Factors influencing scoring in the NBA Slam Dunk Contest

1.1.Variables

We focused on three broad factors thought to influence the dependent variable, judge-awarded dunk scores in SDCs. The factors were the [i] elements of a dunk such as the distance leapt from or airborne anatomical maneuverings; [ii] formatting and other contest-contextual pressures such as elimination schedule and replacement dunks; and [iii] superlatives that are exogenous of dunk execution such as contestant popularity and home advantage. First, however, we introduce the judging procedures as we understand them.

1.2.Dunk scores

At the beginning of each SDC telecast, commentators introduced the judges, judging procedures, and contestants. All SDCs utilizing judges featured a panel of five judges consisting predominately of former or current NBA players, though a minority were public figures. Telecast commentators or graphics specified that dunks were judged on “style, athletic ability, and creativity. Judges assigned an integer from 1 to 10, with greater values indicating a more athletic, creative, or stylistic dunk.” For SDCs 1989-96, judges could include tenths of points. The values from the five judges were summed to yield the score for a dunk. The maximum score for a successful dunk (i.e., would garner 2 points in basketball) was 50, across contests; the maximum for a missed dunk (i.e., missed field goal in basketball) was 25 until 2000, thereafter it was 30. Scores for all dunks in a round or the highest scoring dunks in a round were summed to determine which contestants progressed to the next round. In SDCs in which replacements for missed dunks were permitted, judges were asked to excuse the attempts that were replaced when evaluating the ultimate dunk.

With the exceptions described below, a contestant performed his dunk and then judges scored the dunk. Scores were always awarded after one dunk and before the next dunk was performed. It appears judges were unaware of what dunks would be performed. Although maneuvers have been disclosed to the press and in other media (Denberg, 1986, Aschburner, 1995, Tillery, 2008), it appears many contestants prefer to keep their strategies guarded (Denberg, 1986, Farrey, 1990, Aschburner, 1995, Schmitz, 2008) whereas others opt for an improvisational approach (Krieger, 2000, Dougherty, 2001, Rudman, 1987, Times, 2006).

There were several exceptions to the dunk-then-judge procedure. In the 1994-97 initial rounds and in the 1995 final round, each contestant received a single score for several dunks he performed consecutively, prior to judging (on the same 0–10, max of 50 scale). From 2009-13 dunks in the final rounds were not judged, rather, viewer submitted votes for a contestant were summed to determine the winner. No dunks were scored in the 2012 and 2014 SDCs when the winners were determined using the viewer voting method.

1.3.Dunk elements

Intuitively, dunk elements should correspond to variability in scores because the elements distinguish one dunk from others. Some elements require greater athleticism and thus are more difficult to execute successfully than others. Likewise, creativity and style are restricted by athleticism. Judging dunks on athletic ability ostensibly corresponds to difficulty as in figure skating (Union, 2016) or gymnastics (Butcher, 2017). This seems to be a reasonable interpretation of athletic ability absent a more precise definition. Insight into which elements might be most influential is inferable from the comments of past contestants.

Dominique Wilkins implied the importance of achieving maximal verticality (Bee, 1988). Clyde Drexler endorsed airborne movements of the legs (Wendy, 1989). Kenny Walker seconded the notion of leg movements and stressed the importance of hangtime and full extension of the arms (Wendy, 1989, Powell, 1990). Comments by Isaiah Ryder suggest leaping over obstructions such as players or motor vehicles (Aschburner, 1995). Julius Erving implied jumping farther away from the goal and approaching it from different angles (Spencer, 2000). Baron Davis indicated exerting maximal force on the basket while finishing (Dougherty, 2001).

These and other elements will be analyzed; the exceptions to the above being, duration of hangtime and the exertion of power at the finish because each is too specific for this seminal analysis. We anticipate that elements will influence judge-awarded dunk scores, with dexterously more demanding kinematics such as the between-the-legs and behind-the-back garnering greater scores. We expect that airborne rotations and leaping farther from the basket, particularly from the free throw line, will also increase scores.

1.4.Contest formatting

Except for 2012 and 2014, SDCs progressed in single-elimination format, with contestants generally performing at least two dunks in each round. Successive rounds culminated in a final round in which the winner was determined. Lower scoring competitors in a round were eliminated whereas higher scoring competitors survived to compete in the next round. Ties were decided with the tied-contestants performing additional dunks and eliminating the lower scoring contestant.

The number of contestants has varied over the years (see Table 1). In 1985, the top-two 1984 contestants and in 1986, the 1985 winner were each granted a first round by. Half or more contestants were generally eliminated in each round. Two contestants survived to the final rounds of all SDCs except 1993-97 and 2000-01, when three survived.

