Never tell me the odds!

Just a quicky. Being a bit of a stats geek, I was interested to see what the probabilities of finishing the Bingo Race looked like, and how we should expect tomorrow to pan out. As a quick primer, the plan is that we each have our own ball bag (giggle) with 30 numbered balls in. After each lap (about 2 miles each), we randomly select a ball. If it matches one of the 3 balls on our bib, it's ticked off (by which I mean a tick is physically placed over the number, not that the balls are somehow anthropomorphic and a bit miffed to be chosen). If not, we just run another lap and try again. Then we keep going until we have ticked off all three numbers. So we may be finished in 3 laps or it may be 30. Interesting stuff. 

Now to be clear - I really don't care about how many laps I will have to run from a racing point of view. Tomorrow is going to be fun, and in all honesty I would be perfectly happy running for the full 100 Km. I'm looking forward to a nice long run with some good friends, and I'll just run until I stop. Run Stupid (TM), and don't think about things as you go. However, it is quite an interesting question to answer - as you go along, what are your chances of the misery finally being over at the end of the current lap? 

So being a stats geek, I thought I'd have a quick play. I won't go into the details, but in a nutshell I treated this as a ball and urn problem - there are 30 balls in total, 3 of which I want to pick (green) and 27 of which I don't (red). I performed a random "race", where each lap I calculated my probability of pulling out the final green ball this time (using a hypergeometric probability distribution), then randomly chose a ball (using a pseudo-random number generator) and updated the numbers for the next "lap". I repeated this whole process a million times and averaged over all of them to get a good model for any given set of idiots runners. 

Simple. Got it? Good.

This figure shows the probability of completing your set of 3 numbers after the current lap. Obviously this is zero for the first couple of laps, and there is a vanishingly small chance of being done on the third. After each lap the odds improve, but really very few of us will be finished in fewer than 15 laps. In fact, if we look at this in a slightly different way and ask what percentage of finishers we should expect to see at each lap, we see that half of the runners will be running over 23 laps.

The odds don't look good for a quick finish I'm afraid, but honestly that's what I'm counting on! But to everybody else that's running and was hoping to be at the pub quickly - sorry guys! I'll be interested to see how tomorrow actually pans out, and how closely it correlates with these predictions. Obviously it doesn't account for people stopping for other reasons along the way, but I couldn't be arsed including a DNF coefficient in the model. 

Right. Let's play Bingo!

Western States 2013 - Live

So, being the incredibly cool guy that I am, I am currently spending my Saturday night watching the Western States Endurance Run unfold live overnight with a cold cider. Because I'm just the coolest, I have been playing around with the times to see what the field looks like to get an idea of who might take the win. Yeah.

As it stands, 6 runners have gone through 70 miles (Peachstone), in the following order:

Timothy Olson	10:43
Rob Krar	10:56
Mike Morton	10:58
Dylan Bowman	11:09
Ian Sharman	11:10
Nick Clark	11:22

Timmy Olson has held the lead for most of the race, but Rob Krar has been hot on his heels, Mike Morton has been edging his way up the field, and the rest of the chasing pack are not far behind. The heat is immense in California at the moment, so the question is; who's going to blow first? Can Timmy hold on until the end, or will Mike's pacing win the day?

This is a figure showing the speed between each checkpoint up to Peachstone for each of the 6 runners in the lead pack. Hal Koerner was in there as well, but something seems to have happened to him since Foresthill. I hope everything's okay. Anyway, take a look and see what you think.

My interpretations are as follows:

1. Timmy has been running incredibly strong so far and has built up a great lead. Of course now we need to see if he can hold this amazing pace.
2. The pace of these 6 runners has been fairly consistent, but in the last 20 miles we have really seen the differences start to creep in
3. Mike's pacing may well be the clincher here - he started off as the slower runner, but now his pace seems to be the fastest. He's slowly creeped up the field, and now is able to hold his pace whilst others are dropping theirs.
4. Similarly, Rob is running at a fantastic pace and could hold this to the end now. 
5. Top 5 for Brit Ian Sharman? Go Ian!

