Pace Judgement - A Statistical Look

Hi to everyone, especially to Thomas L and John K.

A few days ago Thomas on his blog added to the discussion on pace judgement and compared his split time at Rowardennan and his finish time during last year's Highland Fling, with the winner's Jez Bragg. He calculated what his time at Rowardennan was in terms of a percentage of his overall finishing time. It happened to be identical to the winners, being 47%. Thomas therefore concluded "... my race was in fact paced exactly like Jez, and although it felt I was going too slow in the first half I was probably not."

It got me thinking, "Is what the winner does the correct strategy?"

If you have read my earlier posts, especially on pace judgement, you will know instantly the answer to my question! There is not one correct strategy, everyone is different. However, this conclusion of mine doesn't really help anyone in trying to possibly identify what is a strategy that is more likely to lead to an improved performance. Well before I could add a comment to Thomas' blog, John K then raised some further questions by calculating the halfway split time percentages for everyone during last year's Highland Fling race! He then made an interesting comment that got me thinking even more!

Firstly Rowardennan is at 50.6% distance. John then comments "If we take that 50.6% is the 'perfect' equal split then Jez came 2nd and Thomas 7th in the list"

So, is it as simple as that? Is the aim to run as even paced as possible throughout the race?

Well I have my pretty well exactly opposite views, but I thought maybe there is some way to look at the data from last year's Highland Fling to help answer the above question regarding even pace judgement. So here is my attempt at using statistics. Not one of my strengths but maybe worth giving it a go!

Logically, you would think that an even paced split i.e. the closer to 50.6%, the better. This would mean that you haven't slowed down very much during the second half of the race. However, one can also achieve an even paced split by going extremely slow during the first half of the race, so therefore able to maintain the same pace. This strategy therefore 'looses' time during the first half, hence my approach "Run as fast as you can while you can!"

Time for some statistics. If it was as simple as the closer to 50% half way time split the better the performance, then you would expect a strong relationship between the two variables. Scatter diagrams illustrate relationships and the correlation coefficient (r), that is a number between 0 and 1, indicates the strength of the relationship, with 0 being absolutely no relationship and 1 being the perfect relationship.

Before looking at the statistics, one needs to be aware of a few other factors. During the Highland Fling last year it was amazingly hot! This caused problems for a number of runners in terms of dehydration, as experienced by my training partner James Wallis. His halfway percentage was 37.6% ranking him in the halfway time split percentage list as 6th to last! However, this low percentage was not due to poor pace judgement, but to other unforeseen circumstances. This may also have affected a number of other runners who were required to dramatically slow down during the second half of the race, for example due to a strained muscle or twisted ankle, i.e. unforeseen circumstances. I therefore need to remove these abnormalities from the 'equation'. Of the 237 results with the Rowardennan time split I ranked these in halfway time split percentage order and then removed the bottom 10%, i.e 24 runners. This left 213 runners. I then calculated the correlation coefficient between the halfway time split percentage and finishing time for these 213 runners. The correlation coefficient was r = -0.32. What does this value mean? This means that there is a very weak relationship between halfway time split percentage and finishing time. Taking account of all 213 data points , if the halfway time split percentage is higher, i.e. closer to 50%, then the finish time is statistically likely to be slightly lower. However,that result is an overall conclusion, which doesn't always work out for each individual. This is illustrated by the three red circles on the graph below. Nearly identical halfway time split percentages but massive differences in the finish times.

There is a term called 'common variance'. This refers to how much of the variability of one variable, e.g. finish time, is explained by the variance of the other variable e.g. halfway time split percentage. Common variance is given by the r value being multiplied by itself, i.e. r squared. For an r value of -0.32, the common variance is 10%. So only 10% of the variance of the finish time is explained by the halfway time split percentage, the other 90% of finish time variance is determined by other factors.

So to answer the question I asked above, "Is it as simple as the closer to 50% halfway time split, the better the performance", the answer is yes, but to a very small extent, only 10%, the other 90% variation in finish time is due to other factors.

I guess I could stop this post there, however, if you have read a few of my previous posts you will know that they tend to be quite lengthy. I do try to give true value for money! So I will expand on this issue a little more, with a bit more statistics. Hopefully the above hasn't already brought back nightmares of GCSE (O Level) maths!

With regards to the recent discussion on pace judgement, there has been an assumption that the rate at which you slow down during the second half of an ultra race is largely determined by how fast you have run the first half of the race. Now I believe, along with Gavin Woodward (see earlier post) that "no matter what pace you start at, you will slow eventually, so start at a fast pace". Is there any way that the data from last year's Highland Fling can help support this belief? So I started thinking a bit more. What follows is what I came up with. Warning, I am not a statistician so I may be abusing the laws of statistics, but this is a blog, not an academic journal! I think it makes sense. I just hope you are able to follow my logic!