In the words of one Association executive in 1988: judging is “totally subjective” (Denberg, 1988). Another matter to consider then, is how individual judges interpret and apply the scoring criteria when evaluating a dunk. An inter-judge analysis of deviance would provide insight in this regard, but individual judge-scores were rarely displayed on the SDC broadcasts prior to 2000. Even then, of 170 judged dunks from 2000 and after (or 850 possible judge scores), 18.4% of judge-scores were not displayed on the broadcast (or 156 judge scores). To account for potential differences in how judges interpret and apply the scoring criteria, we include year as a random effect in the analysis and include a variable indicating prior judging experience of the judging panel in each SDC.

1.5.Superlatives

In competitive sanctioned sports, judges and referees are asked to maintain impartiality when evaluating performances and enforcing regulatory statutes. This is tenuous in application because myriad variables influence human cognition and behavior, often imperceptibly. Thus, it may be that factors exogenous of the actual dunk execution influence scoring.

2.1.Interrater reliability

To ensure accuracy, dunk elements were identified and recorded by two raters. The first author identified all elements in all dunks eligible for analysis, twice. The second author was enlisted as a rater, pro bono. At the time, naïve to the study, but thereafter contributed significantly to the project. The first author provided the blinded rater an instructional text describing the methods used to identify dunk elements which is available on the ResearchGate page of the first author. The blind rater was supplied 108 dunks selected at random, with≥2 per SDC. This many dunks were needed to conclude that a Fleiss’ Kappa of 0.70 was greater than 0.50 at the 0.05 alpha level, with 0.80 power.

3.1.Dunk elements

To quantitate dunk elements for analysis, we partitioned the dunk into four manageable components. First, there is a stage of pre-launch activity which is described below and is followed by the launch, which entails how a contestant becomes airborne (exclusively by jumping in the SDC). Third, once airborne, a variety of movements, or airborne activity, can be performed with or without possession of the ball. Fourth, during even the most rudimentary dunk, a controlled and possessed ball is manually guided from above the horizontal plane of the basket rim, into the basket. As the ball is guided downward through the basket, the non-dorsal side of the hand(s) (but potentially the arm(s), also) will contact the rim, known hereafter as the finish.

Pre-launch activity, launching, airborne activity, and finishing will always occur in sequence except for additional dunking executed after the finish, without returning to the substrate or hanging on the rim. Supplementary Table 1 contains additional commentary on the elements described below, including kinesthetic descriptions of airborne activity. This content is excluded for brevity but esoteric constructs vital to the analysis are defined below. Table 2 names and provides distributions and levels of each dunk element in the analysis.

3.2.Contest formatting

Year was included as a random effect to account for random year to year variance in scores not explained by other variables. To account for potential differences in how judges interpret scores, we examined several possible variables including, for each dunk, a sum of each judge’s prior exposure to all elements found in that dunk; and for each SDC, counts of judges who were current or former NBA players and the counts of judges who were former SDC contestants. However, the sole variable that influenced scores in the model was the sum of prior SDCs judged by members of judging panel. That is, if, in a given SDC, five judges had respectively judged 0, 0, 2, 4, and 0 previous SDCs, then the judge experience value for all dunks in that SDC would have been 6.

3.3.Superlatives

3.4.Data analyses

All statistical analyses were completed using the R v3.3.2 console. Figures were created using ggplot2 (Wickham, 2016) and its extension, ggthemes (Arnold, 2013). For interrater reliability (IRR), the kappa2() function in the irr() package was used to compute Cohen’s Kappa values (Gamer et al., 2012). The IRR consisted of the primary kinematic and modifiers carrying greater subjectivity: reverse finishes, rotation, maximum vertical, leg-kicking, swinging, and arm extension. Other modifiers such as dunking multiple balls or catching a pass are comparatively unequivocal.

A measure of dunk difficulty was sought and derived in lieu of subjectively deciding which dunks were more difficult than others. Because scores were not used in this part of the analysis, all dunks with available footage were included (n = 645) in the derivation of a measure of dunk difficulty. First, we visually inspected the proportions of instances of each dunk element that had≥1 attempt, ≥1 replacement dunk, ≥1 of both, or was judged as a missed dunk. The premise is straightforward: the more athletic or difficult elements were expected to have a higher likelihood of error in execution. Logistic regression was used to evaluate this expectation. The dependent variable was a dummy variable indicating whether each dunk had > 1 attempt, >1 replacement, or was judged as a miss. All dunk elements except for the arm extension modifier were included as independent variables. Arm extension was excluded because visual inspection indicated that less-than-full had a high proportion of errors that we reasoned were related to something other than dunk difficulty. The logistic regression model was used to predict probabilities there would be an error for each of 645 dunks. An optimal cut-off was identified (0.191) and used to classify dunks as either ‘easier’ or ‘harder’.

