Beyond the High-Tech Suits: Predicting 2012 Olympic Swim Performances

Measurement in Physical Education and Exercise Science, 16: 183 193, 2012 Copyright Taylor & Francis Group, LLC ISSN: 1091-367X print / 1532-7841 online DOI: 10.1080/1091367X.2012.700253 Beyond the High-Tech Suits: Predicting 2012 Olympic Swim Performances Chris L. Brammer, Joel M. Stager, and Dave A. Tanner Counsilman Center for the Science of Swimming, Indiana University, Bloomington, Indiana The purpose of the authors in this study was to predict the mean swim time of the top eight swimmers in swim events at the 2012 Olympic Games based upon prior Olympic performances from 1972 through 2008. Using the mean top eight time across all years, a best fit power curve [time = a year b ] was calculated and used to predict the finish time of the finalists for each event. Every event except the women s 100 breaststroke is predicted to be slower in 2012 than it was in 2008. However, the results of the 2008 swimming competition were shown to be biased, likely caused by the now banned tech suits. The authors hypothesize that the 2012 Olympic performances will realign with the prediction curves, thus demonstrating the reliability and sensitivity of the model and further confirming the suit bias of 2008. Final conclusions will be dependent upon the athletes performances at the 2012 Games. Key words: London Olympics, swimming, textile technology, swim predictions INTRODUCTION The interpretation of performance trends using compiled results of athletic competitions dates back to the end of the 19th century, presumably coincident with the start of the modern Olympic Games. Today, because of the easy and nearly instantaneous access to competition results, there is a renewed interest in understanding the nature and prevalence of outstanding performances, particularly as they relate to Olympic and world records. For example, a real-time comparison of an athlete s performance to the world record performance is commonly used to capture spectators interest. Further, new analytic techniques to evaluate the success of training regimes for individual athletes, team performances, and even national sport agendas are becoming commonplace. The recent movie based upon the book authored by Michael Lewis, Moneyball, does well to illustrate how quantitative analysis is beginning to influence diverse aspects of amateur and professional sports. From the scientific perspective, the analysis of athletic performance provides an illustration of the progress of man s peak performance. Factors affecting performance can then be identified, and our knowledge of how to improve athletic performance expands. For instance, advances in technology and athletic nutrition over the last 25 years may have led to acceleration in Correspondence should be sent to Chris L. Brammer, Counsilman Center for the Science of Swimming, PO Box 1351, Davidson, NC, 28036. E-mail: Brammer.Chris@gmail.com

184 BRAMMER, STAGER, AND TANNER performance improvement. Any significant change in the performance trend represents a bias, favourable or not. This, identifying potential bias in athletic performance, is the primary focus of the current study. In the early 20th century, Hill (1925) described and proposed that common factors contribute to performance in many sports and equally in both sexes (Figure 1, top). Hill s early research on the nature of the changes in athletic performance as the duration of the event increased led to the conclusion that performance was influenced (or limited) by common physiological parameters. FIGURE 1 Men s Freestyle Record Progression (1925 vs. current). Top: World records plotted as a function of average speed vs. event duration (Hill, 1925). Bottom: Recreation of Hill s graph of swimming speed vs. performance time. The solid line represents the current limits to freestyle swimming, whereas the dashed line represents records from 1925. The slopes of the two lines are not significantly different (color figure available online).

PREDICTING 2012 OLYMPIC SWIM PERFORMANCES 185 Nearly a century later, the nature of these relationships appears to be unchanged with no escape from these common limiting factors being evident (Figure 1, bottom). As the required endurance (or rather, the length of the athletic event) increases, the speed at which an athlete can perform the event still necessarily decreases. In addition, at any given event length, the progression or improvement in performance (over the years) has not appeared to disproportionally change. Distance athletes do not appear, for example, to have improved to a greater extent than sprint athletes. Thus, we expect that performances over time have improved similarly, regardless of their duration, although with some amount of variability between events. The variable rate of record progression within an event over time, however, has led recent authors to use S-shaped logistic (Nevill & Whyte, 2005), second order polynomial (Seiler, De Koning, & Foster, 2007), and multiple exponential decay (Berthelot et al., 2008) models to illustrate athletic performance progressions. Although these curves may better fit historical performance data, they may necessarily account for variation due to bias or chance. If these models are to be useful to predict future performance, then they must minimize historical and undefined chance influences since these factors are inherently unreliable (Frucht & Jokl, 1964). Rather, it is likely that a single power curve, one that carries a certain range of error and asymptotically approaches a describable limit, better describes the systematic progression of athletic performance. To do so, however, researchers are forced to focus on group performances rather than individual performance or that of records per se. An example of this is Figure 2, representing the improvement in swim speed in one competitive event, the men s 100-meter freestyle, where speed is the recorded mean time (y-axis) as a function of longitudinal time (years or this case Olympiads ) on the x-axis. This figure supports the fact FIGURE 2 Men s Olympic 100M Freestyle Progression (1972 2008). The average of the top-8 performances for the men s Olympic 100M Freestyle plotted longitudinally over time (1972 2008). The x-axis represents Olympiads beginning with 1972 and continuing until 2008. The solid line represents the best fit for the relationship. The dotted lines represent the 95% confidence interval.

