Defining the wall: pace slowing in marathon runners

03 Nov 2015


To “hit the wall” (HTW) is a commonly described phenomenon among marathon runners that lacks a strict definition in terms of performance effects. Split times from 5000 finishers of the 2010 Boston Marathon were analyzed for a signal that individuals had “hit the wall.” Demonstrated variation in runner paces over the course of the race, as well as effects of changing course elevation, were taken into account using quantile-normalized changes in split times. Runners that slowed their pace relative to other runners in that segment of the race by two of ten quantiles were operationally defined as having HTW. By this metric, 17% of runners HTW, which is lower than previously reported values. This analysis attempts to provide precision to the definition of having HTW that may facilitate understanding of this common event.


Marathons are an athletic event that has been growing in popularity in America in recent decades. In 2014 alone, over a half-million runners completed the 26.2 mile race (Running USA, 2014). While the total number of runners has been growing, the average time to finish has also been rising, suggesting that the change in popularity may be more from amateur runners than elites. Such recreational runners have been suggested as especially susceptible to physical and psychological difficulties during a marathon, as might be expected, and particularly the phenomenon of having “Hit the wall” (Morgan, 1978).

The phrase that one has “Hit the wall” is a euphemism that describes a point in the race marked by pace-slowing and a feeling of discouragement (Morgan and Pollock, 1977). Roughly 50% of amateur participants report having HTW, while some elite athletes have argued that its existence is a myth (Stevinson and Biddle, 1998). Despite these disparate viewpoints, several studies have used post-race survey data to examine the frequency and risk factors associated with having HTW, as well as its psychological impacts (Buman et al., 2008a, 2008b; Stevinson and Biddle, 1998).

Several common features emerge from post-race surveys regarding runners’ experiences of either hitting or not hitting the wall. Buman and colleagues broke these features into the effect categories Physiological, Motivational, Cognitive and Affective. The most common responses regarded Physiological and Behavioral effects, including leg-specific and general fatigue, and slowed pace. The most common Motivational effects were the desire to stop or sit down, which agreed with the Cognitive effects described as “engaging in a mental battle” and the most common Affective effect of discouragement (Buman et al., 2008b).

Moreover, survey responses have been used to identify factors associated with and protective of post-race reporting of HTW (Buman et al., 2009). Notably, being female and having completed at least one training run of greater than 20 miles protected against reporting HTW. The training distance correlated with the most common time to hit the wall, which was found to increase in likelihood until mile 21 and then drop. This is in agreement with other surveys where >70% of racers reported HTW after mile 19 (Stevinson and Biddle, 1998).

Both the reported experiences and the mileage characteristics are in rough agreement with the reported physiological mechanism behind HTW: a depletion of glycogen stores and a shift to ketogenic metabolism (Rapoport, 2010; Stevinson and Biddle, 1998). Other sports report similar effects by the same mechanism (e.g. “bonking” in cycling) though the time in a race is not as clearly defined. While this implies that there is a diagnostic marker for HTW, namely low blood glucose, such a measurement has not been associated with reports of HTW by marathon runners. Such a measurement would prove useful in distinguishing between the commonness of amateur athletes’ reports of HTW and the elite athletes’ argument that it is a myth. Arguing against this strict blood glucose definition is the finding that expecting to hit the wall increases the likelihood of its occurrence (Buman et al., 2008a).

The effect of expectation implies that the mental state of the individual plays at least some role in the likelihood of HTW. While it is possible that the expectation is just an accurate prediction (i.e. a person is able to correctly estimate their blood glucose while running) it is also possible that this is a bias of the methods used to report these effects. Specifically, it may be that those who expect to HTW are more likely to report HTW in post-race surveys, irrespective of their performance. Lacking from the current literature is a quantitative definition of HTW that is based on performance metrics rather than survey data. Specifically, one could target the most commonly reported effect in the Buman et al survey: slowed pace. For this one would need more data on runners’ pacing than strictly finishing times, as has been used to estimate the effects of HTW to date. Such pacing information is increasingly common; marathons will often report splits at regular intervals. In the case of the Boston Marathon, runners’ times are recorded every 5 km, as well as at 13.1 miles. These times may show signatures could be used to generate an operational definition for HTW, which would lead to a better understanding of its likelihood of occurrence, associated risk factors, and methods to prevent it.

The present study uses a subset of the data from the 2010 Boston Marathon to predict runners that HTW. Split data are used to determine characteristics consistent with published survey reports, namely slowing. A definition of HTW is proposed and used to compare cohorts that HTW and did not.



Data from 5000 participants in the 2010 Boston Marathon were obtained from Hammerling et al (Hammerling et al., 2014). Times were collected for each runner through the mandatory wearing a timing chip associated with each bib number. The chip recorded times as runners crossed over a timing mat at the start line, each 5 km interval, the 13.1 mile mark, and the finish line. Timing began as runners crossed over a timing mat at the start of the race, rather than at a fixed time (i.e. net time rather than gun time). These 5000 participants were randomly subsampled from the larger dataset.