Nonparametric regressions were conducted using the npregbw(), npreg(), and npsigtest() functions of the np package (v0.60-2; Hayfield and Racine, 2008), for bandwidth selection, model computation, and significance testing, respectively. Least-squares cross-validation was used to estimate fixed bandwidths for explanatory variables in local-linear least-squares regressions (LL). To avoid potential model misspecification due to the presence of local minima, the cross-validation procedure was restarted 100 times. 399 IID bootstrap replications were used to test significance of explanatory variables in LL model.

Upperbounds for bandwidths are specified as: 2 SDs for continuous variables; (d – 1) /d for nominal categorical variables, where d = levels; and 1 for ordinal categorical variables. As a bandwidth approaches zero, more weight is assigned to nearer values and less weight to farther values. Conversely, as a bandwidth approaches its upperbound, the difference in weights diminishes. Thus, the LL will essentially ‘smooth out’ or render irrelevant noninfluential explanatory variables. Readers interested in a more thorough, applied treatment of non-parametric regression using the np package are directed elsewhere (Delgado et al., 2014, Peiró-Palomino, 2016).

To test the validity of newspaper mentions as a measure of contestant popularity, a generalized linear mixed-effects model (GLMM) was conducted with the glmer() function of the lme4 package (v1.1–12) specifying a Poisson distribution (Bates et al., 2014). Contestant mentions was the dependent variable and it was offset by NBA mentions of the SDC year (producing a proportion). The ordinal All-star status variable entered as a fixed-effect. Year and contestant entered as random-effects with random intercepts. The cld() function in the lsmeans package (Lenth, 2016) was used to compute pairwise comparisons between All-star statuses.

The examination of randomness in sequence had two steps, whether popularity and home status influence sequence and whether those variables influenced surviving the initial round. First, a simple linear regression was conducted with a popularity and home-advantage interaction as independent variables and an alternative sequence variable as the dependent. The alternative sequence variable was computed using only the assigned position in the initial round of each SDC, that is, whether a contested performed first, second, third, etc. The alternative sequence variable was normalized as (assigned position – 1) /(total competitors in round – 1); the first contestant equaled 0 and the last contestant equaled 1. Second, a dummy variable indicating whether a contestant survived the initial round, or survived, was created as a proxy for scores (as to include all initial round contestants). SDCs 2012 and 2014 had only one round and the winner was indicated as having progressed (indeed, dunks were not scored by judges but the results are unchanged if excluding these years). A logistic regression was performed with survived as the dependent; sequence and a popularity-home status interaction were covariates.

To examine contest format and superlative variables, linear mixed-effects models (LMMs) were conducted with the lmer() function of the lme4 package (v1.1–12; Bates et al., 2014). Functions in the influence.ME (Nieuwenhuis et al., 2012) and LMERConvenienceFunctions (Tremblay and Ransijn, 2013) packages were used for LMM diagnostics. Tests of significance of fixed and random effects in LMMs were computed using the lmerTest (Kuznetsova et al., 2015) package. Confidence intervals for coefficients were computed at the 95% -level based on likelihood tests.

Figure 1 indicates that mean scores (white lines) increase from the initial to the final round. Simple regression slopes of score regressed onto the interaction of sequence and round indicate that the effect of sequence differs between rounds.¹ Sequence, round, and the interaction of the two entered the LMM as fixed effects. The dummy variable indicating whether a contestant won the previous SDC (hereafter, WPS) and the WPS-sequence interaction entered as fixed effects.

Fig. 1

SDC Mean Scores ±1 SD by Round with effect of sequence superimposed. Differentiation between 2-and 3-round SDCs was only recognized after the analysis was complete. Hence, the analysis is based on the interaction of sequence×round whereas the figure suggests an interaction of sequence×round×total rounds is appropriate. The points are jittered to prevent overplotting, the points neither differentiate between SDC rounds nor correspond to sequence. Black lines are trend lines of scores regressed onto sequence×round, which yielded slightly improved fit over the main effects of each alone, R2 = 0.105 compared to R2 = 0.099. The trendlines are superimposed such that the leftmost point of each line is the first position in sequence and the rightmost point of each line is the last position in sequence. White line bisecting bars represents mean and the bars correspond to ±1 standard deviation in score.