186 BRAMMER, STAGER, AND TANNER that 1) there has been a non-linear, longitudinal progression in performance, and 2) certain data can be identified as being statistically inconsistent with the preceding data (swim performances) and/or all subsequent data. In Figure 2, for example, only two Olympic Games during which swimmers did not perform as expected (outside of the 95% confidence interval): once in 1980 and again in 2008. One caveat to any mathematical analysis of performance based upon available records of historical performances is to accept that undefined and confounding variables may introduce biases into the analysis and potentially perturb the ability of any subsequent modelling to be accurate. As time goes by, additional performances will act to correct the model, allowing for any earlier unconfirmed bias to be obvious (assuming that which caused the bias is no longer present). However, the causes of the temporary perturbations will be speculative at best, until reinforced by historical confirmation. The Olympic boycott by the USA in 1980 may have been cause for the relatively slow Olympic performances at these games and the subsequent return to the normal progression with the USA s participation thereafter. To illustrate this effect further, the focus of this paper will be upon the progression in athletic performances (within competitive swimming), where a known and artificial perturbation was introduced in 2008 and was subsequently removed two years later in 2010. Specific to the present discussion is the recent, hugely controversial technical suit issue in competitive swimming. In 2008, with the introduction of high-tech body suits, the swimming community experienced an extraordinary advancement in performance. At the 2008 Beijing Olympic Games, elite swimmers were shown to perform significantly faster than predicted (Brammer, Tanner, & Stager, 2009). The increased performance was speculated to be due to changes in body buoyancy caused by the new fabrics incorporated into these suits. It was also determined (by the athletes) that the performance effects of these suits could be magnified by wearing multiple suits simultaneously. In 2010, the Federal International Natation Amateur (FINA) proposed and enforced new rules that prevent swimmers from competing while wearing the newly introduced swimwear with which the athletes had achieved obvious success in the previous two years. The obvious question to pose is how will the swimmers accommodate to the new level of performance, now that artificially enhanced speeds have become normal and expected? Interestingly, because none of these new suits existed prior to 2000 and because it is possible to document when newer versions have been introduced, the athletes and their performances can be used to test if these suits have introduced unnatural rates of improvement in swim performance. It is reasoned that the influence of the new high-tech suits can be measured if swim performance models are sensitive enough to do so. The governing bodies and swimmers in 2012 will participate in an experiment that will allow further understanding of the progression in athletic performance and the ability to quantify performance bias. Our primary purpose in this research was to use past Olympic performances to predict 2008 and 2012 Olympic swim performances and to determine if the exceptional performances in 2008 were biased. We hypothesize that, based on the predictive model, 2008 performances will not fit expectations, but the 2012 Olympic performances will. The swimmers choice of swimwear in 2008 will explain our failures, and the suit restrictions imposed in 2010 will explain the accurate prediction of the 2012 Olympic Games.