As we enter the final 30 miles, the real race begins. Now we see if people have set off too fast, or if the hot weather is going to affect things. My money is on Mike Morton coming through in the final hours as Timothy's pace slips. But I could be completely wrong, and we might see another epic finish from Olson! In particular, will he pick up the pace when Morton and Krar attack? Let's see!

It's looking like we will be seeing a podium of Timmy, Rob and Mike, but as to the order; I couldn't say. Whatever happens, I look forward to seeing the results. Maybe we'll see a sprint finish at the Placer High School track?!

Good luck guys!

Update:
Hal has now been updated as being in 7th through Peachstone. Not sure what happened, but his pace has dropped dramatically on the last section. Also, Olson, Krar and Morton are through the Rucky Chucky river crossing. Olson is still 10 minutes up.

Ultramarathon Running Research Project - Pilot Study

Towards the start of the year, I contacted James Elson (Race Director of Centurion Running) about an idea that I had had. I had recently read a few papers by Martin Hoffman's group from the Western States Research Committee looking at factors that affected a runner's ability to complete the Western States 100 mile race. I had also signed up to the Ultrarunners Longitudinal TRAcking project at Stanford, which aims to follow ultrarunners and track their health over many years. I thought that it might be quite interesting to do some of our own researchr here in this country, and thought that James' series of 100 mile races was a perfect opportunity to do something similar, as they are very well organised, they are quite homogenous in their organisation, and James has a particular interest in delving into the stats behind ultra running.

The plan that I proposed to him was to create a couple of surveys for runners of his events to fill in: one before the race, asking questions relating to the runners themselves (biometrics, professional status, running history, etc.); and another survey after the event asking questions relating to how the race went, what their strategy was for the race, their nutrition, etc. By putting this information together with the split times from the event itself, my hypothesis was that we may be able to see some trends dropping out from the data. Yes, this is the kind of thing that I do for "fun"!

In the short term, this approach would give us a good overview of the race itself, the sorts of people who entered, and which runners took a sensible approach to racing. But my main aim was for the long term, building up a database of survey results and race performances for ultrarunners that, over time, will allow us to look at more specific questions relating to performance: Do certain training choices improve your chances of finishing a 100 mile race? Are certain racing strategies more likely to result in a finish/win? Do people with green eyes run faster than people with blue eyes? These burning questions and more may well be answerable in the future from such a database.

To kick things off, we organised a pilot project for the South Downs Way 100 at the end of June. This went very well, and we found some (I think at least) very interesting things from this that bode very well for the future. James has created a research page on the Centurion Running website where you can download the report that I put together (using my official "Dr" title to make it seem to people that don't know me that I have some air of professionalism about me...). Alternatively, I have replicated the report below so that I have a record of it on my little blog. Hopefully you find it interesting, and any comments will be gratefully received. Hopefully we can get even more people interested in taking part in the full project at next year's races!

Pacing the Western States Endurance Run

I recently saw a post on the Runner's World Sweat Science blog regarding pacing of swimmers and runners, and how this affects their performance. One of the papers that is discussed is this paper by Tucker et al. (2006), which shows pacing over a number of intervals for world record times at a variety of middle distance events (800m, 5 km, and 10 km). The results of this study seem to suggest that the optimum way to run these events is to go out strong at the start, settle into an even pace for the majority of the event, then finish strong again at the end (a so called parabolic profile):

A "parabolic" pacing strategy seems to be optimal for middle distance events (from Tucker et al.  (2006) c/o Sweat Science)

So I got to thinking - is there an optimum way to run a 100 mile event? Now, I think that this is a very difficult question to answer. Unlike track events, the terrain and conditions for a 100 miler event are so variable that judging pacing becomes a complex interplay between many different factors throughout the race; weather conditions, ground conditions, elevation change, fueling, hydration, navigation, gear choice - there is just much more to consider, and much more that can go wrong. Even ignoring the variable effects like weather, the elevation profile and terrain is so different between any two races, coming up with a simple strategy that would apply to all races is likely impossible. The optimal pacing strategy for UTMB (31,496 ft of ascent) is unlikely to be the same as that for the Thames Path 100 (2,100 ft of ascent) for instance.

