Feeling fast? Beliefs and performance among high school sprinters

1 Introduction

The impact of beliefs on performance and productivity is evident intuitively across many domains and disciplines although empirically isolating and estimating these effects is challenging. In economics, recent work on aspirations and self-efficacy has grappled with how beliefs can alter individual productivity relative to hard external constraints (e.g., Appadurai 2004; Bernard et al. 2014; Dalton, Ghosal, and Mani 2016; Lybbert and Wydick 2018; Wuepper and Lybbert 2017). One common reaction to this research might be called “The Peter Pan Critique”: Believing doesn’t make it so! While this is certainly true when biophysical constraints bind (e.g., flying in the Peter Pan case), it may be less valid as a concern in contexts where such constraints are partially non-binding. In such cases, beliefs can and often do directly shape effort, productivity and outcomes.

Competitive sports are frequently used as the prototypical case for how mindset can shape performance (e.g., Imperiale-Hagerman 2011; Johnson et al. 2009; Shafizadeh and Gray 2011), but statistically isolating these effects is notoriously difficult. We argue that the 100 meter (100 m) sprint event in high school track and field offers a unique setting for teasing out these psychological effects. A prevailing headwind or tailwind directly changes the wind resistance (i.e., drag) faced by the sprinter, but its effect on finishing times is also a function of indirect psychological effects. For elite world-class sprinters, these indirect mindset effects are largely neutralized by years of intense mental and physical training. Their sprint times in windy conditions therefore reflect predominantly changes in drag with only minimal psychological effects. Elite sprinters therefore provide a useful benchmark for high school sprinters, who—with less experience and training—are subject to both direct physical and indirect psychological wind effects.

We use data from high school track meets in the U.S. to test how wind conditions affect finishing times for boys and girls. We proceed in two empirical parts. First, comparing these effects to elite sprinters, we establish the presence of slack in the performance of high school sprinters: headwinds slow high school sprinters more than wind resistance alone affects performance, an effect that is particularly pronounced for girls. This implied evidence of measurable mindset effects opens the door for the second part of our data analysis, which explores the effects of a vicarious self-efficacy boost among these sprinters.

Bandura (1977) first formalized the concept of self-efficacy and triggered a generation of research in psychology on the effects of self-efficacy beliefs on performance. Taken as a whole, this work demonstrates the conditions under which self-efficacy—individuals’ perceptions of their ability to achieve a desired outcome—can directly enhance performance. Many of the earliest tests of Bandura (1977) involved physical or athletic tasks. For example, Weinberg et al. (1979) devised a competitive leg-endurance experiment in which they exogenously vary subjects’ self-efficacy by leading them to believe they were competing against a varsity track athlete (low self-efficacy treatment) or an individual who recently sustained a knee injury (high self-efficacy treatment) and found that those with experimentally-induced self-efficacy exert greater effort and are more persistent. Bandura (1977) included such vicarious experiences as one of four main sources of self-efficacy and later described “efficacy appraisals [as] partly influenced by vicarious experiences mediated through modeled attainments” (Bandura 1997, p. 86). Feltz et al. (1979) and McAuley (1985) demonstrated how improved self-efficacy based on such modeling can directly enhance sports performance, something effective coaches obviously know and actively leverage.

Instead of experimentally manipulating the self-efficacy of experimental subjects, we use data from high school track meets in California (CA) and leverage an exogenous and vicarious shock to self-efficacy beliefs for our test. Specifically, we consider Matthew Boling’s record-setting 9.98 s 100 m sprint on April 27, 2019, video of which went viral among track fans and athletes and was covered by general media outlets as well. His race not only set the record as the all-time fastest “all conditions” 100 m sprint for high school boys, but also made him the youngest sprinter to ever break 10 s.^[1] Discussion of this remarkable performance often emphasized the fact that Boling is white.^[2]

To explore the potential effects of Boling’s record-breaking performance on subsequent 100 m times posted by high school sprinters, we use a difference-in-difference (DiD) identification strategy and a statistical approach that incorporates entropy balancing weights (Hainmueller 2012; Hainmueller and Xu 2013) and corrects for multiple hypothesis testing. This empirical approach provides second-best causal inference while allowing for several dimensions of heterogeneity, including gender, wind conditions, and the racial composition of teams, which we predict using a modified version of the Bayesian Improved Firstname Surname Geocoding (BIFSG) algorithm proposed by Voicu (2018). Because we neither manipulate nor measure athlete beliefs, we can only hypothesize the role mindset effects may play as an explanation. Since our first set of results suggest that headwinds introduce psychological effects into sprinter performance, however, this seems plausible.