PREDICTING 2012 OLYMPIC SWIM PERFORMANCES 187 METHODS The top eight times from the finals of Olympic swimming events from the years 1972 through 2008 were obtained on-line from www.swimnews.com and www.usaswimming.org. Data were analyzed for mean and standard deviation. A best-fit power curve of the form Time = a year b was computed across all years for each event, where a and b were coefficients, and year was the code for the year of the Olympics (1 = 1972, 2 = 1976, and so on up to 10 = 2008). Using year = 11 to indicate 2012, the power equations were used to predict the mean performance time of the eight finalists for each individual event for the upcoming 2012 London Olympic Games. The percent difference between the predicted time and the actual time (absolute value) was calculated for each past year and averaged within each event. This number was used to estimate the standard deviation of the predicted time for each event using the formula 1.25 (mean percent difference) (predicted value)/100. This standard deviation was used to establish the 95% confidence interval for that event (predicted time ± 2 standard deviations). The actual mean time of the finalists of the 2012 Olympics will be compared to this 95% confidence interval. Actual times that fall outside the interval will be considered significantly faster or slower than predicted performances. In addition, each of the previous six Olympic competitions was examined by using the same analysis. Furthermore, the number of instances where the actual performance time was above or below the corresponding prediction curve was counted. A binomial test of statistical significance was then used to determine if the number of events that were faster or slower than predicted was not expected due to chance alone. The results of this analysis determined whether or not a particular year was faster or slower, in general, than predicted. 2008 Olympic Analysis RESULTS AND DISCUSSION The historical progression in elite swim performance is such that improvements tend to get smaller from year to year, and thus, the line describing them is not linear but rather one with a decreasing slope as time progresses. Because of the small variance within elite swim times, a performance progression line based on Olympic finalists can be used to extrapolate future performances. Stager, Brammer, and Tanner (2010) tested the accuracy of their predictions by comparing them to actual performances at each of the previous six Olympic Games (1988 2008). Adding data obtained from competitions before that time did not strengthen the nature of the relationships generated as might have been hypothesized. In other words, events two decades prior to the current competition were shown to have little predictive value on future competitions occurring more than twenty years later. In contrast to the analyzed results for 2000 and 2004, the actual competition results for the 2008 swimming events were, in general, exceptionally fast and did not fit the expectations of the mathematical model. The model successfully predicted the outcomes of the 2000 and 2004 competitions with only a few exceptions. In 2000, the outcome of only one of 26 events exceeded

188 BRAMMER, STAGER, AND TANNER predictions (men s 100M butterfly), and in 2004, only two events (men s 100M butterfly and 200M individual medley) failed the model. In contrast, for the 2008 Olympic Games, 10 out of 13 (77%) men s and 7 out of 13 (54%) women s events recorded mean times for the eight finalists that were significantly faster than the predicted outcomes. In several cases, the actual performances were in excess of five standard deviations from the predicted mean. Only 34% of the events in the 2008 Games were successfully predicted by the models. To put this in context, between 1988 and 2004, 87% of all events were successfully predicted. These data are presented in Table 1 and Figure 3. Similar calculations comparing actual versus predicted performances for each of the previous six Olympics were performed. The number of standard deviations the predicted performance differed from the actual in each event was averaged by Olympic year. When all events are pooled, the 2008 Games deviated from the model based predictions more than any previous Games, with the average event offset being faster than statistical models by nearly three standard deviations (Figure 4). From 1988 until 2004, only one other Games stood out significantly. In that case (1996), however, the swimmers were slower than predicted, not faster. Additionally, unlike in 2008, the events of the 1996 Games were, on average, within the predicted range of outcomes (i.e., within the 95% confidence interval). For prior Olympics (1988 2004), the performances of the women were significantly slower than expected (p <.05) in 1992 and 1996. In contrast, for the Olympic Games in 1988, 2000 and 2004, women swimmers performed as expected. Performances of the men were significantly faster than expected in 2000 (p <.05). However, the Games in 1988, 1992, 1996, and 2004 were as predicted. The men and women combined swam significantly slower than expected (p <.05) in 1996, significantly faster than expected in 2000 (p <.05), and as expected in 1988, 1992, and 2004. The binomial test of statistical significance revealed that the 2008 Olympic swimming TABLE 1 Summary of Men s Olympic Prediction Results in 2000, 2004, and 2008 2000 prediction analysis 2004 prediction analysis 2008 prediction analysis Men s event Pred M Actual M (SD) Pred M Actual M (SD) Pred M Actual M (SD) 50 Free 22.28 22.19.85 22.10 22.11.12 22.00 21.57 5.46 100 Free 49.28 48.95 1.17 49.00 48.80.74 48.79 47.77 3.36 200 Free 1:47.58 1:47.43.19 1:47.13 1:46.49.96 1:46.61 1:45.81 1.23 400 Free 3:47.10 3:46.21.59 3:45.90 3:45.92.01 3:45.09 3:43.72 1.13 1500 Free 14:59.22 15:01.67.26 14:56.68 14:58.05.16 14:54.18 14:48.61.63 100 Back 55.03 54.85.39 54.76 54.52.57 54.50 53.28 3.04 200 Back 1:59.79 1:58.43 1.75 1:58.97 1:57.98 1.17 1:58.31 1:55.54 3.44 100 Breast 1:01.47 1:01.25.66 1:01.14 1:01.15.02 1:00.91 59.64 4.45 200 Breast 1:12.86 1:12.85.02 1:12.21 1:11.14 1.32 2:11.34 2:09.44 2.06 100 Fly 53.16 52.53 2.16 52.77 51.98 2.41 52.38 51.23 3.29 200 Fly 1:57.54 1:56.69 1.37 1:56.92 1:55.89 1.51 1:56.33 1:53.86 3.87 200 IM 2:01.26 2:01.13.42 2:00.74 1:59.71 3.55 2:00.02 1:57.88 5.46 400 IM 4:15.79 4:16.74 1.49 4:15.00 4:14.71.42 4:13.99 4:10.54 5.45 Note: Predictions were based on extrapolation of the mean of top 8 performances for each Olympics since 1972. (SD) = the number of standard deviations between actual and predicted means. = significantly faster than predicted, p <.05.

