You finished your Spartan race. Congratulations! You checked your finishing time, and you posted your awesome fire jump picture on Facebook. As you start planning for your next race, you wonder: How did I do compared to everybody else? Should I sign up for an Elite or Competitive wave next time? Does that twenty-year-old kid have an advantage over me? Is there a significant difference in performance between age groups? How fast do I need to be on a single lap Beast to complete an Ultra Beast?

To answer these and some more questions for myself, I decided to take a deeper look at the finishing results of the Spartan Vermont Beast, Ultra Beast, and Sprint weekend in September 2017 as published on the Spartan website. Read on, and learn how the data tells you if you’re ready for your next Spartan challenge. You will see that the cold facts show that your age and gender have little influence on your results. And as we zoom in on the small group of die-hard multiple-laps runners, you will be astounded by some real badassery.

Before we get going: this post is kinda geeky. I could not resist to occasionally add some statistical gibberish into the text. Don’t get intimidated and feel free to skip those passages. You won’t miss anything…

# Overall Stats

Let’s start by looking at some overall numbers. A total of 8011 racers finished on the slopes of the beautiful mountains of Killington, Vermont. Below is a break down by type of race and gender.

The first side note to make here is that these numbers represent only participants who actually finished their race. Information about the total number of racers who started is not publicly available. As we will see later, it is likely that the number of DNF Beast and Sprint racers is small. However, this number is significant for the Ultra Beast.

Unconfirmed information (aka rumor from Facebook) is that slightly over 1,000 racers started the Ultra Beast in Killington this year, which results in an estimated completion ratio of around 49%. Compared to previous years, where ratios in the 20-30% range have been reported, this is a high number. Is this because the course was easier or were the runners better prepared? It’s not easy to give a definite answer. One clue is that the course this year may have been up to two miles shorter than in 2016, which at a pace of ~30 min/mile, results in a full hour more to go. An hour that many racers would not have had–as we will see later.

With 5459 male and 2552 female runners, the number of men is roughly twice as large. That said, if we look at the percentage M/F per race category, there is some significant variation. There’s a nice 50/50-ish distribution for the Open Sprint, while the women are clearly under-represented in the Ultra Beast. Ladies: I’ll show later on that on average the men hardly perform better than the women, so if you are considering joining an Ultra–go for it!

In fact, the table below shows the average finishing time per race group. Even though it would seem that the men have a natural advantage, it is clear from these stats that overall the difference between the two sexes is small. Taking the biggest group, i.e. the Open Beast on both days, which represents more than half of all participants this weekend, with an average time of 8h37 the women finished around 37 min after the men, which is only 7% slower. Just saying.

F | M | |
---|---|---|

Sat Beast Comp | 07h40m47s | 06h59m17s |

Sat Beast Elite | 06h14m42s | 05h19m46s |

Sat Beast Open | 08h33m45s | 07h57m54s |

Sat UB Comp | 13h49m12s | 12h36m36s |

Sat UB Elite | 12h38m32s | 12h15m11s |

Sat UB Open | 13h19m47s | 12h56m29s |

Sun Beast Comp | 07h37m15s | 06h44m25s |

Sun Beast Open | 08h48m54s | 08h06m17s |

Sun Sprint Comp | 02h25m55s | 02h09m03s |

Sun Sprint Elite | 01h55m34s | 01h35m29s |

Sun Sprint Open | 03h12m60s | 02h52m48s |

# Saturday and Sunday Beast

Let’s break down the race results for the Beast on both days. In the figures below you’ll see a scatter plot of finishing time versus age, for male and female runners separately. Each dot represents one runner, and the colors of the dot differs depending on whether the runner was in the Elite, Competitive or Open waves.

Some interesting conclusions can be drawn from these figures. To start, we can see from these graphs that the relationship between age and finishing time is very weak. To highlight this, a straight line is added to the scatter plots that best describes the trend (in statistical mumble jumble: this is the linear regression model representing the data, with the shaded area representing the 95% confidence interval of that regression). For most waves there is a slight connection between age and finishing time, but the magnitude of this is in the order of minutes. In other words, you’re never too old to do a Spartan race, and even runners of fifty-and-over can be fierce competition for the young folks in their twenties. The oldest male runner was 67 and the oldest female runner 66! Particularly noteworthy also is that the data shows that the elite women seem to get faster as they get older.

These lines are obviously highlighting the average trends. When we only look at the top performers in the male elite wave on Saturday the picture looks different. Here the faster runners are in their late twenties, and the finishing time of the fastest runner for each age group after that steadily increases.

Also remarkable from these point clouds is the significant overlap of the Elite, Open and Open wave runners. The histograms below, which count the number of runners finishing within successive intervals, visualize this.

The far majority of all runners finished in a time between six and ten hours. The group of runners that completed in under five hours is predominantly in the Elite waves. On the other hand, these plots confirm the significant overlap between the distribution of the Elite, Competitive and Open Waves finishing times.

What should be the conclusion from this? It’s hard to tell based on this analysis alone. Is it possible that a runner in a Competitive wave ran faster than he or she would have done in an Open wave? Perhaps, but if you’re on a budget and not aiming for a podium place or place in the world ranking, don’t waste your money. This analysis shows that running in an Open wave does not give you a significant disadvantage.

The last observation is that the histograms are pretty symmetrical, and have the shape of a ‘Bell’. This means that roughly as many runners are faster than the average time as the number that are slower (more statistical blah blah: the distributions are approximately normal, having a median value that is similar to the average value). If the DNF count due to runners not meeting the time cut-off would be high, the distribution would look more skewed to the right. There have been Spartans who started in one of the last waves and did not make it to the cut-off in time, but for the majority there was sufficient time to make it to the finish. Stated otherwise: the Beast participants were well prepared for their challenge. This says something about this group of athletes, as we all know the Killington Beast is no joke.

