The impact of club sports on student experience in higher education

ABSTRACT 

Purpose:

This paper analyzes the long-term effect of carbon plated running shoe technology (super shoes) on the performance of elite female and male marathoners.

Methods: 

 In order to do this, we collected data on the number of male sub-2:08 and female sub-2:26:50 marathons in years both prior to and after the introduction of such shoes.  Regression models were then constructed to assess the yearly trend in these data both pre and post super shoe introduction (this was done separately for each gender). 

Results:

We found a statistically significant increase in the slope following the introduction of super shoes, with the annual number of sub-2:08 performers increasing by approximately 11.8 more athletes per year for men and 22.2 for women.  Additionally, we compared the change in men’s slope to the change in women’s slope, finding that women’s times responded significantly more to the introduction of super shoes than did the men’s times.

Conclusions:

In summary, super shoes not only provide an immediate boost to race day performance, but also appear to have ongoing time improvement effects over time.

Applications in Sport:

This research will allow runners to make informed decisions regarding their use of shoe technology in competition.   These findings suggest that performances in elite marathoning are improving at a faster rate since the introduction of super shoes.  This implies that athletes, coaches, and governing bodies must account for the ongoing effects of shoe technology in training, competition, and qualification standards.

Keywords: Marathon, carbon plated shoes, performance benefits from shoes

INTRODUCTION AND LITERATURE REVIEW

The marathon race traces its origins back to the legend of Pheidippides.  We owe the standardization of the distance to the royal family at the 1908 London Olympics, who requested the race to pass the palace, and thus at 26 miles and 385 yards, and a tradition of long distance racing was born.

Following the running boom of the early 1970s, marathon running has become increasingly popular at both a recreational and elite level.  Currently, the most competitive marathons are part of the Abbott World Marathon Majors. 

One noteworthy thing about long-distance running is that it requires minimal equipment.  Perhaps the greatest innovation in equipment technology was the introduction of carbon plated shoes by Nike in 2016.  Initially, knowledge of their existence was rather limited, although the three male marathon medalists at the Rio De Janeiro Olympics all wore some prototype of these shoes (5).  These shoes, however, did not become widely available until 2017 and, therefore, we use 2017 as their year of introduction for the purposes of the analyses we conduct in this paper.  Over time, the use of these shoes has grown to encompass recreational runners as well, and they have become increasingly popular for use in training, due to their extensive cushioning. 

Previous work by Bjorkelo et al. (2024) has shown that the use of these shoes has an immediate effect on performance.  In particular, they found an immediate increase in the number of sub-2:08 marathons run per year by male marathoners.  The goal of this paper, however, is to determine what, if any, long-term benefits these shoes offer.  In other words, our goal is to see, if, in addition to the aforementioned immediate benefit, this shoe technology also affects the rate at which the number of sub-2:08 marathons per year is increasing.  We assess the same relationship for the number of women’s marathons run under 2:26:50 each year.  Mathematically, this study models elite marathon performance counts as a piecewise linear time series with a structural break corresponding to the introduction of new shoe technology.  To provide background for these analyses, we now turn to a review of the literature.

A great deal of research into the various factors affecting long distance running performance has been conducted over the years.  Running shoe technology has become an increasingly popular area of research following the introduction of super shoes.  Much of this research has involved the effect of these shoes on running economy (RE).  Morgan et al. (8) define RE as the volume of oxygen that must be consumed (per kg body weight) in order to support a particular running velocity.

While many factors affect RE, the one most relevant to this study is related to running mechanics.  Specifically, this factor involves the force with which an athlete’s foot can hit and depart from the ground (3).  Much of the research into the efficacy of super shoes in reducing marathon times has been lab research related to these ground forces.  For example, Herbert-Losier and Pamment (5) found that while the Nike Zoom Streak 6 (a traditional racing shoe) had an energy return of 65.5%, the Nike Vaporfly (a super shoe) returned 87% of the expended mechanical energy.  They found that this increase in energy return results in approximately a 4% increase in RE and a 2% increase in performance.  Similarly, Hunter et al. (7) found runners’ oxygen consumption to be between 1.9% and 2.8% lower in carbon plated shoes, as opposed to traditional racing shoes.

The aforementioned laboratory gains in RE can, naturally, vary quite a bit from one individual to another.  For instance,  Paradisis et al. (9) found that, among recreational runners, the reduction in oxygen consumption attributable to carbon plated racing shoes can be up to 3.8%.  It is also important to note that most of the studies on RE focused on male subjects or pooled male and female subjects (1).  As we will shortly see, one of the analyses performed in this study attempts to discern any differences in separately averaged male and female response to super shoes.

