September 12, 2005 Archives

12 September 2005

Marathon finish times

Martin, I think the peaks you see in your graph are real.

Personally, I kept no particular track of the race time, or my own pace on a mile by mile basis during the race. However once I passed the last corner, I could see the clock above the finish time, which was just reaching the 2:08 mark. At this point I figured if I pushed it, I could make it inside 2:10, and sprinted the finish. I'm also pretty sure if the time said 2:11 I wouldn't have bothered.

I would therefore hypothesise that the number of people finishing in a time ending in a nine will be greater than any other digit. Similarly I thing the quarter hour marks would be attractive for similar reasons, therefore 4s are to be expected too.

In the histogram below, the last digit of the finishing time in minutes has been calculated. This clearly fits the hypothesis.

Histogram of finishing minute

My A-level statistics somewhere in the back of my head tells me that:

Actual Hypothesis: Finishing time is influenced by human desire to beat certain time barriers.
Null Hypothesis: Finish time is random, therefore probability of a runner finishing in a time ending in a "9" is 0.1
  1. Assume the Null hypothesis is true.
  2. Using binomial theory calculate probability of 779 or more runners out of 7086 finishing in a time ending in 9.
  3. If probabilty is less than 5%, Null Hypothesis is rejected and Actual Hypothesis is accepted.
According to gnumeric, the chances of 779 or more successes out of 7086 trials with a success rate of 0.1 is a mere 0.28%. The AH is accepted.
The 95% confidence interval is between 666 and 750 successes.


Bit of a thinko there. 666—750 is the 90% confidence limit for the mean (assuming binomially distributed, p=0.1, n=7086). The 95% confidence limit is more like 659—757. Can't be bothered to update the graph.

Posted by Robert Hart | Permanent Link

12 September 2005

Marathon time distribution

This is a graph of the cumulative distribution of times in the Robin Hood half marathon.
Distribution of marathon times
  • The median time is 2:02:02
  • The mean time is 2:05:45
The skew is probably due to the tails of the distribution. The fastest runners cannot realistically do much faster than about 60 minutes, whereas the slowest runners could conceivably take any length of time.

Posted by Robert Hart | Permanent Link

12 September 2005

Robin Hood Half Marathon

Yesterday I completed the Robin Hood half marathon. Officially my time was 2:09:14, (my "chip time" was 2:05:46) and I came 4381st.

Although the position itself isn't that stunning (61% of people beat me), I was only six minutes behind the median time.

The main achievement for me though was not only finishing the race (which I was never 100% sure I could manage), but actually running the whole way.

I also took part in the Cooper Parry Corporate Relay Challenge on behalf of Freeth Cartwright, because somebody dropped out. The teams consist of 5 runners each completing around 2.5 miles each. Somewhat bizarrely I manage to beat my own team.

I although I didn't set out with the intention of raising money for charity, and haven't collected any sponsorship, it would be great if somebody benefitted from my efforts yesterday and my inability to walk today. Therefore if anybody feels inclined to donate, I will be donating money to the State School for the Deaf in Ghana, where my sister worked on her year out.


That should have said "median time" and not "mean time". oops. Thanks Martin.

Posted by Robert Hart | Permanent Link