# Racing, Pacing, and Hitting-the-Wall

## A Data Analysis of the 2017 Virgin Money London Marathon

### TLDR;

- A data analysis of 39,349 race records from the 2017 Virgin Money London Marathon.
- We look at participation and performance as well as pacing and hitting the wall, comparing runners by gender, age, and ability.

### Introduction

Yesterday saw the completion of the 37th London Marathon, since the event was first held in 1981. This year the race was won by Daniel Wanjiru and Mary Keitany of Kenya in 02:05:48 and 02:17:01, respectively, and by wheelchair athletes, David Weir (Great Britain) and Manuela Schar (Switzerland) in 01:31:06 and 01:39:5 7, respectively.

It was the usual fantastic spectical of human endeavour and enthusiastic crowd-support. The thrills and spills came in all shapes and sizes as almost 40,000 runners particpated in one of the largest mass-participation sporting events in the world.

In this article we will describe an initial data analysis of the race itself. For this we will focus on *non-elite* runners only; for convenience we will often refer to these as *recreational runners*, meaning no disrespect to the many very talented and serious club runners that this includes.

The Virgin Money London Marathon results site, as of late last night, included race records for 39,349 runners, 23,881 men and 15,468 women, and in what follows we will look at how these runners participated on the day: who they are and where they come from; their finish-times and pacing; and whether they hit the dreaded wall. The data we use contains information of gender, age (or, rather, *age groups*), country of origin, finish-times, and, importantly, 5km split-times. Thus, each race record includes timing information from each of the 5km segments of the course, plus the final segment; that is, 0–5km, 5km-10km, …, 35km-40km, 40km-42.2km.

### Participation & Participants

Let’s start by looking at the participants themselves. The field of recreational runners was made up of 60% male and 40% female runners (the bar-graph below) with an average age of approximately 38 years-old for men and 36 years-old for women (the line-graph below). Note these ages are *estimates* only, because the London Marathon data only provides age ranges for its athletes (typically in 5-year blocks) rather than exact ages; in this analysis we estimate a runner’s age based on the mid-point of their age group range.

In the graph below, which shows the percentage of male and female runners by age group, we can see below that most of these runners, more than 55% of males and almost 50% of females, fall into the youngest age group (18–39) and after that there is a gradual decline in the percentage of runners from increasingly senior age groups. It is interesting to note that while men tend to dominate the youngest age group, proportionally more women participate in the older groups, when compared to men.

In total participants ran from 111 different countries, from the Åland Islands (which apparently belong to Finland) to Zimbabwe, and with more than 34,000 local runners from Great Britain. The graph below shows the total number of runners from all countries with more than 50 participants, excluding Great Britain. The USA leads the way, followed by France, Italy, and Ireland.

When we normalise by population we can see that Ireland sends more runners per capita to the London Marathon than any other country, with Norway and Switzerland as distant runners-up.

What about finish-times I hear you ask? Well the graph below shows the average finish-time by country, computed across *all* participants from that country, and the average fastest finish-time by country, computed based on the *top-10 *finishers from that country. We can see that Great Britain and Ireland win out in terms of the finish-times of the top-10 fastest runners, with Great Britain’s fastest (recreational) runners averaging 138 minutes to Ireland’s 156 minutes. Poland and Spain (ESP) win in terms of the average finish-time of *all* their runners with 222 and 227 minutes respectively; incidentally, it’s 272 and 242 minutes for Great Britain and Ireland, respectively, when we include *all* their runners.

### Finish-Times, Gender, and Age

Let’s dig a little deeper into finish-times and the relationship with gender and age. The average finish-time for men is 256 minutes, compared to 290 minutes for women, and we can see in the graph below, which shows the relative proportion of male and female finishers for different finish-times, how there are more men than women finishing up to the 260 minute mark. After that female finishers are more common.

#### Finish-Times & Age

We can also get a sense as to how finish-times vary with age; once again bear in mind that these are age *estimates* rather than *precise* ages. The graph below shows the average finish-time for runners across the different ages. The fastest times are registered for those runners, male and female, in their 40s, but from then on we start to slow.

#### Closing the Gender Gap

Interestingly the gap between male and female finish-times tends to close with age. For example, the difference in finish-times between men and women in their 40s is about 15% (approximately 250 minutes for men versus 290 minutes for women) but for runners in their 60s this gap has closed to only 30 minutes (about 8%).

We can see this more clearly in the graph below, which plots this percentage difference in finish-times between men and women for different ages. In fact the graph shows the gender gap, as calculated across all runners, and also the gender gap calculated across the *top-10* fastest male and female finishers for each age group. As mentioned above the gender gap reduces with age for *all* runners but not so for the top-10 runners, where the gender gap is seen to widen with age. It seems that, as we age, men and women perform more similarly in general, but the very fastest men tend to buck this trend and gain more time on their fastest female counterparts.