PREDICTING 2012 OLYMPIC SWIM PERFORMANCES 189 FIGURE 3 Predictive Success Rate of All Olympic Events (1988 2008). Percentage of total events successfully predicted (within 95% C.I.) for each Olympic Games for men, women, and combined men and women categories. FIGURE 4 Olympic Prediction Model Accuracy (1988 2008). Average difference, in standard deviations, between actual and predicted performances of Olympic swimming events. A positive value denotes the average of actual event means were faster than the predicted event means. denotes significant difference compared to all other groups.

190 BRAMMER, STAGER, AND TANNER TABLE 2 Binomial Distribution Analysis of the Difference Between Actual and Predicted Performances Men Women Total Slower Faster Slower Faster Slower Faster 1988 2 9 4 7 6 16 1992 4 8 10 2 14 10 1996 8 4 12 0 20 4 2000 2 11 4 9 6 20 2004 4 9 7 6 11 15 2008 0 13 0 13 0 26 Note: Values represent the count of events that were faster or slower than predicted (below or above the regression line). = probability that x number of events is slower, p <.05. = probability that x number of events is faster, p <.05. events were, as a whole, significantly faster than expected (p <.05). Surprisingly, all 26 events (men and women) were faster than the equations predicted, though they were not necessarily significantly faster than predicted. The results of binomial tests of statistical significance are presented in Table 2. Until 2008, predictive modelling was largely successful in describing swim performance at the elite level. Performances in 2008 were significantly faster than predicted, in a manner inconsistent with the natural progression of swim performance observed over the last half century. Although depressed performances in 1980 were largely a function of an Olympic boycott that affected the participating athletes, there is little to no evidence to suggest any pervasive performance enhancing bias existed before 2008 for men or women. Despite the introduction of new fabrics and greater skin coverage beginning prior to the 2000 games, there was limited evidence of a noticeable effect upon performance until the hightech suits were introduced immediately prior to the 2008 Beijing Games. Contributing to this effect was the swimmers practice of wearing two or three suits during competition to increase buoyancy. While there is no documentation of what swimmer wore what suit during the competitions in 2008, it became even more difficult to determine performance benefits as swimmers wore multiple suits and different manufacturers products in various combinations. FINA rule changes since 2008 have eliminated this practice. Coaches and athletes at the elite level have not suggested any definitive alternate explanations for the dramatic improvements in swimming performance other than the introduction of the so called high-tech suits. Due to the nature of commerce and claims of proprietary knowledge, very little specific data exist identifying the magnitude and/or specific causes of the effects of these suits upon swim performance. While the current study does not directly measure the effect of the new technology swim suits in the water, the athletes and their performances suggest that these suits introduced unnatural rates of improvement into the sport. 2012 Predictions The causes of this temporary perturbation may be reinforced by historical confirmation in 2012. The 2008 performances were determined to be significantly biased; therefore, they were excluded

PREDICTING 2012 OLYMPIC SWIM PERFORMANCES 191 TABLE 3 2012 Men s Olympic Swimming Predictions Predicted 2012 Men s Events 2008 Actual Pred M ± S.D. 95% Confidence interval 50 Free 21.57 21.91.08 21.75 22.07 100 Free 47.77 48.64.25 48.15 49.13 200 Free 1:45.81 1:46.27.64 1:45.01 1:47.53 400 Free 3:43.72 3:44.35 1.23 3:41.95 3:46.75 1500 Free 14:48.61 14:51.59 7.34 14:37.21 15:05.97 100 Back 53.28 54.32.38 53.57 55.07 200 Back 1:55.54 1:57.96.86 1:56.27 1:59.65 100 Breast 59.64 1.00.70.27 1:00.17 1:01.23 200 Breast 2:09.44 2:10.80.89 2:09.06 2:12.54 100 Fly 51.23 52.21.38 51.47 52.95 200 Fly 1:53.86 1:56.01.77 1:54.51 1:57.51 200 IM 1:57.88 1:59.62.47 1:58.70 2:00.54 400 IM 4:10.54 4:13.13.65 4:11.85 4:14.41 Note: Shows a comparison of 2012 Olympic predictions to the 2008 actual Olympic performances in each event. The 2012 predictions were based on Olympic data from 1972 2004 (without the inclusion of 2008 results). All of the event outcomes are predicted to be slower than in 2008. from the 2012 prediction analysis. If the advancement in performance was not due to the introduction of the suits but rather due to better coaching or enhanced training techniques, then the bias should persist in 2012, and the prediction model will again fail. Alternately, if the suits did artificially improve performance, then the 2010 ban on high-tech swimwear will cause 2012 to return to the pre-2008 performance progression curve, and the prediction model will be deemed accurate. Given the results of the 2012 Olympic prediction analysis, we predict that the aggregate 2012 swimming performances will be, on average, slower than in 2008 (Tables 3 & 4). The predicted 2012 Olympic performances in Tables 3 and 4 represent the predicted mean of the top-eight performances for each event of the 2012 Olympic Games, based on Olympic data from each of the last ten Games, except 2008. Each prediction includes a standard deviation and a 95% confidence interval. Results that fall outside of this boundary will be deemed significantly faster or slower than predicted. The prediction model predicts that every event except the women s 100M breaststroke will be slower in 2012 than in 2008. If we attempt to predict which events are most likely to be faster than in Beijing, then it is best to do so under the context of its historical progression. Comparing actual 2008 performances to the prediction model, the corresponding year reveals either the length of time we are behind expectations, or the length of time that we need to catch up with the artificially enhanced 2008 performances. Assuming each event improves at a unique pace, then some events necessarily lag behind others in terms of the global performance progression. Indeed, the model predicts that certain performances in 2008 are not expected to be achieved (unaided) until many years down the road. Other performances from Beijing, because these events have not progressed to the same degree, have a greater potential of being improved upon in London. Based on the pre- 2008 prediction curve, performances in 4 out of 13 men s and 9 out of 13 women s events are expected to be faster in 2012 than they were in 2008 (Table 5).

192 BRAMMER, STAGER, AND TANNER TABLE 4 2012 Women s Olympic Swimming Predictions Predicted 2012 Women s Events 2008 Actual Pred M ± S.D. 95% Confidence interval 50 Free 24.36 24.67.09 24.50 24.84 100 Free 53.80 54.28.30 53.70 54.86 200 Free 1:56.35 1:57.76.58 1:56.63 1:58.89 400 Free 4:04.89 4:06.42 1.65 4:03.18 4:09.66 800 Free 8:24.42 8:24.69 3.28 8:18.26 8:31.12 100 Back 59.53 1:00.65.35 59.97 1:01.33 200 Back 2:07.77 2:09.45 1.01 2:07.47 2:11.43 100 Breast 1:07.30 1:06.98.32 1:06.35 1:07.61 200 Breast 2:23.30 2:23.80.83 2:22.17 2:25.43 100 Fly 57.70 58.36.48 57.42 59.30 200 Fly 2:06.58 2:07.77.71 2:06.38 2:09.16 200 IM 2:10.86 2:12.26.42 2:11.44 2:13.08 400 IM 4:35.15 4:36.96 2.46 4:32.13 4:41.79 Note: Shows a comparison of 2012 Olympic predictions to the 2008 actual Olympic performances in each event. The 2012 predictions were based on Olympic data from 1972 2004 (without the inclusion of 2008 results). With only one exception, the women s 100M Breaststroke, the event outcomes are predicted to be slower than in 2008. TABLE 5 Predicted Year the 2008 Olympic Performances were Expected Men Women Men Women Event 2008 top-8 Year 2008 top-8 Year Event 2008 top-8 Year 2008 top-8 Year 50 FS 21.57 2020 24.36 2016 100 BR 59.64 2024 1:07.30 2001 100 FS 47.77 2023 53.80 2009 200 BR 2:09.44 2008 2:23.30 2005 200 FS 1:45.81 2002 1:56.35 2015 100 FL 51.23 2017 57.70 2006 400 FS 3:43.72 2002 4:04.90 2001 200 FL 1:53.86 2021 2:06.58 2009 1500 FS 14:48.61 1996 8:24.42 1995 200 IM 1:57.88 2021 2:10.86 2017 100 BK 53.28 2019 59.53 2021 400 IM 4:10.54 2018 4:35.15 2000 200 BK 1:55.54 2020 2:07.77 2008 Note: Using the pre-2008 progression curve for each event, the year in which the 2008 performance is predicted to occur is provided. For example, the 2008 men s 50 Freestyle top-8 average performance of 21.57 seconds was expected to occur in the year 2020. However, in many cases, the 2008 performances are between one and two standard deviations faster than the predicted 2012 values (Tables 3 & 4). Thus, these predictions would have to be globally underestimating 2012 performances in order for the London Games, as a whole, to be faster than the Beijing Games. Given the results of the previous analysis (Table 2, Figure 3, & Figure 4), it is just as likely that, rather than underestimating 2012 performance, the model either accurately predicts, or overestimates actual performance. Unfortunately, predicting swim performance is a complex endeavour, and too often significant variables are not taken into account. If perceptions of what is possible and what comes

