What difference does a bit of mud make? Ever since the days of Socrates, mathematicians and philosophers alike have pondered the question “what difference does a bit of mud make?” How might human history have been different if the going had been muddy when the Greek soldier Pheidippides made that famous run from marathon to Athens in 490BC? In this ground-breaking piece of research I can now reveal the answer to the ultimate question: … but you have to read on. As you may have read, this year’s Mortimer Forest Trail Run(*) took place in exceptionally muddy conditions, being both cold and wet with an air temperature of just 39 degrees at the start of the race. In contrast last year’s race was run in cool but much drier conditions, with some sunshine and an air temperature of around 45 degrees. Given the popularity of the course and the fact that it followed an identical route in both years, some statistical analysis is possible, so back to the question: what difference does a bit of mud make? Statistically, we want to know whether there was a significant difference between the times of competitors in last year’s and this year’s races and how likely it is that the difference was simply down to random chance or some other factor. Since the air temperature was similar in both years that can safely be ruled out. On the other hand, wind conditions were slightly more favourable this year, with a 4 mph ESE wind compared with an 11mph SSW wind last year. This means that if wind speed was the only difference then this year’s race should have been run slightly more quickly. Therefore conditions underfoot were the biggest physical difference. The 282 runners that completed the race in 2014 did so in an average time of 91.72 minutes, while this year’s 359 finishers took much longer, with an average of 101.76 minutes. However this year’s larger field also included a longer ‘tail’ of very slow runners, which skewed the average. To account for this I have calculated two further ‘means’ (arithmetic averages) for this year’s race. Firstly I have calculated the mean for this year’s race if all runners slower than last year’s slowest finisher are excluded from the sample. This would bring this year’s average finishing time down to 97.51 minutes, still a whopping (not a statistical term) 5.8 minutes slower than last year. Finally, I have calculated the average times in 2014 and 2015 of the 79 runners that ran the race in both years. This provides the most reliable comparison, although with a larger possible sampling error. The results are quite remarkable. Among these 79 runners (on average keener and faster than the average for the whole field) last year’s race was completed in an average time of 88.26 minutes, while this year’s race was completed in an average of 93.10 minutes, a difference of 4.85 minutes longer. Astonishingly, out of these 79 runners, only 12 ran this year’s race faster than last year’s. But could the difference still have been down to random chance? To address this question, statisticians calculate something called a ‘confidence interval’. The mean and standard deviation (average difference from the average) for the two races were 88.26 minutes and 15.63 minutes in 2014, compared with 93.1 minutes and 18.31 minutes for 2015. A 99% confidence interval gives a result of 4.5 minutes for the comparison between the two means, compared with an actual difference of 4.85 minutes. This means that there is a less than 1% probability that the difference in times between the two races was down to random chance and a more than 99% probability that it was due to differences in the running conditions. So there you have it. What difference does a bit of mud make or should I say “what difference does a lot of mud make”? Answer: about 5 minutes. You heard it here first. Or did you hear it years ago from one of Croft Ambrey RC’s grizzled old-timers (with or without the statistical analysis)?
Note (*): the Mortimer Forest Trail Run is a challenging and popular annual event of approximately 8.8 miles, organised by Ludlow Runners that starts and finishes at Moor Park School, near Ludlow, Shropshire.