Raw counts of replacement dunks and attempts for each dunk entered as fixed-effects. Judge experience, dunk novelty, contestant popularity and height, and the dummy indicators for histrionics, functional histrionics, and home-status entered the model as fixed-effects. SDC year entered the model as a random effect, as did contestants, due to repeated measurements; both were set with random intercepts. Score was the dependent variable, offset by the fitted values from the LL model to control for the influence of dunk elements.

4.1.Dunk elements

Figure 2A was plotted to inspect the proportions of each primary and modifier with at least one replacement dunk, attempt, or that was a judged missed dunk. Interestingly, dunks with less-than-full extension had a higher proportion of attempts and replacements. This suggests contestants might have become fatigued after repeated misses and were less able to achieve full extension or that they became warry of committing another error and extended less to increase the likelihood of successfully dunking. Similarly, dunks with obstructions and limiters of trajectory plausibly are more difficult because airborne contestants must avoid colliding with an obstruction or the underside of the goal, respectively. However, in lieu of subjectively evaluating difficulty, logistic regression was used to predict probabilities and classify each dunk as easier or harder. The classifications of primaries and modifiers are shown in Fig. 2B.

Fig. 2

The X-axis of Panel A represents the proportion of all dunks with a given Primary or Modifier that required ≥1 attempt, replacement dunk, ≥1 of each, or a missed dunk that was scored. The Y-Axis of Panel A is sorted by total proportion of a given Primary or Modifier that required any of the four. The X-axis of Panel B represents the proportion of a given Primary or Modifier that was classified as easier or harder using logistic regression. The Y-Axis of Panel B corresponds to the Primary or Modifier, with the count of each that was classified as easier (left) or harder (right).

Overall, harder dunks (M = 45.8, SD = 3.77) were scored significantly higher than easier dunks (M = 44.99, SD = 3.88), t(386.5)=2.23, p = 0.03. Although some of the more athletic modifiers were less frequently classified as harder, the disparity is justifiable. For instance, dunks from the freethrow line were largely classified as easier likely because they were typically basic primaries without other modifiers. That is, assuming a contestant can leap the necessary distance, there is a reduced risk of error because those dunks were generally free of additional airborne activity. Likewise, dunks with passes reasonably require more attempts due to the triangulation and coordination necessary to locate and possess the ball in space while airborne. Summarily, the findings presented in Fig. 2 are interpreted as evidence that some dunk elements are harder to execute successfully than others, dunks with harder elements receive higher scores, and the objectively measured difficulty of elements are in line with our expectations.

All dunk element variables were included as explanatory variables with judge-awarded dunk scores as the dependent variable in the LL. Bandwidth estimates appear in Table 4 along with the upperbound for each variable. Figure 3 contains the partial means of primary kinematics with each of the relevant modifiers held constant and how each modifier influences scores with other modifiers held constant.

Fig. 3

Expected Primary Scores with and without Modifiers. The horizontal grey lines represent the mean score of a given Primary Kinematic without Kinematic Modifiers, as predicted by the LL model. The bars associated with each Kinematic Modifier represent how a given Modifier is predicted to change the mean for a Primary, with each white line through the bar representing ±2 points. Some Modifiers are not shown in the figure because little or no change appeared for all Primaries. For each Kinematic Modifier in the figure, all other Kinematic Modifiers are set at their absence (the levels are specified in Table 2).

The results of the LL indicate that primary kinematics, catching a pass, rotation, reverse finishes, arm extension, approaching from the baseline, covering the eyes, limits of trajectory, and jumping from a distance are explanatorily relevant to judge awarded dunk scores. That these variables are also statistically significant at or near conventional significance levels, tends to support our hypotheses. Leaping over obstructions and leg-kicking could be irrelevant elements in SDC judge awarded dunk scores given that the bandwidths for the variables are essentially equal to the upperbounds. Other modifiers, however, such as maximum verticality and swings appear to be relevant but not statistically significant. The distinction between relevance and significance is important. For example, excluding baseline approach, leg kicking, and limited trajectory from the model yields an R² = .441 whereas excluding all explanatory variables with p > 0.10 yields an R² = .356 (each with 10 restarts of cross-validation procedure).

