing the models, it could be that prior March Madness experience, like
Future studies in this realm can now focus on validating these findings, perhaps through the creation of more predictive models that incorporate prior experience variables in their forecasts. If this study provided any sort of insight in that area, it would be to suggest that variables denoting team quality should account for strength of schedule. Then, once teams become evenly matched in the later rounds of the competition, prior tournament experience should be introduced as a means of further separation. Subsequent examination is also needed in order to discover the more specific ways in which prior experience affects team performance. That is, are late-round tournament teams shooting poorly from the field or free-throw line because they have less experience handling the pressure? Are they turning the ball over more frequently because they are nervous? When questions like these are answered, coaches will be able to manage their teams more effectively.
Until then, those who are in charge of mentally and physically preparing the players for upcoming games will have to judiciously adjust their tactics and plans according to the degree of experience or inexperience that exists between a team and its opponents. Coaches or team personnel, for instance, could employ a variety of training methods and psychological techniques to ensure that inexperienced players are putting in the time to develop the proper mindset and appropriate coping mechanisms. Halliwell (2004), for example, highlighted the benefits of interactionist techniques that can help place athletes in the proper mood and mindset ahead of a big event. In particular, it was noted how veteran players should be instructed to “let their training and talent come out,” while the more inexperienced players should be given access to the “timeless wisdom” of the veterans through special meetings, video clips, and inspirational quotes (p. 30). Ultimately, while some amount of psychological training could prove helpful, the more data-driven, focused interventions could eventually yield more powerful results.
Current limitations and recommendations for future research
One of the clear limitations of this study is that it is only focused on one specific postseason within one specific sport. While March Madness holds a prominent place in the wider realm of collegiate sport, one cannot generalize these findings to football, women’s basketball, or other team-based competitions until further analyses are conducted. Looking ahead to subsequent studies in this area, it would be interesting to see if some of the more discrete variables underlying overall performance are affected by experience. This might help quantify some of the more intangible qualities of a team (e.g., confidence, composure, and hustle). For instance, do teams with more prior experience shoot better from the foul line or make a higher percentage of their shots from the field? Do the teams with more upperclassmen turn the ball over less frequently or fight harder for rebounds? This could be viewed at the team level or by comparing relative experience across positions that match up with one another. For example, experience levels could be averaged according to each position, much like height was for centers and power forwards in Pomeroy’s (2008) effective height measure. The relative levels of experience among players at these positions could then be compared across the statistical categories that are commonly associated with them. Power forwards and centers, for example, could be compared in terms of rebounding while guards could be compared in relation to how they shoot and handle the ball.
In addition, one of the limitations of this study was that it did not incorporate any specific time or game-scenario variables. It is therefore suggested that future studies collect and incorporate some of these measures in order to provide more powerful and interpretable estimates of performance under pressure. For example, one study by Goldman and Rao (2012) on NBA players performing under pressure assigned a value of importance to each free-throw based on the time remaining in the game and the score differential between the two teams. A similar method could be adopted to include experience variables in an effort to see whether or not a player’s level of experience helped him or her perform better or worse at shooting under pressure. Another recommendation involves the use of more longitudinal, team-specific models. Instead of observing individual, head-to-head matchups, future analyses could employ methods such as multinomial logistic regression to examine the impact that the explanatory variables have on the number of March Madness games that a team can be expected to win. Methods and variables that better account for the potential latent talent issues that exist between the control variables for team quality and player experience could also be introduced in an effort to shed further light on the significant or non-significant impacts of experience on performance. Lastly, future researchers could develop variables that account for postseason experience in college basketball tournaments outside of March Madness, such as the National Invitation Tournament (NIT) or College Basketball Invitational (CBI).
Conclusion
In closing, this study showed that the experience assumption so frequently espoused by media members and other March Madness affiliates is largely overstated. Simply being a more veteran team with a higher class rank does not appear to offer any significant advantages outside of being a vehicle for prior March Madness experience, which did display a significant and positive (albeit small) effect on margins of victory in the later rounds of the tournament. Therefore, under the right conditions, prior experience may be beneficial to high-level athletic performers in the college setting, a finding that differs marginally from previous studies that have attempted to invalidate the experience assumption at the professional level. From a theoretical perspective, the findings align with the assumptions of the inoculation hypothesis, whereby previous exposure to a stressor can reduce anxiety in future encounters with that stressor. The results also hold practical implications for team personnel and bracketologists who may wish to implement measures and models that account for intangible attributes like experience. Nonetheless, it is important to remember that these findings were taken from one specific sport within one specific context. Future studies will need to validate and test this proposition across a wider variety of sports and settings.
Notes
It is up to the discretion of the conferences to determine how the units earned by their participating teams are allocated. While the NCAA encourages conferences to share this money equally, each conference is allowed to distribute the money as it sees fit. Some conferences do not fully disclose how they distribute basketball fund revenues to their member teams. The study by Tarlow (2012) did find that NBA player experience positively predicted the number of regular season games a team won. The author concluded that experience may help a team make the playoffs, but that it does not help a team win once it is in the playoffs. In addition, the study found that coach experience did increase a team’s ability to win in the playoffs. Despite Pitts’ (2016) assertions that experience did not matter in the NFL postseason, a categorical variable signifying whether or not a team was starting a new quarterback in the playoffs was shown to significantly decrease a team’s chances of winning. This shows that extreme cases of inexperience at a key position may be detrimental to team performance. If the individual teams are treated as the observations in a binary probit regression model, then the outcomes for two teams competing in the same game are errantly considered to be independent events such that P (team For a more detailed explanation of the strength of schedule ratings, visit https://www.teamrankings.com/blog/site-updates/site-update-new-rankings-beta-college-football-polls-page. Second-order, quadratic terms for the Logistic regression methods were also performed and yielded nearly identical results. Models were constructed with interaction terms between
Footnotes
Acknowledgments
The authors would like to extend a special thank you to David Schmidt and Britton Gallardo for their efforts in helping collect the data that were used in this study. In addition, they would also like to acknowledge the helpful feedback provided by the anonymous reviewers for the