Our second set of results are consistent with Boling’s record triggering complex and distinctly heterogeneous effects on subsequent finishing times. In contrast to a simple vicarious self-efficacy response, we find evidence of a complex Boling effect^[3] consisting of two opposing impacts on performance: some types of athletes indeed seem to run faster immediately after this exogenous shock, but other types appear to run slower. Since slower times are most apparent in tailwind conditions, this might reflect amplified overconfidence due to feeling fast. These opposing effects appear to be moderated importantly by gender and the predicted race of athletes and teams. Overall, the results suggest that in the presence of psychological slack in performance, vicarious self-efficacy beliefs can have measurable impacts on performance, but subtle contextual and salience cues shape these effects.

This paper makes three primary contributions. First, our conceptual approach uses predictions from fluid dynamic models of drag on elite sprinters to benchmark the physical effects of wind on sprint times. This benchmark then allows us to identify additional indirect effects of wind that operate through the psychology of amateur sprinters. Second, our modification of the BIFSG algorithm for predicting race of individuals (Voicu 2018) opens new possibilities for empirical analysis, in particular using administrative or online records of elementary or secondary school performance, whether academic or athletic. Third, the results of our analysis indicate a clear role of gender in mindset effects on sprinter performance and suggest that vicarious self-efficacy effects are nuanced and distinctly heterogeneous, but may nonetheless be empirically detectable.

2 Conceptual approach

In this section, we describe two core dimensions of our analytical approach in this paper. In the first, we describe in greater detail the way we parse out the direct effect of wind on sprinter performance via drag and the less direct (but no less real) effect of wind via the psychology of the sprinter. In the second, we discuss potential heterogeneity in vicarious self-efficacy that may shape what we call the “Boling effect”: the impact Boling’s viral and record-breaking 100 m performance had on subsequent high school sprinter times as mediated through self-efficacy beliefs. These conceptual details influence our empirical approach described below.

3 Data

We use data collected from a website used to post results from high school track and field meets from both 2018 and 2019.^[9] A unique athlete identifier tracks individual athletes both within and across these two years. Names of schools allows us to track high school track teams within and across years as well, in addition to enabling us to merge other school data (e.g., location and ethnic composition). In addition to athletes’ times and grade level, we observe the name and date of the meet, whether the race was a preliminary or final heat, time gaps between runners for a given race, whether the race was at the varsity or junior varsity (JV) level, the total number of competitors in a particular event at a given meet, and whether the meet was timed using ‘fully automated timing’ equipment. For meets with automated timing equipment, which tend to be more competitive on average, we also observe the wind speed registered at the time of the 100 m race.^[10]

The race results recorded online that are the basis for this analysis are quite clean. There are, however, some clear errors in the data, which we clean by dropping any times that are faster than current records. We also trim the slowest 1 % of times for boys and girls 100 m races. We exclude wheelchair and para-ambulatory races, which constitute a tiny fraction of the total observations. While we use athletes across all states for some of the analysis that follows, as explained in the preceding section we restrict our focus to those competing in CA when quantifying the potential impacts of Boling’s race on high school sprinter times.

Table 1 shows descriptive statistics for our outcome variable of interest (Time) and a set of other variables that feature in our subsequent specifications. For both boys and girls 100 m races, we show these summary statistics for all states and for CA only. The average 100 m time for boys is about 2 s faster than for girls. Total observations for boys and girls (and for all states and CA only) are split evenly between 2018 and 2019 (51 % in 2019). The indicator variable ‘Post’ defines the post-period for the DiD empirical strategy described below. Specifically, in 2019 we set Post = 1 after the April 27, 2019 meet in Texas at which Boling set the all conditions 100 m record. In 2018, this same meet was held on April 28, 2018, but the post-season competition in CA concluded with the state championship meet one week later that year. To reflect this shift in the timing of the competitive and selective post-season meets, we define the post-period for this comparison year by setting Post = 1 after May 5, 2018.^[11] About 30 % of all observations across these events come from meets held in this later portion of the season, which we will refer to as the post-period. In CA, the share of post-period observations drops to about 13 % because the track and field season in CA starts and ends earlier than many states in colder northern locations. In CA, the post-period coincides closely with post-season competitions that become progressively more competitive and culminate in the state championship meet held in late May. Whereas 17–18 % of all meets in our data were equipped with automated timing equipment, this is much higher (43–44 %) in CA.