### Pacing & Pace Variation

How do runners pace London? We have looked at this before using historical data from the last few London Marathons. What about the pacing in 2017? The graph below shows the pacing (mins/km) of average male and female runner as well as the pacing for the top-100 (non-elite) finishers, for each of the 5km segments of the race; remember, the segment labeled 5km denotes the start segment from 0–5km, and so on.

The key message here is that on average runners tend to start fast and gradually slow towards the finish-line. The pacing of the average runners slows quite considerably as the race progresses: men starting a little over 5 minutes per km gradually slow to just 7 mins a km by the end of the race. However, a key point is that these runners also include those who hit the dreaded wall — the marathon ‘*bonkers*’ — and these final paces are no doubt impacted by the significant slow down that is associated with hitting the wall (*HTW*).

#### Pacing & Bonking

To get a better sense of this we can separate out those runners who hit the wall; we will talk about how we determine whether a runner hits the wall later, for now it is sufficient to say that we look for runners who slow-down by more than 33% in the second half of the race. In the graph below we show the *pacing profile* of runners in the London Marathon; rather than *actual* pacing values in mins/km we show *percentage* pacing values, by calculating the percentage pace of a runner in a given segment as a percentage of their average race pace. We do this so that we can directly compare the relative paces of runners of different ability levels.

The graph shows this percentage pacing for the fastest (top-100) recreational runners, as above, as well as the all recreational runners who *do not* hit the wall, and separately the pacing profile for those runners who *do* it the wall (HTW). We can see how, on average, the fastest runners enjoy the most even pacing profiles: they start about 5% faster than their average race pace and finish about 5% slower. Well-paced recreational runners — those who avoid the wall — start slightly faster (about 7–8% faster than their average race pace) and finish slower (about 8–9% slower than average race pace), and those who bonk present with a very uneven profile. They tend to start more than 15% faster than their average race pace and finish up to 25% slower.

We will return the issue of hitting the wall later, now that we have a sense of how it impacts on pacing.

#### Pace Variation by Ability & Age

Another approach to understanding pacing is to look at the *pace variation of *runners. That is, rather than look at actual, or percentage paces, across individual race segments, we can compute an *overall* pace variation value for a runner, which reflects how much their pace varied during the course of the race. A *high* pace variation value means that the runner changed their pace a lot during the race. A *low* value means they ran a more evenly paced race. The conventional wisdon is that *even pacing* is a sign of a more disciplined runner, and so evaluating pace variation in this way can help us to understand how well a runner ran their race, in a finish-time independent manner. As an aside, to measure pace variation we use a metric called the *coefficient of variation*, which is essentially a normalised standard deviation of pacing.

The graphs below show the average pace variation for male and female runners, based on their finish-times and ages. In each case we separate out those who hit the wall (dash lines) from those who do not. In terms of the relationship between pace variation and finish-time (as a proxy for *ability*) we can see how faster runners enjoy less pace variation (more even races) than slower runners; as finish-times increase so do pace variation values regardless of gender or whether the runners hit the wall. Moreover, women tend to enjoy less pace variation than men, an observation that has been made before, especially when it comes to hitting the wall. This suggests that women run more disciplined races than men, and when they hit the wall they are less adversely affected than men, at least in terms of the impact on their pacing.

Based on the results below, age has much less of an impact on pace variation. The youngest runners have marginally higher pace variation values than those in the 40s and older. And the distinction between men and women is no longer material. In other words, men and women of the same age tend to present with the same pace variation, but when they have the same finish-times men tend to present with more varied pacing than women. The latter is deserving of further study and may, in part, be explained by physiological differences between the genders that contribute to their very different finish-times.

So far we have seen how runners tend to pace their races, on average running positive splits, starting faster and finishing slower. For example, overall London runners registered a +15% positive-split — they ran the second half of the race 15% slower than the first — with those who avoided the wall managing a more even, but still positive, split of +10%.

### Hitting the Wall

Next, let’s look at those poor souls who hit the wall. Hitting the wall (or bonking) refers to the sudden onset of debilitating fatigue, and a near-complete loss of energy, which can occur during the second-half of the marathon, typically around the 20mile/30km mark. At best, it temporarily slows even the swiftest of runners, and, at worst, reduces them to a shuffling gait for the remainder of the race. The conventional wisdom is that the condition is caused by the depletion of glycogen stores in the liver and muscles, typically as a result of poor race nutrition or excessive pace, or both; the course profile and weather conditions also play an important role.

#### Recognising a Bonk

How can we tell if someone hits the wall? For the purpose of this analysis we deem a runner to have hit the wall if their pace slows by at least 33% during any of the segments in the second half of the race (the 25k, 30k, 35k, 40k, and final segments). But 33% relative to what? We need a *baseline *pace. The obvious answer is to use the pace of the first-half of the race. That’s not a bad approach, but it is not ideal to include the opening 5k of the race, because it is well known that many runners pace themselves erratically during the opening few miles; most runners start too fast, which will impact the pace of the first-half of the race, if we include the start segment. So, in this study we *exclude* the first segment from our baseline pace. Thus, our definition of hitting the wall is as follows:

A runner is deemed to havehit the wall, orbonked, if their pace, duringat least one second-half segmentof the race, slows by atleast 33%relative to their average pace during the first-half of the race, excluding the opening 5km segment.

