Aches and Analysis – Ultras in Numbers

So, the title of this blog is The Running Pharmacologist. The ‘running’ bit is fairly obvious, but the ‘pharmacologist’ bit might be less so. Essentially I study the interaction of drugs with their target proteins, how they function and what impact they subsequently have. Before I stray too far here (I really could go on for hours), it involves a lot of data analysis. I very much enjoy running, so imagine my delight when I realised that there were data to be analysed…

This short blog was inspired by a lie. Not a full-blown lie, but more me being ‘economical with the actualité’, as the late Alan Clark would have put it. Anyway, in my blog for Tarawera, I claimed that I was very happy to finish the ultra in 9.36. In truth, I had hoped to go faster and was a little frustrated that it was my conditioning, rather than  lungs or endurance that gave out on me.

It led me to think about how I had done compared to others. So I downloaded the results for all of the 60 km finishers to see what was the range of times. As you can see, whilst there were some super quick runners (and some super slow), most people finished between 8 and 10 hours:

Histogram of Data 2

Frequency of runners’  finish times for Tarawera 60km

So, perhaps my time was more ‘average’ than I thought. How did it compare with other, similar races like Two Bays or Duncan’s where I had also run (albeit the shorter distances, but there were ultra distances). This was where the fun really started – downloading the results from the respective websites and plotting the % of finishers versus time:

Histogram of Data 1

% of race finishers versus time for Tarawera 60, Two Bays 56 and Duncan’s 50 km races

It should be said that there were a lot fewer runners for Duncan’s, so the dataset is very small. Furthermore at Two Bays there is a cut-off, prevent the very slowest runners from recording a time, although the numbers affected are again quite small.

Even so, the results were really quite surprising. The median finish time (i.e. the time for the runner in the middle of the pack) was 9.07 for Tarawera and only 6.27 for Two Bays and 6.12 for Duncan’s. This comparison could be a bit misleading – after all, the distances are all different and this makes the comparison a little unfair. However, the running community has long been ahead of the game on this. For all its faults, we have long had a formula to predict race times for a given distance courtesy of an American researcher, Peter Riegel ( This is the formula that we all use when trying to extrapolate our 5km time to imagine what we potentially could do for the marathon, should we be willing to put in the time and effort.

So, although the formula has been much debated and adapted, it’s a simple way to work out what would have been everyone’s time had Two Bays or Duncan’s actually been run over 60km, rather than 56 or 50km. Using these predicted data, we get the following:

Histogram of Riegel conversion

% of race finishers versus time for Tarawera 60, Two Bays ’60’ and Duncan’s ’60’ km races

So, it seems that overall the field was still much slower for Tarawera than either Two Bays or Duncan’s ’60’ km races – their median finish times were 6.56 and 7.31, respectively. What to make of this? Well, perhaps the Tarawera course was much harder than I gave it credit for; it was certainly more technical than I had imagined and helps put my time into context. It could also be that the field was stronger for Duncan’s and Two Bays. This is also pretty feasible – after all, the former was only in its second year and perhaps attracted more ‘hardcore’ ultra runners. Two Bays, whilst super friendly and welcoming, has a very clear cut-off and qualifying time – which may have skewed the field towards stronger runners.

The take home message? All ultras are hard and take a long time to run! Perhaps I didn’t need to analyse data to work that out…


One thought on “Aches and Analysis – Ultras in Numbers

  1. Love the ‘dose response’ curve of the % of race finishers vs time graphs. Also pleasantly surprised by the normal curve for the times to Tarawera. Do you have this graph for the other two races? Might back up your assertion about the stronger fields, although you can see that in the lack of a tail on the % finishers vs time graphs for both of the other races.

    Very nice – keep it up! I was a pharmacology major, now science teacher – and totally get the nerding out on run data. Have missed some recent GPS/HR data due to some error, and its a major first world problem for me. 🙂

    Liked by 1 person

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