As a preliminary look at the times we use in the analysis below, we show in Figure 1 the full distribution of 100 m times in CA for boys and girls in 2018 and 2019. Foreshadowing our DiD approach described in the next section, we display these distributions separately by pre- and post-periods (i.e., according to ‘Post’ in Table 1) for each year. The ‘2018 pre’ and ‘2019 pre’ distributions of finishing times are indistinguishable from each other. The post-period distributions are completely to the left of the pre-period distributions, which is to be expected because (i) athletes tend to get faster as the season progresses and, more importantly, (ii) the post-period coincides in CA with the start of more competitive and selective post-season meets for which only fast sprinters qualify. For girls a slim wedge separates the 2018 and 2019 post-period distributions with faster times recorded in the 2018 post-period. For boys, post-period distributions are nearly indistinguishable.

Figure 1:

Cumulative distributions of times for boys and girls 100 m races in CA. Distributions shown separately for pre- and post-periods in 2018 and 2019 as defined for the purposes of DiD specification.

Progressive improvement across the track and field season is a key feature of our data, as is the onset of the increasingly selective post-season that ends with the state championship meet. To visually depict these aspects, Figure 2 shows binned scatterplots of finishing times across the season—relative to the Boling meet—for boys and girls.^[12] While pre-period average times are consistent with gradual improvement due to training and experience, the selective post-period shows more dramatically faster times as the fastest athletes progress through post-season meets.^[13] Again, the fact that the average times and trend prior to the Boling meet are nearly indistinguishable in 2018 and 2019 bodes well for our DiD identification strategy.^[14]

Figure 2:

Non-parametric visualization of times for boys and girls 100 m races in CA using a binned scatterplot (each point represents the average time of 50 equally-sized bins by date of meet). The post-period for 2019 is defined by the actual date of Boling’s record-breaking sprint (i.e., the ‘Boling meet’). The post-period for 2018 is defined by the same point relative to the start and end of the CA high school track season and constitutes a ‘pseudo’ post-period as a DiD comparison with the true post-period in 2019.

As a methodological innovation, we modify the algorithm published in Voicu (2018) to predict the race of each athlete in our data.^[15] Predicted sprinter race and racial composition of teams enable us to test for a wider range of relevant heterogeneous Boling effects. Specifically, we use the BIFSG predicted probabilities that a given boy is white and average Pr(white) across high school teams (see Appendix). We modify the BIFSG algorithm for this application by integrating school-level racial composition data as the basis for the location predictions of race, instead of relying on census block data, which can only improve the resulting racial predictions.^[16]

4 Empirical approach

We describe in this section the two main empirical analyses that follow. First, we present the specification we use to estimate the effect of wind on 100 m sprint times. Then, we discuss the DiD approach we use to test for the presence of a Boling effect and the triple DiD (3DiD) approach we use to test for heterogeneous effects by (predicted) race of athletes.

In order to estimate how wind affects high school sprint times and to test for differences in these wind effects by gender, we use the following piecewise-linear specification, which we estimate separately for boys and girls in 100 m sprint races:

where Time _ijt is the time posted by athlete i in race j on date t, W _jt is the wind as recorded during the race, Head _jt is an indicator for races conducted in headwind conditions (i.e., W _jt < 0), and X _ijt is a vector of control variables including the time gap at the finish line to the next fastest finisher, the date, type and size of the race, and fixed effects for athletes’ grade (i.e., year in high school (e.g., freshman, sophomore, etc.)).^[17] We report results from this estimation with and without athlete fixed effects. In this specification, α ₁ < 0 indicates that stronger tailwinds (headwinds) decrease (increase) finishing times, and α ₂ < 0 indicates the additional time effect of a headwind. By comparing these wind effects for boys and girls with the wind effects for elite sprinters, we can infer the presence of psychological factors in high school sprint performance. In other words, we posit that the systematic effect of a headwind on finishing times over and above its impact via wind resistance is attributable to psychological effects of the wind conditions that prevail at the time of a race.

