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Who Is the Fastest Man in the World? Author(S): Robert Tibshirani Source: the American Statistician, Vol Who Is the Fastest Man in the World? Author(s): Robert Tibshirani Source: The American Statistician, Vol. 51, No. 2 (May, 1997), pp. 106-111 Published by: Taylor & Francis, Ltd. on behalf of the American Statistical Association Stable URL: http://www.jstor.org/stable/2685397 Accessed: 06-09-2016 17:35 UTC REFERENCES Linked references are available on JSTOR for this article: http://www.jstor.org/stable/2685397?seq=1&cid=pdf-reference#references_tab_contents You may need to log in to JSTOR to access the linked references. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms Taylor & Francis, Ltd., American Statistical Association are collaborating with JSTOR to digitize, preserve and extend access to The American Statistician This content downloaded from 171.67.34.69 on Tue, 06 Sep 2016 17:35:33 UTC All use subject to http://about.jstor.org/terms Who is the Fastest Man in the World? Robert TIBSHIRANI Table 1. Results for 1996 Olympic 100 m Final; The Reaction Time is the Time it Takes for the Sprinter to Push Off the Blocks after the Firing of the Starter's Pistol; DQ Means Disqualified I compare the world record sprint races of Donovan Bailey and Michael Johnson in the 1996 Olympic Games, and try Name Time Reaction time to answer the questions: 1. Who is faster?, and 2. Which 1. Bailey, Donovan (Canada) 9.84 +.174 performance was more remarkable? The statistical meth- 2. Fredericks, Frank (Namibia) 9.89 +.143 ods used include cubic spline curve fitting, the parametric 3. Bolton, Ato (Tobago) 9.90 +.164 bootstrap, and Keller's model of running. 4. Mitchell, Dennis (United States) 9.99 +.145 5. Marsh, Michael (United States) 10.00 +.147 KEY WORDS: Sprinting; World record; Curve fitting. 6. Ezinwa, Davidson (Nigeria) 10.14 +.157 7. Green, Michael (Jamaica) 10.16 +.169 8. Christie, Linford (Great Britain) DQ Wind speed: +.7 rn/s 1. INTRODUCTION At the 1996 Olympic Summer Games in Atlanta both Donovan Bailey (Canada) and Michael Johnson (United obtained from Swiss Timing and reported in the Toronto States) won gold medals in track and field. Bailey won the Sun newspaper. These times were not recorded for John- 100 meter race in 9.84 seconds, while Johnson won the son. The value 7.7 at 70 m is almost surely wrong, as it 200 meter race in 19.32 seconds. Both marks were world would imply an interval time of only 0.5 seconds for 10 records. After the 200 m race, an excited United States tele- m. I contacted Swiss Timing about their possible error, and vision commentator "put Johnson's accomplishment into they rechecked their calculations. As it turned out, the split perspective" by pointing out that his record time was less times were computed using a laser light placed 20 m be- than twice that of Bailey's, implying that Johnson had run hind the starting blocks, and they had neglected to correct faster. Of course, this is not a fair comparison because the for this 20 m gap in both the 70 and 80 m split times. The start is the slowest part of a sprint, and Johnson only had corrected times are shown in Table 3. to start once, not twice. The estimated times at each distance shown in Table 4 Ato Bolton, the sprinter who finished third in both races, were obtained manually from a videotape of the races. Here was also overwhelmed by Johnson's performance. He said is how I estimated these times. I had recorded the 100 m that, although normally the winner of the 100 meter race hurdles race on the same track. Using the known positioning is considered the fastest man in the world, he thought that of the hurdles, I established landmarks on the infield whose Johnson was the now the fastest. distance from the start I could determine. Then by watching In this paper I carry out some analyses of these two world a video of the sprint races in slow motion, with the race record performances. I do not produce a definitive answer to clock on the screen, I estimated the time it took to reach the provocative question in the title, as that depends on what each of these markings. one means by "fastest." Hopefully, some light is shed on Table 5 compares the estimated and official split times. this interesting and fun debate. Some empirical data might After the 40 m mark, the agreement is fairly good. The soon become available on this issue: a 150 meter match race disagreement at 10, 20, and 30 m is due to the paucity of between the two runners is tentatively scheduled for June data and the severe camera angle for that part of the race. 1997. Fortunately, these points do not have a large influence on the results, as our error analysis later shows. Overall, this agree- ment gives us some confidence about the estimated times 2. SPEED CURVES The results of the races are shown in Tables 1 and 2. A straightforward measure of a running performance is Table 2. Results for 1996 Olympic 200 m Final; "?" Means the Information was Not Available the speed achieved by the runner as a function of time. The first line of Table 3 gives the interval times for Bailey, Time at Reaction Name Time 100 m time 1. Johnson, Michael (United States) 19.32 10.12 +.161 Robert Tibshirani is Professor, Department of Preventive Medicine 2. Fredericks, Frank (Namibia) 19.68 10.14 +.200 and Biostatistics and the Department of Statistics, University of Toronto, 3. Bolton, Ato (Trinidad and Tobago) 19.80 10.18 +.208 Toronto, Ont., Canada M5S 1A8. The author thanks Trevor Hastie, Ge- 4. Thompson, Obadele (Barbados) 20.14 ? +.202 off Hinton, Joseph Keller, Bruce Kidd, Keith Knight, David MacKay, Carl 5. Williams, Jeff (United States) 20.17 ? +.182 Morris, Don Redelmeier, James Stafford, three referees, and two editors for 6. Garcia, Ivan (Cuba) 20.21 ? +.229 helpful comments, Cecil Smith for providing Bailey's official split times 7. Stevens, Patrick (Belgium) 20.27 ? +.151 from Swiss Timing, and Guy Gibbons of Seagull Inc. for providing the 8. Marsh, Michael (United States) 20.48 ? +.167 corrected version of the Swiss Timing results. This work was supported by the Natural Sciences and Engineering Research Council of Canada. Wind speed: +.4 rn/s 106 The American Statistician, May 1997, Vol. 51, No. 2 (?) 1997 Americani Statistical Associationt This content downloaded from 171.67.34.69 on Tue, 06 Sep 2016 17:35:33 UTC All use subject to http://about.jstor.org/terms Table 3. Official Times at Given Distances for Bailey; The "?" Indicates a Suspicious Time, Later Found to be in Error Distance (m) 0 10 20 30 40 50 60 70 80 90 100 Original time (s) .174 1.9 3.1 4.1 4.9 5.6 6.5 7.7? 8.2 9.0 9.84 Corrected time (s) .174 1.9 3.1 4.1 4.9 5.6 6.5 7.2 8.1 9.0 9.84 Table 4. Estimated Times at Given Distances; Bailey Starts at the 100 m Mark; "+" Denotes Distance Past 100 m: For Example, "+ 12.9" Means 112.9 m Distance (m) 0 50 100 + 12.9 +40.3 +49.4 +67.7 +76.9 +86.0 +100 Bailey: .174 2.8 5.0 5.7 7.0 7.8 8.5 9.84 Johnson: .161 6.3 10.12 11.4 14.0 14.8 16.2 17.0 17.8 19.32 Table 5. Comparison of Official and Estimated Interval Times for Bailey Distance (m) 0 10 20 30 40 50 60 70 80 90 100 Official .174 1.9 3.1 4.1 4.9 5.6 6.5 7.2 8.1 9.0 9.84 Estimated .174 2.1 3.4 4.3 5.1 5.7 6.4 7.2 8.0 8.9 9.84 Table 6. Estimated Times (seconds) for Johnson for Distances over 100 m 100 110 120 130 140 150 160 170 180 190 200 Johnson 10.12 11.10 12.09 13.06 13.97 14.83 15.61 16.40 17.26 18.23 19.32 for Johnson, and some idea of the magnitude of their error. the 100 m mark was 12.4 m/s, and his speed was decreasing The speed curves were estimated by fitting a cubic smooth- by only .036 m/s every 10 m. Johnson's estimated time at ing spline to the first differences of the times, constraining 150 m was 14.83 s, as given in Table 6. In order to beat the curves to be 0 at the start of the race. The curves for that time Bailey would need "only" to maintain an average each runner are shown in the top panel of Figure 1. Because speed of more than 10.02 m/s for another 50 m. Of course, Bailey's 100 m was much faster than Johnson's first 100 m it is not clear whether he could do this. In the next section but slower than his second 100 m, it seems most interest- we appeal to a parametric model to perform the necessary ing to make the latter comparison.
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