Although much of the research into carbon plated shoe technology has been conducted in the laboratory, some work has been done outside of the laboratory.  In particular, Bjorkelo et al. (2) found that the introduction of super shoes in 2017 was associated with a 91 second decrease in elite male marathoning times.  Additionally, Robbin et al. (11) found that, since the introduction of super shoes, elite male and female marathoning times have improved according to the 3 following criteria:  (1) the arithmetic mean of the medians of the 100 best performances per year was at least 0.3% faster than the reference value, (2) at least 50% of the years in the observation period were faster than the reference value, and (3) two years within the observation period were the fastest years analyzed.  Most notably, they found that arithmetic mean of the medians decreased by 1.45% for the females and by 0.73% for the males.  This corroborates the 1.174% decrease in elite male times found by Bjorkelo et al. (2). 

In this paper, we will take the previous research several steps further.  While the previous research looked at the one-time effect of super shoes on race times (e.g. a 1.45% decrease in marathon times for women and a 0.73% decrease for men) (11), we will address the question:  on a yearly basis, are race times improving more rapidly than they used to for elite male and female marathon runners?  Additionally, we will statistically quantify any differences that exist between this rate of improvement for men versus women.

METHODS 

In order to address the questions posed above, we collected data on the number of male individuals running under 2:08 for the marathon for each year from 1985 through 2024, and similarly, collected data on the number of female individuals running under 2:26:50 for each year from 2002 through 2024 (note that we examine the number of unique individuals under these time standards, not the total number of performances under these standards).  These data are publicly available, and were obtained from the World Athletics database (6). We then conducted several linear regression analyses. Due to the time-series nature of the data, we used Cochrane-Orcutt transformations on all continuous variables, in order to remediate the autocorrelation of the residuals (4).  This transformation transforms the regression variables such that the correlation of model errors over time is dramatically reduced.  After correcting for autocorrelation, no evidence of heteroskedasticity or non-normality of residuals was detected.  Additionally, in order to minimize the multicollinearity in the models, we centered the year about 2017.  Note that all hypotheses are tested at the 0.05 level of significance.

In each of the aforementioned regressions, the dependent variable is either the number of individuals who ran sub-2:08 marathon in a given calendar year (when dealing with men), or the number of individuals who ran sub-2:26:50 marathon times in a given calendar year (when dealing with women).  The times of 2:08 and 2:26:50 were chosen for the following reasons:  (1) they allowed us to find data dating back a few decades, (2) they would still be considered an elite marathon time today, and (3) the data for this particular set of times was readily available.  Further, the choice of 2:08 allows for a nice comparison to work previously done by Bjorkelo et al. (2), and as 2:08 is near the 2024 Olympic standard for men, the Olympic standard for women seemed a compatible complement. That said, we note that there is nothing intrinsically special about the times of 2:08 and 2:26:50.

While we acknowledge that the use of counts of performances below a fixed threshold differs from directly modeling finishing times, this approach offers two advantages. First, it provides a consistent and interpretable measure of performance depth over time, allowing us to assess how many athletes are achieving historically high standards in any given year. Second, threshold-based measures such as ours are less sensitive to extreme outliers (e.g., world records) and instead capture overall changes in competitive field quality.

In each regression, the year (e.g. 2010) is used as an independent variable.  As noted in the introduction, we consider 2017 to be the first year for which super shoes were widely available.

In practical terms, the approach outlined above allows us to compare how quickly elite-level performances were improving before and after the introduction of super shoes. Instead of focusing on individual race times, the model captures changes in the depth of elite performances over time.

RESULTS

We now address the first research question:  has the annual rate of increase of the number of men running under 2:08 changed since the introduction of super shoes?

Men

To clarify the above statement, we assume (and can see from the data) that the number of men running under 2:08 each year has been increasing over time, independent of shoe technology.  This may be attributable to such things as improved nutrition and better training methods.  Our goal is to see if that rate of increase changed in 2017, upon the introduction of super shoes.  In order to do this, we estimate the following equations:

Y = b₁₁ + b₂₁X, where Y = the number of men under 2:08, and X = year (for years 1985-2016)

Y = b₁₂ + b₂₂X, where Y = the number of men under 2:08, and X = year (for years 2017-2024). 

In the first equation above, b₁₁ is the estimate y-intercept and b₂₁is the estimated slope.  Similar notation is used throughout the remainder of this section for the remaining equations.  In practice, b₂₁  is the pre-super shoe slope and b₂₂ is the post-super shoe slope.  b₂₁ tells us, on average, how many sub-2:08 performers were being added per year prior to the introduction of super shoes (presumably due to things like improved nutrition), while  b₂₂ tells us, on average, how many sub-2:08 performers have been added per year after the super shoes were widely available.