We estimate Equation (1) using all races with automated equipment to record wind speed conducted in 2018 and 2019, except those held after Boling’s race on April 27, 2019.^[18] As an alternative specification, we estimate a panel version of Equation (1) that includes athlete fixed effects. We also estimate a version of this panel specification that includes quadratic wind speed to allow for more flexible wind effects on finishing times.

As part two of our empirical analysis, we use a DiD specification to test for possible impacts on subsequent race times. Attributing differences in sprint times after Boling’s race to a “Bolling effect” requires a causal identification strategy. In our case, no such strategy will be perfect given our use of observational rather than experimental data. We use 2018 as the counterfactual for 2019 based on the assumption that these two years are comparable up until Boling’s 9.98 s race marked the beginning of the post-period in 2019. The indistinguishable pre-period distributions in Figure 1 provide initial visual evidence that these two years are comparable in this way.

This identification strategy also assumes that the timing of Boling’s record-breaking race was random. This is supported by the fact that his time was aided by a tailwind of +4.2 m per second (m/s) that was strong enough to push his time below the symbolic threshold of 10 s and created the buzz that caused his performance to go viral. To underscore this point, two points are noteworthy. First, if the wind at the time of the race had not gusted to such a stiff tailwind, Boling almost certainly would not have broken the 10 s barrier, and the sprint would not have gone viral. The boys 100 m final was the only wind-registered race held at that meet that day with wind recorded over ±2 m/s.^[19] This random (and essential) wind gust during the boys 100 m final rules out the presence of other date-specific factors affecting both Boling’s performance and other high school sprinters’ subsequent times. Second, since that record-setting sprint, Boling has only broken the 10 s barrier twice at official events: one of those was also wind assisted (+3.2 m/s) and the other was within the allowable tailwind range (+1.6 m/s). The confluence of factors that enable a talented athlete like Boling to run 100 m under 10 s are simply very rare and entail an element of randomness in race conditions.

Conditional on this DiD strategy producing at least weakly causal estimates, we hypothesize that any changes in 100 m times are attributable to mindset changes since, as mentioned, the post-period observations in CA occur too soon after Boling’s race for increased training intensity to increase athletes’ physical potential. While we believe this is a defensible approach to estimating the Boling effect, it clearly does not approximate an ideal (hypothetical) experiment that randomly varies exposure to Boling’s race and does not entirely rule out possible confounding factors. In the absence of such an experiment, our second-best DiD approach (further enhanced with additional adjustments described below) provides suggestive evidence of an effect that is unlikely to arise purely from correlation.

Our basic DiD specification is as follows:

where Time _ijt is the time posted by athlete i in race j on date t, β ₃ is the DiD coefficient of interest that indicates the Boling effect on subsequent times, and X _ijt is a vector of control variables including the time gap at the finish line to the next fastest finisher, the date, type and size of the race, and whether the meet was using fully automated timing equipment.^[20] We restrict our focus to CA schools and meets as described above and estimate this DiD specification separately for boys and girls. In addition to the specification in (2), which is estimated using all meets in our data and controlling for those with automated timing, we also estimate a version of this specification separately for races run in headwind and tailwind conditions (and therefore only including only races with automatic timing).

Evidence of Boling’s performance inspiring faster times would come in the form of β ₃ < 0. As described in the conceptual framework above, there are, however, a host of potentially important heterogeneity considerations to take into account. While boys may be most responsive to the Boling effect since he posted his record time in the boys 100 m, the scope of salience in this case could easily extend to girls competing in the 100 m sprints. To further explore this scope of salience in this case, we include racial predictions in two ways. First, we estimate Equation (2) separately by tercile of team average Pr(white) (maintaining the disaggregation by gender and wind conditions). Second, we estimate a 3DiD specification as follows:

where β 3 ′ is the base DiD coefficient and γ ₄ is the 3DiD coefficient that provides a further adjustment of finishing times based on the predicted Pr(white) of athlete i. As with the DiD specification, we separately estimate this equation by gender, wind conditions and team average Pr(white). Evidence that the vicarious self-efficacy Boling effect is concentrated in white sprinters would come with the result γ ₄ < 0.

