Skip to content

The Great Race

This post is by Phil.

Last summer my wife and I took a 3.5-month vacation that included a wide range of activities. When I got back, people would ask “what were the highlights or your trip?”, and I was somewhat at a loss: we had done so many things that were so different, many of which seemed really great…how could I pick? Someone said, wisely, that in six months or a year I’d be able to answer the question because some memories would be more vivid than others. They were right, and I was recently thinking back on our vacation and putting together a list of highlights — enjoyable in itself, but also worth doing to help plan future vacations.

One of the things we did was go to four evenings of track and field events at the London Olympics. After we got back, people would ask what we had seen at the Olympics. I would say “We saw Usain Bolt run the 200m, we saw the women’s 4x100m relay and the men’s 4×400, we saw the last events of the decathlon…lots of great stuff. But my favorite was the men’s 800m.”

Trying to figure out why that was one of my favorite events to watch, I looked up some facts and statistics about the race. Perhaps unexpectedly, I think that some of the things that made it great, as both an athletic contest and a spectacle, are reflected in the stats.

The 800m is not one of track’s marquee events: it’s much too long for an all-out sprint, so it doesn’t have the intensity of a 100m or 200m. It has even less of a following than most track events, which is saying something: I’m going to guess that most readers of this blog cannot name a single U.S. track athlete, and that only a tiny fraction can name a competitor in that 800m Olympics final.

Me, I’m more of a track fan than most — my wife and I have gotten interested, especially since discovering that during our fitness workouts we were sometimes sharing the track with Alysia Montano and  Magdalena Lewy-Boulet, and we spectate at track meets occasionally — but although I recognized a few of the names in the 800m Olympics final I didn’t really have any context for what I was about to see. Like most people in the stadium, I expect, I was looking forward to the highly-anticipated 200m final later in the evening and hadn’t even thought about the 800. That 200m final was exciting and electrifying, but to me it was no match for the 800.

When the race started…it’s hard to say how this could possibly be, but I could just tell that something special was happening. Maybe everybody in the stadium could tell.  One of the runners — David Rudisha of Kenya, the record-holder at the time — went to the front and was pushing hard, and everyone else was going hard too.  Of course.  It’s the Olympics! Finals! Of course they’re running hard!  Well, yes, but… it’s hard to explain…it just seemed more intense even than the other finals we had seen, which seems paradoxical because, this being the 800m, the runners weren’t running as fast.  I’ve tried to tell if you can see in the video what I’m talking about (the race starts at about 3:15), but I’m not really sure, you tell me. (One thing that you can see on the video is how easily these guys seem to cruise through the 400m mark in under 50 seconds, incredible).

So, here’s what happened:

Rudisha, the pre-race favorite, won the event, beating his own previous world record.

The times flashed up on the scoreboard, with indicators to say if the time was a World Record, National Record, Junior Record, Personal Record, or Season’s Best.  That column on the scoreboard looked like this:WR, NR, PB, PB, PB, NR, SB, PB  In other words, seven out of the eight runners had run their personal best time.

That’s all I knew at the time, and it’s only recently that I learned some other facts: All eight athletes went under 1:44, the first time that has ever happened; and the first place time was (obviously) the fastest first place in history, but also, the second place was the fastest second place in history, and third was the fastest third in history, and so on all the way down the line.


It obviously takes a special effort to set a personal record, and those records usually come when the athlete has something at stake: the chance to finish on the podium at their national championships, or to qualify for the Olympic team, or whatever.  For a guy who is rounding the final curve 20 meters behind the leaders, a guy who is going to finish in 8th place, to push himself to the fastest that he has ever run, that seems to me to be even more remarkable than someone running a personal best in order to set a new world record. I tip my hat.

So  I think it wasn’t the effort by the top finishers that made the race seem so special at the time — we had seen other records set[correction, this was the first WR we saw], we would see records set the following day, and they were great and exciting but they didn’t have the same magic for me. I think what made this special was the effort all up and down the line, every runner trying his hardest right to the end. Maybe the best 800m races to watch are the ones where the last-place finishers run their hardest, not where the first-place finishers run theirs. Just a thought.

This post is by Phil.


  1. Brian Godsey says:

    It is great to read about the experience of someone who was there, in the stadium, when David Rudisha ran his incredible race. I’ve been involved in competitive track and field, cross country, and road racing for almost 20 years now, longer than I’ve been a mathematician. It has surprised me on many occasions that there is such a lack of statistical analysis of athletic competitions, particularly when compared to statistics-laden sports like baseball, though admittedly, many of these analyses aren’t very sophisticated or rigorous.

    In 2009, after the world championships of track and field in Berlin, I was tired of all of the discussion of the “best” world record and which performance from athletes in different events was “more impressive” than the others. Typically, these conversations were among armchair fans or even active participants in athletics or coaching, and very few went beyond a very basic level of analysis. So, I created a basic probabilistic model for the top annual performances and wrote a paper on it ( citing Gelman and Rubin for a convergence diagnostic. The model is pretty simple, but got some attention on, including an article about the men’s 800m final that you mention above ( that quoted me (hooray for self promotion!).

    Anyway, thanks for giving a new perspective on an absolutely astonishing race in my favorite sport. If you’re interested in related statistical analyses, have a look at the links above. Cheers!

    • Phil says:

      Brian, that looks pretty interesting, based on the abstract anyway (for $42 I can’t quite bring myself to buy the paper). I like the simple way you suggest for stabilizing estimates so they’re not highly sensitive to one great runner or a really good year or whatever. Years ago I commented on an article in Chance that looked at third-best performances in a year rather than best, for similar reasons. That article (and my comments) is available here but you are way beyond this.

      Thanks for your comment, and congratulations on predicting that the 800m record was likely to fall.

      • Brian Godsey says:

        I don’t blame you for not wanting to spend the money; I wouldn’t either. I’m not a fan of pay-for-access journals, but that’s just the way it worked out for this paper. The good news is that the one-year exclusive copyright of the journal expires in about a month, so I’m planning on posting a copy of the paper on I’ll post a link here after I do.

        The gist is that I downloaded the top recorded performances in track (and field) from and treated these as a tail of a log-normal distribution. So, I had hundreds of performances for each event (e.g. the top 500 times ever in the 200m dash) and I used a probabilistic model to generate actual probabilities of achieving certain performances. one downside is that it’s hard to fit a distribution to data when all you have is the tail, but it seemed to work in most cases, and made better year-over-year predictions than the IAAF Scoring Tables. There is certainly still room for improvement, but it seemed better than anything else I could find.

        The article you linked to has some interesting things to say. The lines drawn on the plots are definitely misleading since clearly running times cannot decline linearly for very long, and even log-linear is probably over-estimating the future change. It will be nice to check back on some of these conclusions in a few years when we have even more data.

  2. middle professor says:

    I wouldn’t be surprised if there are many track fans here. At the local high schools where I live, most of the runners are math geeks and quite a few go on to major in math (or physics) in college. That may vary regionally though. The olympic 800 was special – thanks for the reminder. The 800 is just a very different race than shorter and longer. Longer races are typically run (and records are set) with negative splits (when the 2nd half of the race is faster than the 1st half). That’s not the case with the 800. The 800 is all about going out fast and slowing down the least. It’s also a good reminder that when you see the last 100 m of an 800, it looks like the winner is the one who speeds up the most but s/he’s actually the one that slows the least – they are all slowing but our mind mentally processess it as some are speeding up.

  3. Steve Sailer says:

    The 800m is the most exciting race. In shorter races, runners have to stay in their lanes and there are no tactics. They just run as fast as they can for the whole race. The 800m has tactics but it has the minimum number of pre-final lap timekilling, too.

    Here’s a video of the 1972 Olympic 800m, with it’s unbelievable finish, which made me a track fan for life:

    • Phil says:

      I hadn’t seen this video, this is great. An exciting race, indeed.

      As for tactics, though, Rudisha’s race didn’t really have any: nobody was hanging back in the draft, or trying to box anyone in or to avoid being boxed in. Rudisha’s fast pace strung the field out right away and it was just a flat-out footrace. Maybe that’s part of what I liked, that after a few days of seeing tactical races as top guys tried to advance to the finals with minimum effort, we finally got to see what they could do when they opened ‘er up all the way.

  4. Steve Sailer says:

    Also, if you like human biodiversity, the 800m has the most diverse set of contenders (other than, maybe, the marathon). Most distances are dominated by one or two racial group, such as men of West African descent in the 100m. But the 800m falls right between the short distances at which West Africans dominate and the longer races (3000 to 10,000) where East Africans dominate. In the 800m, you can see top performers of East African descent, West African descent, European descent, Northwest Africans, and Brazilians.

  5. Tom says:

    Great post.

    The 800m final was without doubt the highlight of the track and field games last year (along with the womens 4x100m final). Rudisha is without doubt one of the finest athletes I’ve ever seen run – great style and imperious on the track.

  6. Paul says:

    Thanks for a great post!