Based on this definition, just over 21% of all runners in London this year hit the wall; more than 26% of men, but only 13% of women.

#### Where we Bonk

The graph below shows the percentage of men and women who hit the wall in each of the second-half segments of this year’s London Marathon. For example, only about 2–3% slow by more than 33% in the 25k segment (20km-25km); that’s not so surprising since the conventional wisdom says that most people who hit the wall do so around the 20 mile (30km) mark. Sure enough, as the race proceeds, the percentage of runners slowing by at least 33% steadily grows, at least up until the final segment when some runners manage to recover their pace for a faster finish. For males, the 40k segment attracts the highest percentage of bonkers (over 20%); for females the 35k and 40k segments see about 7% of runners hitting the wall.

The most striking initial conclusion, is the extent to which male runners tend to hit the wall so much more frequently than female runners. For instance, during the penultimate 40k segment (35km — 40km), there are over 3-times as many men hitting the wall than women. Ouch!

#### Bonking, Ability, and Age

Does whether we hit the wall depend on our ability (finish-time) or our age? The graph below shows the percentage of male and female runners hitting the wall based on various finish-times. There is a steady increase in the percentage of people hitting the wall as finish-times increase. A similar effect is seen for both men and women, but once again male bonkers greatly out-number female bonkers, this time for any given finish-time. For example, over 40% of men crossing the line at the 5-hour mark (300 minutes) are deemed to have bonked. For women, with the same finish-time, less than 20% hit the wall.

Bear in mind that these finish-times *include* the fact that these runners have significantly slowed during a portion of the race and so, presumably, they do not reflect their *true* ability; if they had managed to avoid hitting the wall then presumably they would have finished faster, but right now we cannot say how much faster; some of these runners will have hit the wall sooner, slowed by more, and for longer, than others.

The good news for us older runners is that we are less likely to hit the wall (in London at least). The graph below estimates the rate at which male and female runners hit the wall across the different age groups. The youngest runners hit the wall more often than older runners, and the best time to run, if you want to avoid the wall, is around about the 50 years-old mark, for men and women.

Now we should say that this is likely influenced by race experience too: older runners will have run more marathons than younger runners. We don’t have this information in this study, and so the precise relationship between hitting the wall, age, and experience will remain as a matter for future work. It is worth pointing out, however, that for older men (>50) the bonk rate seems to rise again, and for older women (>50) it stays reasonably level. This might suggest that experience does not play such as significant role in the end.

#### Fast-Starts & Bonking

There is one final factor to consider in all of this talk about bonking and hitting the wall: the *start-pace* of a runner. Starting too fast has long been considered as a recipe for disaster in the marathon, and one of of the dangers is that it increases the likelihood of hitting the wall. The graph below considers this by comparing the percentage of male and female runners hitting the wall to their *percentage start-pace. *This percentage start-pace is defined as the pace during the opening 5km of the race *relative* to the pace during the remainder of the first-half of the race. Thus, a percentage start-pace of 90% means the runner starts 10% *faster* than their average pace for the remainder of the first-half of the race. A percentage start-pace of 110% means they start 10% *slower*.

We can see clearly that runners who start fast are much more likely to hit the wall, compared to those starting more conservatively. For example, over 50% of men with a percentage start-pace of 80% (that is, men starting 20% faster) go on to hit the wall, compared to only 25% of men who start at their average first-half pace (a percentage start-pace of 100%). And men who start slower than their average first-half pace (percentage start-pace > 100%) are even less likely to hit the wall; although the rate tends to rise again for very slow starter. It is the same pattern for women, although the actual likelihood of hitting the wall is much less than for men, as expected, at every percentage start-pace.

### Conclusions

That’s the London Marathon done and dusted for another year. In this article we have taken a whistle-stop tour of some of the key statistics arising out of the event, in order to understand how gender, age, and ability influence participation, performance, pacing, and hitting the wall. Our key finding include:

- London enjoys a wide field of runners at all levels of ability and from more than 100 countries. It continues to be dominated by male runners (60%) and younger runners (approx. 50% < 40 years-old).
- On average men are faster than women, but the gender gap closes for older runners.
- Not unexpectedly, the average runner completes the flat-ish London course with a positive split. On average, runners start faster than their average pace and finish slower.
- While men may be faster than women, they are not as disciplined: women enjoy more even pacing than men and they hit the wall far less often.
- Whether a runner hits the wall is linked to their finish-time and their age. Faster runners tend to avoid the wall, as do older runners, to a point.
- And how fast runners start their race has a significant impact on whether they are likely to hit the wall: the faster the start, the greater the chance of bonking.

If you like this article you can find many more looking at the data of marathon running in Running with Data including the following on the London Marathon and others.

- Perfect Pacing at the London Marathon
- Race Expectations: An Analysis of PBs at London
- Should I Run with a Pace Group
- Fast Starts = Slow Finishes

I’d love to hear your comments and please do share if you like what you read.