We make two statistical adjustments when estimating these DiD and 3DiD specifications to improve identification and statistical inference. First, to strengthen our DiD identification strategy, which takes athletes competing in 2018 as our counterfactual for those competing in 2019, we use entropy balancing (Hainmueller 2012; Hainmueller and Xu 2013) to ensure balance between these “control” and “treated” athletes. We then use the resulting entropy balancing weights (EBW) in our DiD and 3DiD regressions. This adjustment is potentially important because while the composition of high school sprinters between the post-period of 2018 and 2019 in CA is surely comparable, the composition of those included in the online results platform we use may not be.^[21] Entropy balancing and weighted regression using EBWs ensures that the pre-period means of key covariates in 2018 match their counterparts from 2019.^[22]

As the second adjustment, we correct for multiple hypothesis testing since we separately test heterogeneity by gender, wind conditions, and racial composition of teams. In order to reduce the likelihood of false rejections when we separately estimate the same DiD (or 3DiD) specification for several sub-samples of our data, we compute sharpened False Discovery Rate (FDR) q-values (Anderson 2008), which we report in the results tables along with standard errors. The sharpened q-values are the results of a two-stage Benjamini–Hochberg (BH) procedures that incorporates the number of hypotheses rejected in the first stage into the second stage to achieve greater power.

5 Results

In this section, we present and discuss results from our two sets of analyses. First, we estimate the effect of headwinds and tailwinds on high school sprinter performance. These results establish the prevalence of systematic indirect effects of wind on finishing times that work through psychological channels. We contrast these wind effects for the average high school sprinter to those of elite sprinters and differentiate these effects for boys and girls. Second, we estimate DiD and 3DiD specifications to test for a Boling effect using high school track meets in CA. These results, which should be interpreted with the causality caveats discussed above, reveal a number of potentially important dimensions of heterogeneity in this effect, including by gender and predicted racial composition of one’s team.

5.1 Gender-differentiated wind effects on performance

Table 2 reports the estimation results from Equation (1) with and without athlete fixed effects (FE). While we focus primarily on the two coefficients on Wind, the control variables are generally statistically significant and contribute to the relatively high R ². The FE results suggest that the tailwinds reduce finishing times equally for boys and girls, but that headwinds penalize girls’ performance more than boys. To see this asymmetric gender difference graphically, we estimate a version of this FE specification separately for headwind and tailwind conditions, allowing for non-linear (quadratic) wind effects and show the marginal effects of wind in Figure 3. The headwind penalty is particularly pronounced for girls: the same 6 m/s headwind slows boys by 3.2 % and girls by 3.8 % on average.

Table 2:

Wind effect on 100 m times for boys and girls for high school track meets with automated timing equipment with and without athlete fixed effects (FE).

	Boys		Girls
	Without athlete FE	With athlete FE	Without athlete FE	With athlete FE
Wind	−0.055***	−0.050***	−0.064***	−0.049***
	(0.002)	(0.001)	(0.003)	(0.001)
Headwind × wind	−0.042***	−0.037***	−0.061***	−0.053***
	(0.004)	(0.002)	(0.006)	(0.002)
Time gap	2.125***	0.562***	2.150***	0.345***
	(0.013)	(0.008)	(0.017)	(0.008)
Finals	−0.712***	−0.021*	−0.997***	−0.039***
	(0.023)	(0.011)	(0.033)	(0.012)
Prelim heat	−0.145***	0.069***	−0.175***	0.078***
	(0.010)	(0.005)	(0.015)	(0.006)
Varsity	−0.104***	−0.002	−0.047***	−0.010***
	(0.005)	(0.003)	(0.008)	(0.004)
JV	0.351***	−0.004	0.643***	−0.023***
	(0.010)	(0.005)	(0.014)	(0.006)
Race size	0.008***	0.001***	0.014***	0.001***
	(0.000)	(0.000)	(0.000)	(0.000)
Race size2	−0.000***	−0.000***	−0.000***	−0.000***
	(0.000)	(0.000)	(0.000)	(0.000)
Date	−0.004***	−0.005***	−0.007***	−0.007***
	(0.000)	(0.000)	(0.000)	(0.000)
Finals × size	0.023***	−0.000	0.033***	0.002*
	(0.002)	(0.001)	(0.003)	(0.001)
Prelim × size	−0.004***	−0.001***	−0.006***	−0.001***
	(0.000)	(0.000)	(0.000)	(0.000)
Finals × time gap	−0.763***	0.277***	−0.988***	0.249***
	(0.059)	(0.025)	(0.077)	(0.026)
Constant	12.693***	13.024***	14.356***	14.828***
	(0.011)	(0.007)	(0.016)	(0.008)
R-squared	0.44	0.40	0.35	0.35
Observations	102,920	102,920	90,510	90,510