Are ultrarunners slow?

So tell me if you've heard this one before?

"Pft. Ultra running? Ultra walking more like!"

Reading around various forums and blogs, it seems that some people have a negative view of ultrarunners. The main trope seems to be the opinion that ultrarunners are slow, and are basically speed-walking. Other more extreme views are that ultrarunners are failed marathon runners who weren't able to cut it. Rather than putting in the training to push their marathon PB to a new level, they just go a little bit further.

Of course, the obvious response to this is that, well, I'm sure 100m sprinters look at marathon runners and think exactly the same thing. My wife was a 200m sprinter when she was younger, and she couldn't understand why anybody would want to run any further than that. So if ultrarunners are slow and shambling in the eyes of some marathon runners, does that mean that marathon runners are viewed in the same way by sprinters? No. There is mutual respect - they're just two very different events; one focuses on pure explosive power, while the other focuses on endurance. When you get up to ultra distances, particularly those out on the trails, up mountains, or in other inhospitable parts of the world, additional factors come into play - gear selection, nutrition, hydration, pacers and crew are all important for marathon racing but are more complex for ultras, plus you also may have to deal with tougher terrain, navigation, etc. Is it any surprise that ultrarunners are slower than marathon runners when running up and down mountains?

But even despite this, is it really fair to claim that ultrarunners are slow? In many of these discussions, it seems to me that the comparisons being made are between top-class marathon runners and the average middle of the pack ultrarunner who typically is not out for a podium place, and is just there for the experience and the love of running. But there are ultrarunning guys and girls out there with blisteringly fast times. So when we compare apples with apples and look at the times for the top marathon runners vs. the top ultrarunners, does the accusation of being slow still stack up?

I decided to do a bit of digging; a bit of Google-ing and Wiki-ing and I had put together a list of the fastest times over a range of distances ranging from 100 meters to 100 miles (apologies if I've got any of these wrong, but if it's on Wikipedia it must be true...):

Tick tick tick...

I recently wrote a blog post looking at a recently published paper looking at the effects of endurance sports on cardiac function. Or, more specifically, I was looking at the reporting (and unsurprising overhyping) of this story by the media. What struck me while looking through the comments section of the Daily Mail's take on the story was how many people believe in the idea that we are all allocated a certain number of heartbeats in our lives, and so we shouldn't waste them doing stupid things like running marathons. As in example, this is a quote from Bobby from Inverness:

"You are allocated only so many heartbeats for a lifetime - don't waste them up in silly fruitless 'exercise' - live longer, have a nap"

I suspect that this quote was actually written in jest, but it seems that a lot of people think like this and use it as another excuse not to exercise. The theory is that, since when we exercise our heart beats faster, every hour of exercise is using up 2 or 3 hours of your life that you could be sitting on the sofa doing nothing. Now don't get me wrong - I like to lounge on the sofa as much as the next person. In fact, my second biggest hobby is playing on the XBox; an interesting juxtaposition to my favourite hobby of running. But could I really be reducing my lifespan with all of this running?

First of all, let's look at this theory. It's actually quite an interesting premise, and the evidence for it seems to come from the idea that animals with shorter lifespans have quicker heart rates than those with longer lifespans. So if you take the average lifespan of a species (in minutes) and multiply it by the average heartrate (in beats per minute), you get an estimate for the average number of beats of the heart in a lifetime. And this value seems to be similar amongst different species. I was pretty skeptical, so decided to have a look at a few examples for myself: