The 2016 Olympic Games got Alan Parr thinking about measurement.  In this brief article, he reflects on various measurements recorded during an Olympic Games, from the accuracy of timing in the pool to the point system in the heptathlon ...

In the pool Michael Phelps and two others tied for a silver medals with each given a time of 51.14.  Now, today's systems would allow times to be recorded to far greater accuracy - in cycling for example times are reported to thousands of a second, so surely there's no problem in giving times in swimming to three decimal places?

No there's not, but in a thousandth of a second Phelps will travel a bit under 3mm, and when a 50m pool is constructed the tolerance allowed is more than ten times that - as much as 3cm in a lane.  In the extreme case in the pool one contestant could be swimming 49.97m and another 50.03m.  (That seems quite a lot; however, it's pointless trying to build to a greater accuracy - the length will vary not only with the temperature, but even with the number and position of people in the pool).  In a sport where everyone uses the same track - motor-racing for example - it doesn't matter, but whenever you have lanes then you'd have a problem. 

So the swimming authorities seem to have got things right.  If you use technology to give you times more accurately you run the risk that the technology will also demonstrate that the reason someone finishes before someone else, and hence records a shorter time, is because they've had to complete a shorter course than their opponent.  This might be terrific news for the manufacturers of measuring equipment and for a host of lawyers but the extra accuracy would cause more problems than it solved.

Incidentally, some back of the envelope calculations tell me that if there is just 2cm (well under the allowed tolerance) difference between two lanes that equates to around 0.01 second - in other words, even giving timings to hundredths of the a second is bit dubious.  Good news for the lawyers after all!


There are plenty of mathematical expressions that are simple and elegant, but they don't include the following, which gives you the number of points won in the high jump in the women's heptathlon:  

1.84523(M-75)^1.348  

where M = height in cm.

And just in case you were interested, here are the other formulae.  They've been in use since 1984 and are scaled with the intention that a good performance should gain 1000 points and a minimal performance (e.g. 0.75m in the high jump) gets 0.  They're designed so that regular increments in performance gain fair increments in points scored: 

4.99087(42.5-S)1.81	200 metres
0.11193(254-M)1.88	800 metres
9.23076(26.7-X)1.835	1 00 metres hurdles
0.188807(Z-210)1.41	long jump
56.0211(D-1.50)1.05	shot put
15.9803(W-3.80)1.04	javelin

I've never seen it mentioned as an issue, but the range of accuracies implied varies from three to six.  In particular, the performances themselves are measured to an accuracy of three figures in the jumps, and to five figures in the 800m.  They're then plugged into the values in the brackets, which are to three figures.

Now I was going to say that conditions are the same for all competitors in all seven events, so none of them suffers from anything corresponding to the variable lane situation.  But I'm not sure that's true.  Aren't the jumps weak links here?  Aren't there problems at both ends of the long jump?  Can we be certain the plasticine is identically positioned for each competitor (Greg Rutherford certainly felt he was hard done by in the men's event)?  And how you determine the exact point of the depression produced on landing seems very uncertain.

What about the high jump?  Each time anyone knocks the bar off it has to be replaced.  Can the bar be repositioned, even automatically, so that the next competitor faces an identical height to the last?  And can we be sure the bar hasn't been minutely distorted by the previous failure?

Can contestants really be certain that when the bar is set at 1.92m this is actually is 1.92m, and not a few millimetres either way taking it closer to 1.93m or 1.91m?  A measured high jump of 1.92m is worth 1132 points, but someone at the very limit of her range who attempts what is actually nearer to 1.93m is likely to have to settle for her previously attained height of 1.89m, worth just 1093.   That's a difference of 39 points, and if Jessica Ennis-Hill had scored another 39 points she'd have taken the gold medal.  Indeed, no fewer than four of the top eight in Rio would have been placed higher if they'd scored another 39 points.
 

*****

”‹The ideal heptathlon and decathlon scoring systems (or perhaps the ideal heptathlon and decathlon performances, which is of course a totally different matter) would generate approximately equal points in each event.  That was the aim of the 1984 scoring systems, which were based on the then current world record performance at each of the separate events, but in 2016 we can all think of several different reasons why that might not be such a good idea today.

Whenever we watch British women in the heptathlon they seem to get off to a good start in the 100m hurdles and the high jump, then do less well in the shot and javelin, but actually they're simply modelling the performance of heptathletes as a whole.  In heptathlons generally, the 100m hurdles and high jump produce scores around 1000 points, while in the throws typical scores are closer to 800.  In other words, the scoring systems and indeed the very events in both heptathlon and decathlon favour tall slim athletes who do well in the running and jumping events.

There's all sorts of scope for improving the scoring system in the heptathlon and decathlon - among the many suggestions is one by John Barrow to relate performances to kinetic energy - but one look at the heptathlon performers themselves makes it clear that an event where five of the seven events depend largely on speed and running is heavily biased in favour of tall competitors with low body mass. 

But if we really do want a more balanced event then how about a hexathlon, with a flat race, a hurdles, one of the jumps, and three throwing events?  This would be a much better way of finding a genuinely all-round athlete.


There's one question I've tried to find an answer to for many years.  Shorter track events in imperial units converted very well to metric measurements - 110 yards is 100.58 metres, and 220 yards is just over 201m.  The one-lap quarter of a mile and the two-lap half-mile easily became translated to the 400m and 800m.  So it seems the most natural thing in the world to replace the classic blue-riband track event, the mile, by the four-lap 1600m.

What I've never understood is why the so-called “metric mile” was instead taken as 1500 metres.  This is more than 100m less than a mile (a mile is a little over 1609 metres) so there's about 15 seconds difference in performance.  Taking 1500m as the equivalent event to the mile not only discarded the close link in distance and time, but it also made life far harder for officials, with the need to start the race on a bend the other side of the track.    


This article is an adapatation of one of Alan's blog posts.  You can follow Alan's blog at http://established1962.wordpress.com/