1. Data from U.S. high school track meets in 2018 and 2019 that used automated timing equipment (including wind speed and direction) and were posted at athletic.net. Standard errors in parentheses. Grade fixed effects included. ***p < 0.01, **p < 0.05, *p < 0.1.

Figure 3:

Quadratic effect of wind (m/s) on 100 m times (s) for high school boys and girls based on specification with athlete fixed effects. (Wind < 0 indicates headwind).

As described above, to test whether these wind effects for high school sprinters include a combination of physics and psychology we next compare these effects to elite male sprinters. If this test suggests the presence of measureable mindset effects and therefore slack in high school sprint performance relative to hard biophysical constraints, it seems plausible that we might find evidence of a Boling effect on performance in the subsequent DiD analysis. The left panel of Figure 4 overlays the wind-time function for elite sprinters based on Mureika’s online calculator^[23] on the linear wind-time functions implied by the FE estimates for high school boy and girl sprinters in Table 1. While faster times due to tailwinds for boys and girls are nearly identical to the benchmark wind-time function of elite sprinters, boys and (especially) girls suffer much slower times due to headwinds.

Figure 4:

Estimated linear wind effects for HS boys and girls compared to elite male sprinters in 100 m races (left) and wind effects as a function of drag created by prevailing winds during the race (right).

The right panel of Figure 4 depicts these functions with the added dimension of the drag produced by headwinds and tailwinds. For elite sprinters, we use the drag equation and parameterization of Linthorne (1994). We adapt this equation for high school sprinters using the average times (velocity) in our data and modified drag areas for boys and girls, respectively. Elite sprinters obviously generate greater drag in any wind condition than high school sprinters due to the combination of their greater speed and (generally) larger stature. Visually adjusting for this difference in drag accentuates the asymmetric effect created by headwinds, which is evident in the kink that occurs in the transition from tailwinds to headwinds as well as in the sloping (dashed) iso-wind lines that connect the functions in the right panel. Based on this evidence of physical slack in sprinter performance due to psychological factors, it seems conceivable that Boling’s record setting sprint could have affected performance—even in the very short-run—by vicariously boosting the self-efficacy of high school sprinters.

6 Discussion

Empirical, often experimental, research provides compelling evidence that beliefs about one’s productivity and likelihood of success can affect effort and realized outcomes. Whether beliefs actually affect performance in practice hinges on the degree to which biophysical constraints bind since slack relative to such constraints is a prerequisite for beliefs to enhance measured productivity. Against this backdrop, we offer a modest contribution using observational data from amateur sports to document the presence of slack in baseline performance and, therefore, the potential for beliefs to affect productivity. We then explore how beliefs shape outcomes using a specific potential self-efficacy shock. Although observational studies like this have the potential virtue of better external validity than artificial settings such as lab experiments, they cannot rule out all confounding factors using exogenous treatment assignment. Our results should be interpreted with this potential virtue and limitation in mind.

The context for this study—the 100 m sprint event in high school track—has a number of useful features for our analysis. Performance is objectively and precisely measured. Thousands of athletes compete in this event each week, most posting several finishing times in a given track season. Prevailing wind conditions can drive a wedge between physical and psychological determinants of performance, particularly for amateur athletes without years of experience and professional coaching. Outside of a controlled experiment, this setting is likely among the best suited for exploring the role of beliefs on performance.

