# Running Late: Some Statistics on Marathon Pacing

Robin Barnwell
01/31/2012

Feel like you're running flat out? Columnist Robin Barnwell develops a prediction model to better judge pacing and target times as he analyzes data from London marathons past in preparation for his own run this year.

I’m running the London Marathon this year and what’s top of my mind is my target finish time. This is my first full marathon having previously done half marathons. I’m not all that quick and started training in September thinking I would run around 4 hours 30 minutes. But I’ve got steadily fitter and faster and started to wonder if 4 hours was even possible. I can run a half in less than 2 hours so a couple of those would do the job. Sounds good on paper but sounds very different at 20 miles with 6 to go. To see if it’s at all possible I asked two questions:

• To what degree is first half of the marathon a good indicator of finish time?
• To what degree do people fade in the second half compared to the first?

I downloaded the data which included half-marathon and finish times for the 3862 people in my age range (40-44) who finished the London marathon last year. The finish times ranged from 02:19:57 to 09:17:41 so nearly a 7 hour difference. A simple correlation gave the following results:

 Correlation First Half Second Half Second Half 0.894 Full Distance 0.962 0.982

The second half looks a better predictor than the first, but not by a lot. Also the relationship between first and second half is lower, but still strong. I then looked at the degree of fade in the second half, meaning the time compared to the first. This could be one of three:

• Negative split –the second half is run faster than the first
• Neutral split –both half’s are run at the same speed
• Positive split –the second half is run slower than the first

The general advice is to train for and run a negative to neutral split. Here is a graph showing the differences:

Only 100 of the 3862 people who ran managed a negative or neutral split. All of the top-ten finisher ran the second half slower. Nearly 98% of people running run a positive split, on average by 18%. But statistically there are some big outliers of people who "crashed" over 50%. So I removed the outliers to produce the following graph:

It’s hard to see but there seems to be an increase in the % fade from the top athletes on the left to the slower runner – like me. The correlation was not great, so I thought I would focus specifically on the people who finished between 3:00 and 5:00 hours, more around my area.

To run a 4 hour marathon and allowing for a 17.2% fade (as above) in the second half would mean running the first half around 1:50. To run a neutral split would mean running the first half in 2:00. The fitted line plot below with 95% prediction interval provides a useful tool for understanding where you fit against all the other runners.

The data for last year’s runners suggests that to run the first half in 2:00 and complete in 4:00 is statistically within the 95% boundary, but only just. I’ve now got a prediction model to better judge my pacing and target times against.

Author's note: I hope you found this article of value. I will be running the London Marathon in April 2012 to raise money for the War Child charity. This charity provides life-changing support to children living in some of the world's most dangerous and war torn countries. They have little to no chance in life and I think it’s so important to try to give them every opportunity to live a happy & peaceful life. If you’d like to contribute to this charitable cause and make me run 26 miles at the same time please click here.