European Journal of Sport Science, March 2006; 6(1): 25 /31
ORIGINAL ARTICLE
Variation in performance of elite cyclists from race to race
CARL D. PATON1 & WILL G. HOPKINS2 1
Centre for Sport and Exercise Science, The Waikato Institute of Technology, Hamilton, New Zealand, and 2Department of Sport and Recreation, Auckland University of Technology, Auckland, New Zealand
Abstract The race-to-race variation in performance of a top athlete determines the smallest change in performance affecting the athlete’s chances of winning. We report here the typical variation in competition times of elite cyclists in various race series. Repeated-measures analysis of log-transformed official race times provided the typical variation in a cyclist’s performance as a coefficient of variation. The typical variation of a top cyclist (and its 95% likely limits) was 0.4% (0.3 /0.5%) in World Cup road races, 0.7% (0.7 /0.8%) in Tour de France road races, 1.2% (0.8 /2.2%) in the Kilo, 1.3% (0.9 /2.4%) in road time trials, 1.7% (1.2 /2.6%) in Tour de France time trials, and 2.4% (2.1 /2.8%) in World Cup mountain biking. Cyclist interdependence arising from team tactics and pack riding probably accounts for the lower variability in performance of cyclists in road races and precludes estimation of the smallest worthwhile change in performance time for cyclists in these events. The substantial differences in variability between the remaining events, where riders act independently of each other, arise from various event-specific aspects. For these events the smallest worthwhile changes in performance time (/0.5 / typical variation) are /0.5% in the Kilo, /0.6% in road time trials, and /1.2% in mountain-bike races.
Keywords: Competition, error, reliability, testing and evaluation
Introduction The performance of an athlete who competes as an individual always shows random variation from competition to competition. Enhancements or impairments of performance affect an athlete’s chance of a medal only if they are greater than about half the magnitude of this random variation (Hopkins et al., 1999). Information about the variation in performance of a top athlete from race to race is therefore useful for gauging the impact of factors that affect medal-winning performance. In addition, the typical variation in performance between races is a benchmark for assessing the error of measurement of performance in laboratory and field tests that are used to monitor athletes or investigate strategies affecting performance (Paton & Hopkins, 2001). As yet, the only fully published data on variability of competitive performance are for junior swimmers (Stewart & Hopkins, 2000) and non-elite runners (Hopkins & Hewson, 2001). There is clearly a need
for more studies assessing the variability of competitive performance, particularly for elite athletes. We address here the question of the magnitude of variability in performance time of top athletes competing in various cycling events.
Methods Subjects and races We searched the Web for official result times of national and international events in track cycling, road cycling and mountain biking. For adequate precision of the estimates of variability, we sought a series of races where at least 10 cyclists competed in two or more races within a competitive season. We found sufficient data for male cyclists in the following race series: the US national Kilo (1-km) time trials; international road time trials, including the 2000 Sydney Olympic race and the World championships; the 2000 World Cup road races;
Correspondence: C.D. Paton, Centre for Sport and Exercise Science, The Waikato Institute of Technology, Private Bag 3036, Hamilton, New Zealand. Tel: 64 7 8348800x8600. Fax: 64 7 8580201. E-mail:
[email protected] ISSN 1746-1391 print/ISSN 1536-7290 online # 2006 European College of Sport Science DOI: 10.1080/17461390500422796
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the 2000 Tour de France (road races and individual time trials); and for male and female cyclists, the 2001 World Cup cross-country mountain bike races. Riders in the road race series were all professional whilst all other series had a combination of professional and national amateur riders. We were unable to obtain sufficient data for analyses of top pursuit cyclists of either sex or of females in other race series.
Statistical analysis We derived estimates of variability in performance of individual cyclists from race to race using procedures described previously for competitive runners (Hopkins & Hewson, 2001). The statistical model for the analysis was that recommended for reliability studies (Stewart & Hopkins, 2000), in which the standard error of measurement is estimated after changes in the mean between repeated measurements have been controlled for. Applied to race times, the standard error of measurement is equivalent to the within-cyclist variability from race to race, and the changes in the mean are the equivalent of overall differences in duration of the races arising from any differences in distance, terrain and environmental effects. Analyses were performed with the mixed linear modeling procedure (Proc Mixed) of the Statistical Analysis System (Version 8.2, SAS Institute, Cary, NC). Race times were log transformed for the analysis, because this approach yields variability as a percent of the mean (coefficient of variation), which is the natural metric for most measures of athletic performance (Hopkins, 2000). Within- and pure between-cyclist coefficients of variation were derived by back transformation of the residual and subject random effects in the mixed model. The observed between-cyclist coefficient of variation was derived as the square root of the sum of within- and pure between-cyclist variances and represents the typical variation in performance between cyclists in any given race of the series. We compared the typical variation in performance of subgroups of cyclists by calculating the ratio of the within-cyclist coefficients of variation, and we derived likely limits for the ratio via the F distribution. We regarded CV that differed by a factor of /1.15 or }/ 1.15 (0.87) as being substantially different, because such differences would result in sample sizes differing by a factor of 1.152 or 32% in studies in which race time was the dependent variable (Hopkins & Hewson, 2001). We performed separate analyses for all data and for a top sub-group of 5 /30 cyclists in each series. We combined the data for the 1999 and 2000 Kilo series by modeling the race year as an additional source of within-subject variance.