Our part one results are straightforward and clear: we find evidence of slack in performance relative to the physics that govern drag from wind resistance. This suggests that mindset shapes baseline performance for amateur athletes in distinctive ways relative to elite sprinters. The systematic detrimental effect of headwinds on sprint times beyond increased wind resistance is especially pronounced for girls. This existence of slack in sprinter times is, on average, attributable to mindset effects. This result implies both that self-efficacy beliefs matter in measurable ways in this setting and that a discrete self-efficacy boost could reasonably enhance performance by shrinking the slack in performance.

In part two, we explore these implications using a vicarious injection of self-efficacy that came in the form of Boling’s viral 9.98 s 100 m performance in late April 2019. We use a DiD strategy with entropy balancing and multiple testing adjustments to test for a Boling effect, our shorthand term for changes in sprinter times due to athletes’ self-efficacy beliefs. The results from this analysis are less clear due to less than perfect causal identification and are more mixed and complex than part one, but nonetheless raise some intriguing potential dimensions of heterogeneity. The conceptual framework that motivates this analysis emphasizes the salience of another person’s success as a key factor in the vicarious self-efficacy boost it generates for others. This scope of salience raises a number of facets in our study that likely interact with other forms of mindset heterogeneity, including gender, racial composition of the athlete’s own team, and the athlete’s own racial background.

Mindset effects in our context are potentially subtle and idiosyncratic, but we can only test for heterogeneous effects using broad categories. In the case of race, which is of particular interest here because of the clear racial framing that often accompanied media coverage of Boling’s record sprint, we modify the racial prediction algorithm proposed by Voicu (2018) in order to predict the racial background of athletes in our data. This methodological adaptation may be particularly useful for empirical analyses that use school-level data (e.g., results from high school track and field meets), but these predictions also introduce additional noise and statistical imprecision into our estimates. They also raise ethical issues when the benefit or burden of correct or incorrect racial predictions disproportionately affect specific groups (Lockhart et al. 2023). We consider our use of these predictions to be innocuous since they are not consequential to the individual athletes (e.g., they do not determine eligibility or influence policy or program design). Indeed, we merely use these predictions as an imperfect means of recovering what is often observable by spectators at public track meets, but not recorded in online results repositories. For other applications of this method—adapted for use with school-level data—these potential ethical issues could loom large and must be treated and mitigated with great care.

As a consequence of these heterogeneous results, the empirical evidence we provide suggests that beliefs can indeed shape performance, but these effects do not fit neatly or consistently into a simple model of vicarious self-efficacy. Instead, we find that the Boling effect is a composite of two opposing impacts as enhanced beliefs seem to have improved performance under difficult headwind conditions for some athletes, but slowed times under favorable tailwind conditions for others. The presence of this flipped effect, which we attribute to amplified overconfidence when a race feels effortless, offers an intriguing and unexpected alternative to the vicarious self-efficacy effect we hypothesized in the conceptual framework. The net effect of these forces determines whether we detect faster or slower times for a specific subset of sprinters. This estimated Boling effect therefore varies according to subtle individual and contextual cues.

Although our empirical setting seems well-suited for addressing our research question, these results offer a complex perspective on the functioning of beliefs and performance. Part of this complexity may emerge from the influence of racial cues, context and identities. The dominant social media narrative about Boling’s record-breaking sprint underscored that he is white, but this may have amplified effects on both white and non-white sprinters in different ways—and not just because sprint competitions are zero sum. After all, a ‘chip on the shoulder’ is a highly effective motivator in athletics and life in general, as few things inspire renewed effort and focus more than feeling slighted or disrespected.

We conclude by considering whether these insights from amateur sprinters may extend beyond the high school track. While the presence of hard biophysical constraints on productivity and performance implies that believing doesn’t always make it so, in settings where these constraints are only partially binding—that is, where there is some slack in productivity relative to what is possible given a set of inputs—beliefs can have direct and measurable effects. At least in our context, these effects are complex and reflect subtle contextual and salience cues. Understanding when and how self-efficacy and other beliefs shape outcomes is a worthwhile research goal for economists and social science more broadly. In this sense, this study aims to generate hypotheses that could motivate such follow-on work.