# Saturday Ultra Beast

We’ll move on to the Ultra Beast and start by plotting the same point clouds for the Elite, Competitive and Open wave racers.

The first striking observation is that the clouds for the three categories are overlapping almost entirely. As expected, the fastest runners are in the Elite waves both for the male and female runners. The separation of the best performing Ultra Beasters and the rest of the gang is down right impressive, with over four hours of difference between the fastest runners and the average.

The spread in Elite times is significantly larger compared to the Open wave racers as well. The most logical explanation for this is that the Elites start earlier than the Open wave runners, but all are facing the same cut-off times, meaning that the Elite runners simply have more time to complete the race.

These graphs show again that on average the men tend to get a bit slower as they get older, while the women seem to get faster (geeking out: For the men the regression model shows a slight positive correlation between age and finishing time. For the women, this correlation is negative. However, the 95% confidence interval of the linear fit for the women is large due to relative small number of racers. Therefore it is entirely possible that correlation as depicted is an artifact of the data and that the real correlation is positive).

Looking at the histogram of finishing time for both sexes, shown below, we clearly see the effect of the time cut-offs. The distributions are highly skewed with a sudden drop-off in the number of racers after roughly fourteen hours. Knowing that the DNF percentage is around 50%, we can hypothesize that the distribution below represents the left half of the total population. This means that if there was no time cut-off, the Ultra Beast distribution would have a distribution with its maximum at around fourteen hours and the majority of finishers between ten and eighteen hours. This comes to five to nine hours per lap. That’s a large spread.

The Spartans with an average single lap time of five to seven hours got their buckle. I did not calculate the ratio between the first and second lap time, but my best guess is that most Ultra Beasters need about 20-40% more time for their second lap. My recommendation, based on the data I analyzed: if you want to set yourself up for success and finish the Ultra Beast within fourteen hours, make sure you can do a single lap in Vermont in about six hours and sign up in the Elite wave to give yourself some extra time. Among all waves there were 747 racers out of the 5867 Beast racers on both days who completed within six hours. This means that completing within six hours equates to finishing in the top 13%.

I already mentioned the impact of a mile shorter course compared to last year on the DNF percentage. From this histogram it can be concluded that if everybody had one hour more to run, the DNF percentage would drop significantly. This would be equivalent at putting a virtual time cut-off one hour earlier, meaning that the cut-off we see at the fourteen hour mark would shift to around thirteen hours. This would reduce the number of finishers by roughly 175-225, dropping the DNF percentage to 27.5-32.5%, which get us close to last year’s percentage.

One last observation about this histogram. The distributions for the male and female runners are highly similar in shape. If there had been more women, it is likely that the two distributions would completely overlap, which is another way of saying that the advantage of the men over the women would be negligible (this is assuming that the percentage of men and women who finished is the same, which is reasonable but difficult to prove without stats on the number of UB’ers that started the race). Let this be another encouragement for the women Spartans to sign up for the Ultra challenge.

# Sunday Sprint

The scatter plots for the Sprint look distinctively different from those from the Beast. The dots are more spread out and more ‘rectangular’, which indicates that in all age groups racers participated with varying levels of fitness. The overlap of the Elite and Competitive wave on the Open wave is also noticeably smaller.

This is also clear from the larger separation between the trend lines, which show that in the age group of 30-40 the Elites are almost twice as fast as the Open wave runners. This suggests that the overall level of fitness and preparedness between the Open and Elite wave runners is different than with the Beast. This is intuitively understood, knowing that the Sprint is the entry-level Spartan race.

The histograms of the finishing time of the Sprint show a pretty remarkable picture. In the case of the Beast we saw a ‘Bell’ shape like distribution. The Sprint distribution is more triangular in shape, peaking around two and half hours. What to conclude from this?

The width and shape of the distributions confirm indeed that the level of fitness of the Sprint participants varies much more than that of the Beast runners. The finishing times are up five times (!) as long as the fastest Spartans. The peak of the distributions (the so-called modal finishing time in statistics) is also lower than the average finishing times (see the table in the section ‘Overall stats’ above).

Did you run the Killington Sprint this year and do you want to know how you did? The most common finishing time was around two and a half hours. If you did better than this, well done! Consider signing up for a Super.

# The Real Beasts: Double Lap Runners

I will end my analysis with the stats of the small group of participants for whom one race was not challenging enough. Out of the 8011 medals that were handed out on both days, 247 went to Spartans who did a double lap. There were 84 racers who ran the Beast on both days, and 124 who ran a Beast on Saturday and a Sprint on Sunday. Out of the 486 Ultra Beast finishers there were 37 who went for another lap on Sunday, 6 doing the Sprint and 31 going for the ordeal of another Beast, which essentially meant they completed three laps of the Beast that weekend. To complete the line-up, there were exactly two who ran two Sprint on Sunday. To visually depict the performance of these Spartans, I plotted their Sunday time against their Saturday time, resulting in the scatter plots below. The red dot at (11h05, 6h20) is mine, by the way…

The diagonal lines are added to the plot to help comparing the results: if you add up the Saturday and Sunday time, then all points that have the same total time would end up on a diagonal. There is a lot that can be seen from these plots, and I leave it up to you to draw your own conclusions from these results. But one thing I will say is this. While for all 247 double lap Spartans it can be said their performance is outstanding compared to the averages in the Beast and Sprint waves, the top performers show exceptional accomplishments. I mean, if you can complete a Beast and Sprint in around four hours, two laps of the Beast in less than ten hours, or an Ultra Beast and Beast in 14h33 you are a real machine. Aroo!