ONE TO ONE CHALLENGE OF CHAMPIONS Prognosticators hit stride at conclusions NUMBER CRUNCHING / Statistical methodology runs up against speed curves to find the winner
867 words
29 May 1997
The Globe and Mail
Metro
C2
English
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Here's a dish of the number soup served up by various statisticians and track experts in considering the Fastest Man question:
-- James Christie, The Globe and Mail: "Bailey goes through the 100 metres in 9.84 and Johnson in 10.12. In full flight, Johnson ran his last 100 metres in 9.2 seconds, but Bailey closed the 4 x 100 Olympic relay in 8.95 seconds. Bailey may fade after 100 metres, but he'll have to hit a brick wall to lose an advantage that size in the last 50 metres."
-- Runner's World, the authoritative U.S. running magazine, noted after the Olympics "Bailey ended the controversy when he anchored Canada's 4 x 100-metre relay team to the gold medal with a split timed at . . . 8.95 seconds."
-- John Rucker wrote to The Globe from the University of Toronto's Department of Human Biology to pooh-pooh references to Johnson's superior average speed in comparisons of the Olympic 200 metres and 100 metres. Johnson averaged 37.267 kilometres an hour in his race and Bailey 36.585 km/h in his event.
"The slowest part of any short-distance race is the first 10 metres. Donovan Bailey would obviously have a lower average speed than Michael Johnson because, in a 100-metre race the first 10 metres account for 10 per cent of the race, where as in a 200-metre race they account for only 5 per cent of the race. . . .
"Technically, the world's fastest man is the person who can achieve the highest instantaneous speed, which would be Bailey, who at one point in his race reached 12.1 metres per second (43.6 kilometres per hour)."
-- Rob Tibshirani, statistician at the U of T's Department of Preventive Medicine and Biostatistics and at the Department of Statistics filed this report on The Globe's Science page: "Two definitions of 'fastest' might be a) the highest maximum speed achieved during a race or b) the quickest time to complete the intermediate distance of 150 metres.
"The most straightforward way to address these questions is through speed curves, giving the runner's speed in metres per second at every instant during the race. To estimate speed curves we need split times -- the time it takes a runner to travel various distances during the race.
"From Swiss Timing [the official timekeeper of the Olympics] I obtained split times for every 10 metres of Mr. Bailey's race. These were measured from a laser device situated 20 metres behind the starting blocks, which bounced beams off the backs of each runner. This device was not used in the 200-metre race, so I needed to obtain the data some other way.
"I had videotaped both races, along with the 110-metre hurdles race. Using the positioning of the hurdles, I established landmarks on the infield whose distance from the start I could determine.
"Then by watching a video of the races in slow motion, with the race clock on the screen, I estimated the time it took both Mr. Bailey and Mr. Johnson to reach each of these markings. . . . Using these split times, I developed a curve-fitting procedure to produce the estimated speed curves. If Mr. Johnson's speed curve always lay above Mr. Bailey's, then this analysis would provide convincing evidence in favour of Mr. Johnson, since he achieved his speed despite having already run 100 metres.
"However, Mr. Bailey's curve does rise above Mr. Johnson's, and he achieves a higher maximum speed. Taking into account the uncertainty in the estimated times of these results, I found that the maximum speeds were not statistically different at the 95-per-cent level of confidence. This comparison does not permit a definitive conclusion.
"We turn to the second method: Who would win a race of 150 metres? We could try to extrapolate Mr. Bailey's speed curve out to 150 metres.
However, at the 100-metre mark Mr. Bailey was slowing down and we have no way of knowing what speed he could have maintained for another 50 metres."
Thus, Tibshirani applied a well-known model of sprinting.
"I found an interesting model developed by Professor Joseph Keller of Stanford University in California in 1974. Prof. Keller's model predicts the speed of a sprinter as a function of two parameters for that runner: the force he applies and the resistance he encounters. I fit his model to the speed curves for Mr. Bailey and Mr. Johnson, finding the values for force and resistance that best match the theoretical and estimated speed curves for each runner.
"The estimated 150-metre times from this model were 14.73 seconds for Mr. Bailey and 14.82 seconds for Mr. Johnson. Taking into account the uncertainty in the analysis, Mr. Bailey's winning margin of 0.09 seconds is statistically significant. The model predicts that Mr. Bailey would win by between 0.03 and 0.22 seconds 95 times out of 100."