The estimated equations are presented below (with standard errors in parentheses below the parameter estimates):

(equation 1a)  Y = -2022.04 + 2.595X

                                                              (0.516)

(equation 1b)  Y = -39725.17 + 14.395X

                                                                 (1.973)

Although it is not our primary topic of interest, we note that each of the slope parameter estimates above are statistically significant, and have p-values < 0.001. 

After estimating both equations (using ordinary least squares regression), we test the following hypothesis:

H₀:  b₂₁ = b₂₂

H₁:  b₂₁ ≠ b₂₂

Note that we use the approach above, as opposed to simply estimating one equation with an interaction term, because our attempts to do so were met with serious multicollinearity issues. 

In order to test the hypothesis above, we utilized a modified Sattherthwaite approach (13) to estimating the degrees of freedom for the corresponding t-test.  We utilize this approach because (1) some of our sample sizes are relatively small and (2) the variance of the parameter estimates we are comparing do not appear to be equal. 

From equations 1a and 1b, we find a test statistic value of T = 5.78.  Using the method of von Davier (13), we find an effective degrees of freedom of 8.23.  This results in a p-value = 0.00042.  Hence, we reject our null hypothesis of no difference between the slopes.  Indeed, it appears that the annual rate of change (slope) in the number of sub-2:08’s  during the super shoe era is significantly greater than the rate of change prior to the introduction of super shoes.

The difference between the slopes above is 11.8.  This means that, upon the introduction of super shoes, the rate of increase in the number of sub-2:08 runners each year increased by 11.8.  In other words, we are now adding nearly 12 more athletes per year to the sub-2:08 ranks than was the case prior to 2017.  In a practical sense, this suggests that elite performance is not just improving, but improving at an accelerating rate since the introduction of super shoes.

Women

Similarly, we now address our second research question:  has the annual rate of increase of the number of women running under 2:26:50 changed since the introduction of super shoes?

  In order to answer this question, we estimate the following equations:

Y = a₁₁ + a₂₁X, where Y = the number of women under 2:26:50, and X = year (for years 2002-2016)

Y = a₁₂ + a₂₂X, where Y = the number of women under 2:26:50, and X = year (for years 2017-2024)

The estimated equations are presented below (with standard errors in parentheses below the parameter estimates):

(equation 2a)  Y = -3780.75 + 3.58X

                                                              (1.127)

(equation 2b)  Y = -55464.92 + 25.79X

                                                                 (3.521)

As with the male marathoners, note that both of the slope parameter estimates above are statistically significant, and have p-values 0.008 and less than 0.001, respectively. 

We now test the following hypothesis for the women:

H₀:  a₂₁ = a₂₂

H₁:  a₂₁ ≠ a₂₂

From equations 2a and 2b, we calculate a test statistic value of T = 6.01.  Using the method of von Davier (13), we find an effective degrees of freedom of 5.87.  This results in a p-value = 0.0018.  Hence, we again reject our null hypothesis of no difference between the slopes.  It appears that, as with the male marathoners, the annual rate of change (slope) in the number of sub-2:26:50’s run by females during the super shoe era is significantly greater than the rate of change prior to the introduction of super shoes.

Finding the difference of the slopes above, we are now seeing a rate of increase in sub-2:26:50 runners that is 22.21 athletes per year more than it was previously.

Comparison of Men and Women

We have just seen that there is convincing statistical evidence to show that the rate of increase of both male and female fast (under 2:08 and 2:26:50, respectively) marathons has increased since the introduction of super shoes.  Our final research question involves determining whether or not these two changes in rate of fast times is different between the genders.  In order to do this, we estimate one regression equation for each gender.  Each of these equations involves the entirety of the years available for that gender.  The dependent variable is unchanged from before.  We now use the 3 following independent variables:  X₁ = year, X₂ is a 0-1 dummy variable which indicates whether or not super shoes were available that year, and the interaction term X₁ X₂.  We can then test to see if there is a difference in the changes of the two genders’ slopes by testing to see if the parameter estimates for the two interaction terms are equal or not.  Specifically, we test:

H₀:  c_4m = c_4f

H₁:  c_4m ≠ c_4f,

 Where the c_i are the coefficients of the two equations’ parameter estimates, and m and f refer to the male and female equations, respectively.  The coefficients in the hypotheses above are taken from equations 3a and 3b below, which represent the two regression equations we estimated:

(equation 3a)  Y = 26.71 +1.008X_1m + 25.94X_2m + 2.73X_1mX_2m

                                                       (0.208)        (8.54)            (2.06)

(equation 3b)  Y = 108.85 +3.194X_1f + 321.71X_2f + 20.27X_1fX_2f

                                                         (0.90)        (48.64)            (3.36)

Recall that Y is the estimated number of athletes under 2:08 or 2:26:50 (elite), and each equation above contains an intercept, an intercept additive “shift” for the super shoe era (X₂), a slope representing the estimated annual increase in number of elite marathons from 1985-2024 (X₁),and an additive increase in slope for the estimated additional number of elite marathons each year after the introduction of super shoes (X₁X₂₎).