All of these runners completed the race, and no information was available for whether runners qualified for the race or participated as a fundraising member of a charity. Two of the runners were excluded from the analysis by having final split times >5 standard deviations outside the mean (bib numbers 21716 and 15410).


Scaling and Normalization

Times are reported as per segment, which is 5 km for most sections and 2.2 km from the 40 km mark to the finish line. Split times were modified to “per km” by dividing by the distance in each segment (i.e. 5 for every split except the last, which was divided by 2.2).

Linear Regression

Linear models to predict finishing times were calculated using least squares fitting methods in R using standard formulation:

Equation 1. Least squares fitting for linear regression


Where y is the finish time for each runner i, each x is a parameter including split times, age and gender, is the coefficient for parameter and is the error. The overall model was evaluated using ANOVA implemented in R, and the model parameters were evaluated by both Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) with forward, backward and stepwise parameter changes.

Quantile Normalizaiton

The change in split times per km were calculated as follows:

Equation 2. Normalized changes in split times.


Where z is the per km split time for each split i, and z1 is the split per km over the first 5 km. In order to determine how the normalized per km change in pace related to other runners for that distance segment, the normalized per km paces were assigned to quantiles associated with probabilities at 10% intervals (i.e. 10%, 20%, …, 100%).

Chi-Squared Test

Enrichment in the number of males that matched the criterion for HTW against those that did not match the HTW criterion was determined using a Pearson’s Chi-squared test with Yates’s continuity correction, implemented in R.


A subset of the finishers of the 2010 Boston Marathon were analyzed to identify a signal for HTW. Of the 4998 runners in the dataset were 41.6% female, which is similar to the overall median in the United States for 2010 (41%) (Running USA, 2014). The median age of runners was 42, which is slightly higher than the US median (37) (Table 1). The median finishing time of 3:44:06 is faster than any US marathon with greater than 1000 participants, as is typical for Boston (Running USA, 2014). By contrast, the Walt Disney World marathon in Orlando, FL, has a median finish time of over 5 hours. This is likely due to the qualification requirement for non-charity participants. This is a potentially confounding factor in the analysis, as previous studies have suggested that runners that perform better are less likely to report having HTW (Stevinson and Biddle, 1998). The percent of runners with an observed signal as having HTW may be less than the self-reported values of roughly 50% (Buman et al., 2009).

Table 1. Summary of the data

Runners Gender   Age   Finishing times (H:M:S)   Overall Pace Changes from First 5K    
4998 2079 F Min 19 Min 2:11:48 Min 30% faster
  2919 M Median 42 Median 3:44:06 Median 11.30% slower
      Max 77 Max 7:17:46 Max 134% slower

As the phenomenon of having HTW is described as a marked slowing of pace, one would expect that an individual would slow relative to other runners that have not HTW. This is complicated by the large differences in paces of different runners, where the per km split time for the first 5K varies from under 3 minutes to nearly 10 minutes (Figure 1, left). Normalizing to the first 5K segment shows that the majority of runners slow relative to their initial pace (Figure 1, right). The pace per kilometer increased on average over the course of the race, with a median increase in pace of 11.3% (Table 1). However, one runner’s pace decreased on average 30% from the first 5K, and another slowed by over 130%. The signal that a runner has HTW must take into account behavior outside the variation in the data.

Fig 1. Pace per kilometer for each distance segment.


Similarly, the pace changes that may be signals of a runner having HTW must take into account features of the course. The Boston Marathon is atypical in that it is a linear course, rather than a loop or series of loops, which allows for it to have a net loss in elevation of nearly 500 feet (Figure 2). However, there are also a series of elevation gains from 25-35 km, culminating in “Heartbreak Hill” at approximately 33 km, where runners typically slow. This is followed by a relatively steep descent until approximately 40 km, where runners typically speed up, followed by a flat finish. This can be observed in the normalized per km split times, as a noticeable decrease in pace is seen for many runners the last segment of the race, despite overall slowing for the previous segments (Figure 1, left). The signal for having HTW must therefore take into account the variation imposed by the course profile.

Figure 2. Elevation profile for the Boston Marathon. Distances and elevations obtained from


Stratifying the changes in pace by gender shows that males typically slow more than females from their first 5K pace, though this difference was not significant (Chi-squared, p-value = 0.4945). While previous studies have shown that females are less likely to report having HTW than males, such a signal of slowing is not observed in the overall dataset. Similarly, there was a trend to slow with increasing age, though neither was this difference significant (Chi-squared, p-value = 0.3525). Previous studies have shown no effect of age on having reported as HTW, and no effect is observed on the overall signal here.

A linear regression model was used to determine which split times, as well as the predictors age and gender, would significantly correlate with finish times. In terms of the signal for having HTW, one could imagine particular splits as being more or less critical to the outcome of a race, and therefore more likely to be a split at which a runner would HTW. Regressing finishing times with all split times as well as gender and age showed that all of the predictor variables were significant except the split time from 35-40 km. An ANOVA showed all variables to be significant, including the 35-40 km split. Variable selection by AIC and BIC selected all of the predictor variables by AIC, and excluding only the 35-40 km split time by BIC. While these analyses suggest that the signal for having HTW may not occur during the 35-40 km split, it is important to note that several studies have demonstrated no difference between the median finishing times of racers that report having HTW and not (Buman et al., 2008a, 2009). An alternative method was therefore employed to identify runners that HTW without using finishing times.