4.2.Validity of popularity measure

From 1984-2016, 118 NBA players comprised 178 contestant-spots in SDCs. Of those 178, 27 were All-stars, 12 were All-star starters, and the remainder were not All-stars. The raw mean of popularity was 2.33 (SD = 2.38, range 0 to 12.82). The quantity of newspaper mentions for each SDC contestant was the dependent variable in a GLMM, offset by the quantity of NBA newspaper mentions for a given SDC year. All-star status was a fixed effect. Contestant and year were random effects with random intercepts. Model summary appears in Table 5 and indicates that newspaper mentions increase such that non-All-stars are mentioned in 1.1% of NBA articles, All-stars in 1.9%, and All-star starters in 2.5% of articles pertaining to the NBA when accounting for year and contestant (and holding NBA mentions constant). All-star starters (z = 7.3, p < 0.001) and All-stars (z = 6.9, p < 0.001) were mentioned in significantly more articles than non-All-stars, and All-star starters more than All-stars, z = 2.3, p = 0.062. We interpreted this as evidence that proportional contestant newspaper mentions were an acceptably valid measure of contestant popularity.

4.3.Randomness of sequence

As stated, from 1984-2016 there were 178 contestant-spots in SDCs. Of those, 175 were sequenced in an initial round, 15 of which had home status. Additionally, sequence for 7 contestant-spots was indeterminable leaving 168 for analysis, 14 with home status. The regression indicates variance in initial round sequence was poorly explained by contestant popularity (b = 0.002, p = 0.841), having home advantage (b = 0.011, p = 0.929), and the interaction of the two (b = 0.028, 033 p = 0.395), R² = 0.01, F(3, 114)=0.572, p = 0.63). However, a trend of more popular home contestants being positioned later in sequence is evident in Supplementary Figure 1, as is a very popular home outlier positioned mid-sequence (R² = 0.03, p = 0.14 and significant interaction when outlier is excluded). This finding suggests that sequence might have been coordinated such that more popular contestants with home status were positioned later in sequence in SDC initial rounds. However, the aim of the study is examining how these factors influence scoring.

A logistic regression had the survive dummy as the dependent variable with sequence as well as an interaction between popularity and home status as covariates. The logistic model indicates that sequence was a significant predictor of surviving the initial round (z = 3.09, p = 0.002) whereby performing last carried a 0.97 probability of surviving whereas performing in the middle was 0.48 and performing first was 0.31. Popularity (z = 0.829, p = 0.407), home status (z = –0.603, p = 0.547), nor the interaction (z = 0.661, p = 0.509) were significant predictors. We interpret these results to mean that, whether or not sequence was coordinated around popular and home status contestants, it appears that if such coordination occurred, judging in initial rounds was influenced by sequence more so than the superlative variables.

4.4.Format & superlatives

As seen in Table 1, attempts and replacements dunks increased as time progressed, due to changes in SDC rules. Fourteen SDC winners competed in the following SDC and completed 30 dunks in the initial rounds. Fifteen contestants with home status completed 60 dunks in 11 SDCs. The average and median height of SDC contestants was 78in (SD = 3.61) with a range of 66in to 88in. Sixteen dunks were identified as having histrionics, five of which were also functional. Regarding dunk novelty, dunks had been executed an average of 6.66 (SD = 10.84) times prior. The average judge experience of each panel was 7.14 (SD = 6.26) prior SDCs judged.

Offset by the fitted values from the dunk elements LL, judge awarded dunk scores were the dependent variable in a LMM. All the contest format and superlative variables described earlier were fixed effects. Year and contestant were random effects with random intercepts. No violations of normality or homoscedasticity were evident following visual inspection of the LMM residuals plotted against the fitted values, other than precisely truncated scatter in the upper right quadrant which is plausibly attributable to the maximum possible dunk score of 50. Likewise, the linearity of each fixed effect was evident in plots of profile zeta functions.

Fifty-six potentially influential observations were identified using a Cook’s distance cutoff of 4/432 (0.009); the quantity influential for each fixed effect appears in Table 6 and many were potentially influential over multiple fixed effects. All potentially influential observations occurred in 2009 and after. The estimates most effected by exclusion are those for attempts and replacement dunks. Attempts and replacements began increasing in the mid-2000s. Thus, the influence of these observations is attributable to regulatory and participatory changes over time (as opposed to measurement or model specification). We have no reason to exclude these observations on ecological grounds but do acknowledge their statistical influence and include a summary of the model without these cases in Table 6.

Attempts were significant predictors of lower scores (replacements approached significance). The interaction between WPS and sequence was not significant, indicating the effect of sequence on scores is independent of the initial round positioning of the previous SDC winner. Compared to the initial round, dunks yielded significantly higher scores in the middle and final rounds, the difference for each approaching two points. The interaction between sequence and round was significant for the initial round, the final round approached significant, and was not significant for the middle round. Figure 4 contains the estimated marginal mean dunk scores by sequence, for each round (Lenth, 2018).