From equations 3a and 3b, we used the same techniques as in the first two hypothesis tests, and calculate a test statistic value of T = 4.45 with an effective degrees of freedom of 5.67.  This results in a p-value = 0.0067.  Hence, we reject the null hypothesis and do, indeed, find evidence that the rate of change in the two genders’ slopes is different.  Namely, the women’s slope appears to have changed more than did the men’s slope.  We now discuss the aforementioned results in more detail.

DISCUSSION

The results from the previous section provide several interesting implications for the future of marathoning.  The preceding findings are not only statistically important, but also have applications for coaches and athletes who want to understand how rapidly the competitive standard in elite marathoning is evolving.  To our knowledge, this is the first study to provide statistical evidence that advanced shoe technology is associated not only with immediate performance improvements, but also with an increased rate of elite performance progression over time.

In order to put these new results in context, however, it is important to recall a prior result.  Bjorkelo et al. (2) previously found that the widespread introduction of super shoes in 2017 resulted in an immediate increase in the number of sub-2:08 marathons run per year.  Specifically, they found two things:  (1) the introduction of super shoes was associated with an immediate increase in the number of sub-2:08 marathons by just over 23 per year and (2) after accounting for this shoe effect, there was a trend over time of an additional 2.56 sub-2:08 times per year.  Their data set, however, only included times through 2021.  Combining these results, we can look at number of sub-2:08 times per year as a linear function of time that took a one time jump in 2017. 

Our results extend this past work in a significant way.  Namely, we found that, in addition to this one time jump the number of fast (where, for purposes of this paper, we define fast as under 2:08 for men and under 2:26:50 for women) marathons, the number of fast marathons being added per year has also increased.  In other words, the number of fast marathon times per year can no longer be viewed as a simple linear function.  Rather, the number of fast times per year is a piecewise function of time, with the changepoint occurring in 2017.  At that time, the slope of the function changed.

Regarding the specifics of this change in slope, we find that in 2017, for men, the number of additional  sub-2:08 times per year increased from 2.595 to 14.395.  Similarly, for women, the number of additional sub-2:26:50 times per year increased from 3.58 to 25.79.  There are a few possible reasons for this increase.  One likely reason involves the possibility that training in these highly cushioned shoes allows runners to train at higher volume and/or intensity.  This ability to run hard sessions with less residual fatigue may allow marathoners to improve their times faster than before.  While a thorough discussion of marathon training methods is beyond the scope of this paper, we do mention an example.  First, Ruiz et al. (12) found that carbon plated marathon racing shoes allowed athletes to run faster later in hard track workouts.   Similarly, it would be reasonable to expect that these shoes might allow athletes to recover more quickly following the completion of hard workouts.  If this is true, it would allow marathoners to run more hard workouts during any given time period. 

In addition to the recovery effect noted above, it is possible that there might be a psychological effect influencing the increasing rate of fast marathon times being seen each year.  Pfister (10) found that a super shoe placebo effect might exist.  Specifically, they found that, given 2 structurally identical shoes, runners perceived a reduction in running effort when they were told the shoes were super shoes. 

Related to this is the potential for super shoes to have initiated a “Bannister effect” in marathon running.  The Bannister effect refers to the flood of sub-4:00 miles run in the immediate aftermath of Roger Bannister breaking that long revered barrier in 1954 (14).  It is possible that the physical effects of super shoes resulted in people running faster than before, which, in turn, led to people believing they could run faster than before.  If a 2:08 marathon is no longer seen as especially fast for an elite male marathoner, this belief may result in more elite athletes going after this as a realistic goal, thus increasing the pool of people who may run under 2:08.  It would seem reasonable for all of the aforementioned super shoe effects to hold for both men and women and, indeed, we found statistically significant evidence that the rate of increase in fast marathons did increase for both men and women.

Other possible explanations include that the “slope” and “intercept” considerations are being confounded by the effects of some early adopters and some later adopters. This is less likely for Olympic caliber athletes as those considered here.

Further, it seems that super shoe producers are continuing to innovate. Nike’s original super shoes were named “4%s,” a nod to the purported energy savings.  As time goes by and technologies improve, this 4% number may grow. 