The next question I asked was: "Is the halfway time split percentage influenced by a runner's level of fitness?" For example, do the fitter runners tend to have a higher or lower halfway time split percentage? To try to answer this question I took the runner's time at halfway as a measure of the runner's fitness level, and then calculated the average halfway time split percentage for the fastest 53 runners to halfway, also the average halfway time split percentage for runners at halfway from 54 - 106 place, also 107 - 160 place, and 161 - 213 place. If the halfway time split percentage was influenced by the runner's fitness level then you would expect to see differences between these group averages. The results were:

1 - 53 halfway average time = 4:00:26, halfway time split percentage average = 43.35

54 - 106 halfway average time = 4:35:11, halfway time split percentage average = 43.12

107 - 160 halfway average time = 4:59:10, halfway time split percentage average = 43.37

161 - 213 halfway average time = 5:32:58, halfway time split percentage average = 42.87.

It therefore appears that for the fittest three quarters of the field (1 - 160), the fitness level does not influence the halfway time split percentage. Although for the least fit quarter of the field (160 - 213) there does appear to be an influence with the least fit runners having a lower percentage, i.e. they slow down more in the second half of the race.

So to further my statistical analysis, I then removed the slowest 53 runners, leaving the fastest 160 runners. Which for these runners it appears that the halfway time split percentage is independent from their fitness level.

The question I next wished to answer was "Does the pace you run at for the first half of the race have a strong influence on how much your pace will slow during the second half of the race?" The halfway time split percentage represents how much your pace slows down during the second half of the race in relation to the pace during the first half. So if the race pace to halfway does influence the rate at which you slow down then this would be illustrated in a scatter diagram of halfway time plotted against halfway time split percentage, and the larger the correlation coefficient value (r), the stronger the relationship.

The RESULT! Take a look at the graph below. In all of my reading of journal articles I don't think I have ever seen a correlation coefficient ( r = -0.017) as close to zero as the value representing the relationship between halfway time and halfway time split percentage! In other words, based on the fastest 160 runners in last year's Highland Fling there appears to be absolutely no relationship between the pace one runs the first half of the race and the rate at which they slow down during the second half of the race!

Well all of my effort in giving thought to this topic, and in thinking that all of this data must be able to show us something, appears to have been worthwhile. Obviously if one takes this lack of a relationship to extremes, and runs a ridiculously fast pace for the first half of the race, then one may then expect a rapid decrease in pace during the second half. But by using the database of the 160 runners from last year, where we are only talking about small variations in race pace / race intensities during the first half of the race, not extremes, it appears that it may well be better to run that little bit faster at the start, now knowing that it wont cause you to slow down at a greater rate later in the race.

Just to finish off, with one alternative way to look at the data. I put the 160 runners in halfway time split percentage ranked order ranging from 47.8% at the top, down to 40.0% at the bottom, and again looked at the average values for each quartile i.e. each 40 runners, to see how the average values for each quartile group differ. Here are the results:

% ranking 1 - 40, average % = 45.43, average halfway time = 4:45:22

% ranking 41 - 80, average % = 43.63, average halfway time = 4:45:14

% ranking 81 - 120, average % = 42.60, average halfway time = 4:49:22

% ranking 121 - 160, average % = 41.09, average halfway time = 4:47:38

If the pace one ran at during the first half of the race did directly influence how much one slowed down during the second half of the race, then you would expect that those runners with the highest halfway time split percentage would have a slower time at halfway. This is expected because those runners with the highest halfway time split percentage would have taken it slower over the first half of the race to ensure that they didn't excessively slow down during the second half of the race. As you can see from the results directly above, there is pretty well no difference at all between any of the four quartile groups average halfway times!

If you have managed to get to the end of this post, well done. Even I am getting a bit fed up with numbers. Many apologies for such a boring?, well maybe for some, but more likely many apologies for such a possibly confusing and mathematical post. I will get back to easier reading in my next post, whatever that will me.

All the best to those of you running the Highland Fling this Saturday. I am not running the race this year. It was extremely tempting after last year's disappointment, with the temptation to improve my result after going off course last year. However, I already have four ultra races scheduled for the year, and trying to fit in a fifth ultra race just seemed a bit too much! After all there is more to life than ultra trail running.

This post has talked alot about slowing down during the second half of the race. To sign off, I will leave you with some words from Steve Gurney, arguably New Zealand's greatest ever multisport adventure racer. "If you keep focusing on the problem, it will surely happen. My strategy is to look at the goal, and enhance the positive things that will lead to success." Steve Gurney (2008) p198 Lucky Legs - What I've Learned About Winning and Losing. Auckland: Random House.

Enjoy your next ultra trail race,

Stuart