Fig. 4

Estimated Marginal Mean Scores in Sequence by Round.

A significant home advantage equivalent to a one-point increase in scores was found. Dunk scores increased as popularity increased. The effect of contestant height trended toward significance, with scores increasing as height decreased such that a contestant of 208.28cm of height would receive about ∼1 point less for the same dunk completed by a contestant of 182.88cm. The presence of histrionics was significant, imparting a 2.7-point advantage, but there was no effect of the functionality of the histrionics. Dunk novelty had a significant effect of decreasing scores. A dunk that had been done 20 times before could be expected to lose ∼0.50 point. Judge experience approached significance also, reducing scores.

4.5.Post-hoc examination of scoring in rounds and dunking prowess

Although the LMM indicates that dunks generally receive higher scores in the middle and final rounds, it is unclear what is driving this difference. It may be that contestants with greater dunking prowess generally survive to later rounds. However, it may also be that judges award higher scores in later rounds because they expect that scores should be greater as contests progress. Post-hoc analyses were undertaken to better understand the differences in scoring between rounds.

Using all dunks with available footage and the easier/harder dichotomous variable discussed earlier (see §4.1), the proportion of harder dunks made (i.e., not missed dunks) in the initial round of each SDC was computed for each contestant. The logistic regression used to evaluate randomness of sequence (see §4.3) was recomputed with this proportion included as a covariate. The effect of dunk difficulty on surviving the initial round trended toward significance (β=0.641, p = 0.131), otherwise the model was virtually unchanged. The effect of difficulty would be such that a contestant had a 50% likelihood of survival if he had zero harder dunks and a 58% likelihood if half of his dunks were difficult.

Scores of all made dunks from initial rounds in all SDCs were then regressed onto an interaction between the easier/harder variable and a yes/no indicator of surviving, with contestant as a random effect. This LMM indicated that harder dunks were scored higher (β=1.686, p < 0.001) and surviving contestants produced higher scores (β=3.643, p < 0.001) but the interaction was nonsignificant (p = 0.242). Pairwise comparisons adjusted with Tukey’s method indicated that survivors were rated 4.04 points higher on easier dunks and ∼3 points higher on harder dunks (ps < 0.001) compared to nonsurvivors. For nonsurvivors, harder dunks were scored significantly higher than their easier dunks (p = 0.01). Importantly, easier dunks done by survivors were scored ∼1.9 points higher than the harder dunks done by nonsurvivors (p = 0.018). Dunk difficulty appears to be negligibly influential on surviving the initial round because contestants who survived produced higher scores on easier and harder dunks, suggesting greater dunking prowess.

Data were then subsetted to include only made dunks from participants who survived the initial round (n = 319). That is, made dunks from all rounds in each SDC by all contestants who survived the initial round in each SDC. Easier/harder dunk was the dependent variable regressed onto the interaction of round and a categorical variable indicating whether that year the SDC had two or three rounds. Harder dunks were more likely to be executed in 2-round SDCs (β=1.53, p = 0.003) than 3-round SDCs. The interaction was not significant and there was no round effect. Pairwise comparisons showed that there were no differences between rounds within 2-and 3-round SDCs (ps > 0.95). This demonstrates that, among the more skilled dunkers, the difficulty of dunks has increased through the history of the SDC but there are no differences in dunk difficulty between rounds within eras.

The LMM of superlatives performed in §4.4 was recomputed with this subset of the data (n = 291 eligible); but functional histrionics was dropped due to there being no instances of it in the subset. Scores did not significantly differ between rounds (ps > 0.36), which would suggest that the effect of higher scores in later rounds is plausibly attributable to lower scores for contestants who did not survive the initial rounds. Effects of attempts and replacements (ps > 0.40), sequence (p = 0.34), dunk novelty (p = 0.39), and home advantage (p = 0.11) were no longer significant. Popularity and histrionics remained significant, with similar effects on scores, and judge experience significantly decreased scores (β= – 0.09, p = 0.03).

Lastly, an interaction between round and the categorical variable indicating whether a SDC had two or three rounds was included in the post-hoc superlatives LMM. Pairwise comparisons indicate that the average final round score was 1.32 points higher than that of initial rounds in 3-round SDCs (p = 0.03); middle rounds trended toward having higher average scores,+0.91, than initial rounds (p = 0.16). However, the difference between final and initial rounds in 2-round SDCs, although – 0.69 points, was nonsignificant (p = 0.63). Effects of other variables were comparable to the first post-hoc superlatives LMM (see Supplementary Table 2). Because dunk difficulty for superior dunkers was not different between rounds within either type of SDC, this suggests that scores were inflated in the final rounds of 3-round SDCs but not 2-round SDCs.