In order to identify whether a runner slowed relative to other participants at that segment of the race given the course profile, an analysis of changing quantiles was performed. First, the per km split times that had been normalized to each runner’s split over the first 5 km were used to calculate the change in normalized split time (Equation 2). Quantiles were assigned to these values, with each quantile accounting for 10% of the data points. Runners that had a positive change in quantile during the second half of the race were as having HTW by that threshold (Figure 3). Nearly 3000 runners changed quantiles by 1 or more during the second half of the Boston Marathon, i.e the runner slowed more than other runners during that segment. Fewer runners, 870, had a quantile change of two during the second half of the marathon; that is, the runners slowed significantly relative to other runners at that part of the course, such that their change in pace jumped two quantiles. Only 302 runners had a quantile change of three or more during the second half of the race. Interestingly, two runners had a quantile change of nine during the second half of the race, i.e their paces went from being in the first quantile to the last; such an extreme change is likely beyond one that has HTW and more likely identifies injuries.

Fig 3. Pace Changes stratified by gender and age.


Identifying the correct threshold as those who HTW using only split data requires relying on published values for the expected prevalence of having HTW during a marathon. As described previously, the typical percent of survey respondents reporting that they had HTW is approximately 50%, though none of the surveys were conducted on participants in the Boston Marathon and the qualification requirement for Boston may reduce the percent that HTW. A threshold value of one quantile change during the second half of the race would identify 59% of the runners as having HTW, which would be higher than reported values (Fig 4). A threshold of two includes 870 runners, 17% of the field. While this is lower than reported values, such a difference may be possible for this marathon, as well as for the potential differences between self-reported post-race survey data and empirical times. Therefore, a threshold of two quantiles change in normalized per km pace was selected as the metric to identify those that HTW.

Fig 4. The number of runners that experience positive quantile changes in normalized per kilometer split times during the second half of the race.


The cohort of runners that have the defined signature of having HTW have the same median age as the total group, as well as those that were not identified as having HTW (Table 2). The median finish times for those that HTW were slightly faster than those who did not HTW, though this difference was not significant (Chi-squared, p-value = 0.8777). Both of these findings are consistent with previously reported values (Buman et al., 2009). Strikingly, the percent female in the cohort that hit the wall is nearly half that of the group that did not hit the wall, which is highly significant (Chi-squared, p-value < 2.2e-16). While this result is consistent with previous reports that being female is protective against having HTW, the difference is larger than previously reported values (Buman et al., 2008a).

Table 2. Runners stratified by hitting the wall.

  Total Number Female Number Male Percent Female Median Age Median Finish Times (H:M:S)
All Participants 4998 2079 2919 41.6 42 3:44:06
Hit Wall 870 203 667 23.3 42 3:40:42
Did Not Hit Wall 4128 1876 2252 45.4 42 3:45:00


While many runners describe having “hit the wall” the term is used to convey a wide variety of emotions and physiological effects. Surveys of runners report pace slowing, however no differences in the median finish times have been found, and some groups of runners have even called HTW a myth. Understanding whether or not it occurs and its effects requires more precise measurement of individual runners as they progress through a marathon. Presented here is a suggested operational definition of HTW: those that slow their pace by two or more quantiles (of 10) during the second half of a marathon.

This definition performs similarly to previous reports in that the median finish times between those that HTW and did not are not significantly different, nor are the median ages. The percent of females in the cohort that HTW is significantly different than the percent of females in the cohort that did not HTW, as has been reported previously. However, the percent of runners that HTW is lower than previously reported values (17% vs ~50%). While this difference may be due to the race on which this definition was created, it may also be due to a propensity of runners to report having HTW without having experienced the pace slowing that is one of the key characteristics of having HTW (Buman et al., 2008a). These methods could be applied to the results from marathons with more novice runners to determine if the percent of participants that HTW is more consistent with survey results.

Limitations of this study include not having self-reported information about whether individuals HTW, which prevents direct comparison with previously published results. In addition, using quantile normalization as a metric for determining slowing outside the typical amount may miss runners that slow more gradually or those that change pace near the boundary of a 5 K timing zone, such that their slowing is averaged over two segments. More precise pacing information would be useful to clarify this issue. Moreover, a change in pace may not effectively report on those that HTW; if the definition of having HTW is a shift to ketogenic metabolism than a definition for those that HTW during a race should include a blood glucose measurement.

Such, publicly available performance metrics are becoming more commonly available to researchers. Increasingly, amateur athletes track their races on phones or specialized watches and upload their performance data to publicly available websites. One such website, Strava, shows the race profiles of just 5 individuals that completed the Boston Marathon in 2010, however, for the 2015 race that number is nearly 2000 individuals. Included is continuous pace data and in many cases heart rate information. Wearable continuous glucose monitors are also being used by some athletes (Thomas et al., 2015); such data may provide the resolution to fully define HTW in terms of quantifiable metrics.


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