Our next result of interest involves comparing the super shoe effect in men and women.  As seen in our results section, the rate of increase in women’s fast (2:26:50) marathon times was statistically significantly greater than the rate of increase in men’s fast (2:08) times.  This implies that, for some reason, super shoes may have a greater effect on women’s times than on men’s.  Minimal work has been done comparing men’s and women’s responses to super shoes, so the reasons behind the difference we detected are speculative.  One possible reason could be due to potential differences in male and female physiology and/or biomechanics.  A second reason could be related to the possibility that there may simply be more room for improvement in women’s marathoning than in men’s marathoning (perhaps due to later access).

While this study focuses on elite-level performances, the findings may also have implications for non-elite runners. As improvements in shoe technology continue to influence performance at the highest levels, similar results have been found for recreational runners (9). This could affect pacing strategies, training approaches, and goal setting for individuals whose objectives are things like setting personal best times or qualifying for the Boston Marathon.

As can be seen, maintaining one’s competitive status may increasingly depend not only on talent and training, but also on access to and the use of advanced footwear technology.

This research also provides interesting avenues for future research.  First, it would be valuable for more research to be done comparing the effect of carbon plated shoes on males versus females. Research comparing effects in both training, racing, and recovery would be valuable.  Second, a repeat of the study contained herein in several years would be of interest.  In particular, such a study could shed light on whether or not the change in slope we observed is permanent.  Finally, extending the work done in this paper to track races would be most useful.  The technology present in super shoes was, even more recently, introduced to spikes used for track races.  It would be interesting to see how similar the effects of these spikes are to the effects we found in the marathon shoes.

There are some limitations to the research presented here.  First, and most importantly, our sample sizes are relatively small.  This is unavoidable, however, since super shoes have only been widely available for 8 years as of the writing of this paper.  Additionally, we note that the results we found speak to the evolution of marathon racing as a whole, and do not offer predictions as to the effect of shoe technology on any given runner.  Finally, it is certainly possible that factors such as changes in prize structures and advances in training may have contributed to the observed changes over time.  That said, our inclusion of a time variable in each regression should account for incremental changes in performance over time.  By comparing the change in the time variable’s slope upon the introduction of super shoes, we attempt to isolate this major change as best as reasonably possible.

CONCLUSION 

In summary, we have found that the use of carbon plated shoe technology is significantly related to the rate of increase in the number of fast marathoners per year.  In addition to the immediate performance effect of super shoes, the number of additional fast times being added each year has increased significantly for both men and women since the introduction of these shoes in 2017.  In order to remain competitive in this environment, athletes are going to have to take advantage of every possible opportunity offered by equipment technology.  This increase in competitiveness appears to be even greater in women’s marathoning than in men’s marathon racing.  More broadly, these findings highlight how new technologies can alter the trajectory of performance progression in endurance sports.

APPLICATIONS IN SPORT

The results of this study have important implications for athletes, coaches, and sport governing bodies.  First, the ongoing benefit of super shoe technology provides one important additional reason for competitive runners – both elite and non-elite – to consider the use of super shoes.  As Paradisis et al. (9) showed, the lab effect of super shoes is quite significant, even among recreational competitors.  While elite athletes generally have their shoes paid for by sponsors, recreational athletes must consider the costs and benefits of these shoes.  With most super shoes costing at least $250, it is important to be aware of all of their benefits prior to making a purchasing decision.  For competitive runners, this implies that, despite their cost, not using super shoes may place them at a growing disadvantage as performance standards continue to improve.

Second, as noted earlier, a portion of the ongoing benefit of super shoes appears to be due to their ability to allow runners to perform more frequent high intensity training sessions.  Having empirically verified that this benefit is significant, athletes of all levels may now consider working with their coaches to modify past training regimens, due to the enhanced ability to recover that these shoes provide.  Coaches may therefore consider revisiting traditional recovery assumptions when developing training micro and macrocycles.  For example, coaches may consider modest increases in weekly training volume or intensity, while carefully monitoring recovery, in order to leverage the enhanced recovery capacity offered by super shoe technology.

Finally, there are applications for race directors and governing bodies.  The people in charge of determining qualifying times for events such as the Olympics, Olympic Trials, and Boston Marathon often determine these standards years in advance with a rough idea of the field size they desire.  Since we have now shown, and quantified, that the rate of increase in the number of fast times has increased, it may be useful to consider this information when setting qualifying standards, in order to optimize the number of competitors in a marathon.  Failure to account for these trends may result in the use of qualifying standards that no longer reflect the intended level of selectivity.