PREDICTING 2012 OLYMPIC SWIM PERFORMANCES 193 to be expected mirror the rate of performance improvement, and if these perceptions drive performance outcomes, then it may follow that the suit-aided performances of 2008 changed the perception of what is possible to a point well beyond what would be possible otherwise. If those perceptions have persisted beyond FINA s ruling in 2010, then performance could continue to be elevated. If a number of performances are faster in 2012 than in 2008, the public (especially suit manufacturers) may downplay the effect of the banned suits, which may lead to renewed discussion to allow the use of high-tech suits in competition. In fact, claims are already being made by suit manufacturers that their suits (introduced in 2011 and 2012) provide performance advantages over previous fabrics and technology. Although the existing rules in swimming limit the use of aides to improve performance, commercial manufacturing of these suits has continued to provide a product that purportedly stretches those limits. However, even if the results of many of the 2012 Olympic events are faster than in 2008, they may be within the predicted range. Therefore, faster performances in 2012 than in 2008 do not necessarily mean the high-tech suits of 2008 and 2009 did little to assist performances. Conclusions These results illustrate that prior historical outcomes of athletic competition allow for the prediction of future competition to a high degree of accuracy unless a bias is introduced into the competitive environment. We hypothesize that the 2012 Olympic swim performances will realign with our prediction model, thus demonstrating the reliability of the authors prediction analysis and confirming the suit bias of 2008. We readily admit that these results are only partially complete, as the test of this analysis (i.e., the success of our predictions) awaits the conclusion of the 2012 Olympic Games. REFERENCES Berthelot, G., Thibault, V., Tafflet, M., Escolano, S., El Helou, N., Jouven, X., Hermine, O., & Toussaint, J. F. (2008). The citius end: World records progression announces the completion of a brief ultra-physiological quest. PLoS ONE, 3, e1552. Brammer, C. L., Tanner, D. A., & Stager, J. M. (2009). Identification of bias in the natural progression of swim performance. Medicine and Science in Sports and Exercise, 41, S306. Frucht, A. H., & Jokl, E. (1964). Parabolic extrapolation of Olympic performance growth since 1900. Journal of Sports Medicine and Physical Fitness, 4, 142 152. Hill, A.V. (1925). The physiological basis of athletic records. Nature, 116, 544 548. Nevill, A. M., & Whyte, G. (2005). Are there limits to running world records? Medicine and Science in Sports and Exercise, 37, 1785 1788. Seiler, S., De Koning, J., & Foster, C. (2007). The fall and rise of the gender difference in elite anaerobic performance 1952 2006. Medicine and Science in Sports and Exercise, 39, 534 540. Stager, J. M., Brammer, C. L., & Tanner, D. A. (2010). Identification of a bias in the natural progression of swim performance. In P. Kjendlie, R. Stallman, & J. Cabri (Eds.), Biomechanics and medicine in swimming XI (pp. 294 296). Champaign, IL: Human Kinetics.