It’s seems an age ago, but it has only been just over three weeks since Usain Bolt of Jamaica broke the world 100m record. He was duly dubbed the “fastest man in the world”, a title that is given to the record holder over 100m. Or, in some cases, the world champion, as was the case last year when the record holder Asafa Powell was soundly beaten by Tyson Gay over 100m in Osaka.
An illegitimate title?
However, the debate rages over whether that title is actually deserved or not. People, including exercise scientists, raise the question whether it should not be the 200m event that throws out the real fastest man, because the final 100m of that event are covered in much less time than a 100m race ever is. For example, the 200m record of Michael Johnson stands at 19.32 seconds, with a final 100m covered in 9.20 seconds (Johnson’s first 100 split of 10.12 seconds is pretty quick too, considering it’s on a bend – it would have placed him sixth in the 1996 100m final, incidentally).
However, most people can appreciate that this comparison is hardly fair – the second 100m of a 200m race benefits from a running start, so it should be faster. However, a more subtle version of the argument comes from the English Institute of Sport website, where their Professor Greg Whyte argues that because Johnson had to run for longer at the same speed, he’s the owner of the “fastest man” title. In his words:
“Therefore the average running velocity is higher in a 200m runner as they will run for approximately 160m at peak velocity compared to a 100m runner who will run for only around 60m at the same rate.”
The article (which is actually quite shaky) goes on to make the afore-mentioned error, saying:
“For those still unconvinced, a cursory glance at the record books reveals a simple truth; Michael Johnson’s 200m world record of 19.32 – which he set in 1996 and which has yet to be beaten – equates to 9.66 for each 100 metres, significantly quicker than Asafa Powell’s 100m world record of 9.77 set in early 2005.”
Two things: First, this argument is based on the assumption that the 100m runner and 200m runner do in fact hold the same speed – this needn’t be the case, as we shall see shortly, and the 100m runner may well be much faster once into his running. Secondly, to suggest that the FASTEST man should be so crowned because he runs at a certain speed for LONGER seems to be confusing the whole meaning of FASTEST. In other words, fastest should imply peak speed – speed is absolute. Or is it? When we wrote about Usain Bolt’s performance, people commented that reaction time should be corrected for, and that one should look only at the peak speeds attained. That too defines “fastest” in a unique way.
So as if often the case in science, it all depends on how you ask the question, and how you define the outcome!
A statistical comparison
For answers (or perhaps more debate) we turn to a really interesting comparison between Michael Johson’s and Donovan Bailey’s 200m and 100m world records from the Atlanta Olympic Games. To take you back 12 years, both records fell in the space of a week – Bailey won gold in 9.84secs (Bolt’s recent time was 9.72s, so quite a lot faster) and Johnson won gold in 19.32 secs. Because of the occasion, and proximity, the debate was particularly hot. It even led to the creation of a marketing exercise where the two raced over 150m (which we pick up below).
The study was written by a Robert Tibshirani, Professor in Biostatistics at the University of Toronto, and was published in a journal called The American Statistician. As you might infer, it’s heavy on the stats, so we won’t go into massive detail on the methods and the various analyses performed, but pull out the most relevant information – split times and speeds!
The problem with the study is that split times were not proactively recorded, and so Tibshirani had to go back and estimate some of the times at 10m intervals during the races. He did this off the TV screen, manually, and the result is some very dodgy splits – for example, his estimates give Johnson’s second 50m split as 3.82 seconds, which is far too fast to be accurate. His estimation also gives a third split that is too slow, and so likely the 150m estimate is false. However, his overall model is still revealing, though we’re not going to tackle the exact times, but rather the principle – I just don’t believe the estimates are accurate enough to base any conclusion on.
So the graph below shows a curve that he fitted to his data. This curve is “fitted” using statistical methods, which take care of some of the error in the measurement, but it’s the shape and peaks that are of most interest:
Two things to note:
First, what has been done is to move Bailey’s race along the x-axis so that it corresponds to Johnson’s second 100m interval. When done this way, it’s clear how big the effect of a running start is – Johnson is already moving at over 10m/s while Bailey is accelerating. Bailey takes about four seconds to get up to Johnson’s speed, but you can appreciate that by then, he’s well behind in the hypothetical “race”.
Second, the peak speed achieved by Bailey is faster than Johnson’s. He gets up to 13.2 m/s (47.5 km/hour), compared to Johnson’s 11.8 m/s (42.5 km/hour). Here again, you can see the effect of “estimations”, because the margin for error (about 0.5 seconds) means that the maximum speeds might actually go up to 51.5 km/hour (or it could come down to 42 km/hour). For example, Bailey was clocked with a radar gun in the race, and then the speed was 43.6 km/hour. So the exact numbers are difficult to know outside of exact measurements. But it is clear that Bailey, on the grounds of Peak Speed, is faster than Johnson. For many, case closed…!
For comparison purposes, Bailey’s top speed in this race was HIGHER than the top speed achieved by BEN Johnson in his famous 1988 Seoul Olympic victory – he was later disqualified, but nevertheless, in running 9.79 seconds. But his peak speed, according to Tibshirani, was “only” about 12m/s (43.2 km/hour). His performance was achieved thanks to a faster start than Bailey, which would have seen him a stride clear after about 60 m, which would never quite have been closed. The graph below shows those speeds.
So who is the fastest then?
Well, on the basis of these kinds of results, one suspects that the 100m man, who seems likely to hit a higher top speed than the 200m runner, is likely the rightful “Fastest man” in the world. However, because the data is never really measured accurately, it is still not 100% clear. And so having discovered that research paper courtesy of Jen (thanks very much), we must confess that it doesn’t fully answer the question! However, we will not close the book on this issue just yet, and promise to look up another study or two, where data was more accurately measured as part of a proper study (rather than a retrospective look back on the race).
A promotional opportunity for the sport?
On that note, wouldn’t it be great for the sport if the “powers-that-be” (the IAAF) made an effort to measure these kinds of things properly? Can you imagine if the post-race discussion of the Olympic 100m and 200m finals included an analysis of who was fastest, who accelerated the quickest, who slowed down the most? A bit more detail, in “real-time”. It could only be good for the sport, and make it more attractive to watch for people hungry for information. Those who are not, simply ignore the info while waiting for the next event. If anyone from the IAAF is reading, take us up and use the analysis and information to promote the sport! We’d certainly be interested.