5.1.Elements

Preliminary analyses revealed that more athletic dunk elements had higher proportions of errors of execution. Using an aggregate indicator of error, logistic regression generally classified the more difficult dunk elements accordingly, and in line with our expectations. Despite this, and that harder dunks averaged higher scores than easier dunks, the measure of dunk difficulty cannot capture all the nuances of elements and misses subtle differences in difficulty between the execution of elements in different dunks. This shortcoming could be overcome in future studies by objectively measuring the airborne activity of dunk elements.

The LL supported the hypotheses regarding primaries and modifiers. Although the more athletic primaries such as behind-the-back and between-the-legs were generally scored higher than others when controlling for modifiers, pairwise comparisons were not performed. The model expected more athletic modifiers such as 360° rotations of gross anatomy and launching from the free throw line to increase scores by two or more points for most primaries. Likewise, lesser extension of the arms considerably reduced scores for the cradle, double-pump, and windmill primaries (but it actually increased for tomahawks). Taken together, these findings indicate that executing more athletically-demanding elements increases scores in the SDC.

However, in ordinary least-squares terms, the dunk elements model accounted for less than half of the variance in dunk scores. Some variation may be due, in part, to there being fewer scheduled dunks and the use of fan votes (instead of judging) that restricted sample sizes for many of the elements that emerged or became more prevalent after 2000. Alternatively, factors we did not measure such as judges’ angle of observation (Dallas et al., 2011) or inflated scores for more difficult elements irrespective of the quality of execution (Morgan and Rotthoff, 2014) may be at play. Nonetheless, the model appears to support the system we used to classify the dunk elements. The raw mean score awarded for dunks with the basic kinematic is 44.45 whereas the LL estimated it to be 38.5 in the absence of modifiers (the least of all primaries), indicating that the execution of modifiers contributes considerably to scores of dunks ascribed the basic kinematic.

Although the elements are observable, the system used to identify dunk elements remains imprecise and subjective. Regarding imprecision, for example, the swing modifier most commonly precedes the cradle kinematic; however, swinging was given broader applicability in the analysis. Using swinging to account for appreciable maneuverings of the ball prior to initiating any primary kinematic may have adulterated how swinging behaved in the model. This system also provides little objective measure (e.g., distance and rotation are semi-quantitative) as to the degree of difficulty or athleticism necessary to complete a dunk element. Therefore, concerning subjectivity, a matter for future study is examining quantifiable, objective measurements that correspond to athletic ability or difficulty such as measurement of airborne anatomical motions (e.g., length of the arc of ball movement during a windmill) or the duration of the goal shaking after finishing (as a proxy for dunk power). Notably, the present finding that contestants of shorter stature tend to be scored higher than their taller counterparts suggests that the duration of hangtime prior to finishing is also a target for objective measurement (Harding and James, 2010).

More broadly, this system of identifying dunk elements may also be confounded because it requires every element be assigned to a discrete class. This is highly subjective and, as indicated in Table 3, prone to inconsistent application between raters. For example, a John Starks dunk in 1992 was initially viewed as a double-pump with less-than-full arm extension by the first author but as reaching by the second author (our consensus was reaching). If standardized dunk contest scoring protocols were implemented by a governing body, competition could be unduly influenced by this or a similar nominal system of classifying elements. One concern is discrete classes might portend intuitive score-ranges that could outweigh the assessment of the airborne activity that was observed. Imagine the present authors were judging this 1992 John Starks dunk. JMB may have awarded a lower score simply because he ascribed ‘less-than full extension’ (implying less athleticism) whereas ESR may have awarded a higher score to Starks for outstretching to catch the ball (implying greater athleticism)— for what is the same anatomical motion. Another concern is the use of classes could restrict creativity by compelling contestants to utilize only dunk elements listed in a regulatory document. Thus, future operationalizations in empirical study and protocols of competition should strive to objectively quantify airborne activity.

5.2.Format

The LMM indicated that dunk scores decreased as the judging experience of the judges increased. Scores are estimated to be reduced ∼0.25 point when the judging panel has judged 3 previous SDCs combined. In line with the finding that dunk novelty slightly increased scores, this suggests that scores are slightly lowered when judges have observed more dunks. The present findings cannot directly inform whether this is due to judges’ preference for novel dunks or whether they become more discriminate in their evaluation and scoring of dunks. If judges do become more discriminate in scoring with increasing experience, we might expect judges’ prior exposure to all elements found in a dunk to affect its scores. However, a variable measuring this sort of exposure was discarded from the model due to its lack of influence (even when considering polynomic terms and dunk novelty was excluded) and judge experience reduced scores in the post-hoc model using data from contestants with greater dunking prowess. It appears that judges grant higher scores for novel dunks, which is in line with our conclusions below about their preference for excitement. If additional individual-level judge scoring data were obtained (i.e., pre-2000), this could be further teased apart by examining how each judge scores in the presence of various elements, when controlling for novelty.

5.3.Superlatives

5.4.Shortcomings

The SDC is an exhibition held during All-Star Weekend, a time many NBA players reserve for rest. Although it potentially boosts brand exposure (Blount, 1987, Nathan, 1991, Aschburner, 1995), the SDC in no way affects basketball rankings, other than the risk of injury and how an injury might impact team success. SDC outcomes may then be subject to certain exhibitory trivialities compared to a dunk contest motivated exclusively by intrinsic athletic competitiveness. We are not insinuating that SDC outcomes might be marginalized; rather that, NBA players likely and appropriately train to maximize basketball skills whereas dunking specialists would likely train to maximize dunking skills. Thus, it remains to be seen if the methods and findings of this study are applicable to dunk contests involving dunking specialists.

Given the number of variables employed in the analysis, the SDC offers a relatively small data set. The small n could undermine many of the conclusions we have drawn, particularly those regarding the dunk elements. This latter point can be addressed if future study distills airborne activity into a few continuous and categorical variables that are measurable to some extent in the movements of any primary or modifier. However, despite the relatively small data set, the LMM was relatively unchanged when 56 dunks were excluded due to potential statistical influence.

Also, given the significant effects of several superlative factors, we cannot assume that scoring procedures were consistently implemented throughout SDC history. We do know that the procedure of determining a winner has changed because viewers voted for the winning contestant in some SDCs. That is, the SDC has been used as a promotional vehicle (Nelson, 1995, Latimer, 1994) and the NBA is a commodity of competitive entertainment. Therefore, it is not unimaginable that judges could be encouraged by SDC organizers to evaluate dunks in a way that maximizes entertainment value or could bolster status of a contestant. Likewise, irrespective of encouragement, it may be that judges, like fans, are excited by the SDC and their capacity for subjectivity is reduced— this corresponds to our conclusions about histrionics.

5.5.Applicability

Our findings could be of immediate value for SDC contestants. Consider the 2017 SDC: Aaron Gordon used three replacement dunks while attempting to catch a ball that bounced from the floor after being dropped from a high hovering drone. First, the histrionics of a drone are expected to garner + 2.76 points for whichever dunk he performed as well as some amount of additional points for catching a pass ‘from’ the drone. Second, Gordon was attempting the between-the-legs airborne kinematic which requires greater athleticism and coordination than other primaries, i.e., increased risk for error. Third, by using three replacement dunks, Gordon’s score would be expected to decrease by ∼1 point. The between-the-legs kinematic has an average score of 47 when controlling for other dunk elements whereas, say, the windmill kinematic is 44.9 and demands less athleticism. If we are willing to imagine that Gordon successfully dunks a windmill on his first try, with no replacements, and all else is unchanged, we expect his score to be ∼48.5 whereas with a between-the-legs with three attempts we would expect it to be ∼49. Thus, the reward of a higher expected score for the between-the-legs is not only limited by the maximum possible score of 50 but is also diminished by its difficulty.

Less publicized dunk contests will be staged at a secondary school pep rallies or broadcasted on network television in fringe time slots. Ideally, the findings reported herein are applicable to contestants in those dunk contests, too. Aside from the potential applicability of the foregoing anecdote (i.e., perform creditable dunks one can execute successfully on the first try), the totality of the findings indicates that judges respond positively to excitement that surrounds a given dunk. The influence of excitement on judging may be acceptable or even preferable in exhibitory dunk contests. However, if the dunk contest is to ever become a standalone, sanctioned, athletic competition then the influence of excitement on judging will need to be addressed.

Additionally, the present findings demonstrate the usefulness of newspaper mentions as a measure of popularity for NBA players. Summarily, although more precise and objective methods of quantifying the dunk elements is appropriate for future analysis of the SDC, and dunk contestants in general, the present study is the first to analyze the dunk contest while also contributing to the literature on subjective judging in aesthetic sports.