There was no evidence of non-uniformity of error in plots of residual versus predicted values from the analyses, with the possible exception of an outlier (/3 standard deviations) in the female cross-country series; this cyclist may have had mechanical failure or a severe fall in one race, so we eliminated her data from the analysis. One aspect of nonuniformity that would not be apparent on plots of residuals is an increase in the variation of performance as the time between pairs of races increases. We used two approaches to investigate this possibility. For the Kilo and road time trials, in which there were only three races in each series, we derived the measure of a cyclist’s variability from each of the three possible pairwise combinations of races. For the mountain-bike races, in which there were 7/8 races, we analyzed the data with the autoregressive covariance structure of order 1, which is available as an option in Proc Mixed. This structure accommodates any systematic gradual reduction in test-retest correlation between pairs of trials separated by an increasing number of intervening trials. We converted the covariance parameters provided by Proc Mixed into an equivalent within-cyclist standard deviation that increased in magnitude with increasing intervening trials. This choice of covariance structure failed with the data for the Kilo and road time trials, possibly because there were insufficient data for the iterative mixed-modeling procedure to work.
Results Table I shows the mean performance times and the between- and within-cyclist variation for all cyclists and the fastest subgroup of cyclists for each race series. Table I also includes the number of races, the range of distances and time over which each race series was completed.
Between-cyclist variation The between-cyclist variation, which represents the relative depth of rider ability, was below 5% in all race series. Between-cyclist variations were smallest in the World cup and Tour de France road races and greatest in the mountain bike series (particularly amongst females). Inspection of the performance times of individual cyclists in each road race of the World Cup and Tour de France series revealed large clusters of identical times. Clusters in the hilly and mountainous stages of the Tour were obviously smaller and more numerous than those in the flat stages. A few small clusters were also apparent in the mountain-bike series.
Table I. Between and within subject variability of top cyclists and all cyclists in four types of event. Cyclist group
Mean time
Betweensubject CV (%)
Within-subject CV (%)
95%LR (%)
26 209
381 min 385 min
0.4 1.3
0.4 1.1
0.4 /0.5a 1.1 /1.2a
22 177
292 min 296 min
0.7 1.8
0.7 1.7
0.7 /0.8a 1.6 /1.7a
5 10
68 s 69 s
1.7 2.7
0.7 0.7
0.4 /1.9 0.5 /1.4
6 13
68 s 70 s
2.6 3.3
1.5 1.1
0.9 /3.7 0.8 /1.7
11 25
68 s 69 s
2.3 3.3
1.2 1.0
0.8 /2.2 0.8 /1.4
9 19
68 min 69 min
1.5 2.3
1.3 1.8
0.9 /2.4 1.3 /2.6
16 129
37 min 39 min
2.2 3.5
1.7 2.0
1.2 /2.6 1.8 /2.3
30 120
125 min 131 min
2.1 3.2
2.4 2.4
2.1 /2.8 2.2 /2.6
16 67
117 min 125 min
2.5 4.7
2.5 2.9
2.1 /3.0 2.6 /3.2
a Width of these limits is underestimated owing to the effects of pack riding. CV, coefficient of variation; 95%LR, 95% likely range for the true value of the CV.
Variation in cycling performance
Road races World Cup (10 races of 230 /290 km over 204 days) Top eighth All Tour de France (18 races of 145 /255 km over 21 days) Top eighth All Kilo time trials Series 1 (3 races of 1 km over 115 days) Top half All Series 2 (3 races of 1 km over 121 days) Top half All Combined Top half All Road Time trials International (3 races of 46 /75 km over 26 days) Top half All Tour de France (2 races of 17 and 59 km over 21 days) Top eighth All Mountain bike races Males (7 races of 38 /45 km over 161 days) Top quarter All Females (8 races of 27 /36 km over 160 days) Top quarter All
Number of cyclists
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C. D. Paton & W. G. Hopkins
Within-cyclist variation Effect of race series. We compared the within-cyclist variation between race series (using the ratio of CV) relative to the within-cyclist variation of all cyclists competing in the Kilo time trial. For all cyclists, we observed a trivial overall increase in within-cyclist variation between the Kilo and World Cup road race series (ratio of CV, 1.1; likely range, 0.8 /1.5), but the likely range allows for the possibility of a much larger increase or even a small, but substantial, decrease in performance variability in the road series. In comparison, within-cyclist variation was greater in road time trials (ratio, 1.8; likely range, 1.1 /2.8) and World Cup mountain bike races (ratio, 2.4; likely range, 1.7 /3.2) than in the Kilo series. The within-cyclist variations in performance for the top cyclists were similar to those for all cyclists in the Kilo, mountain bike and time-trial series; however the top road-race cyclists were (on the basis of likely limits) much more consistent in their performance than the other road cyclists. The top road cyclists were also more consistent than the top Kilo cyclists. An analysis of individual stages of the Tour, based upon whether a stage could be classified as predominately flat, hilly or mountainous, revealed a substantially smaller within-cyclist variation when stages were flat (0.7%; likely range, 0.6 /0.7%) as compared to either being hilly or mountainous (1.6%; likely range, 1.5 /1.7%). Effect of gender. The top male and female crosscountry mountain bikers in the sample had similar variability in performance between races, but the confidence interval allows for the possibility that the difference could be substantial (ratio of female/male CV, 1.04; likely range, 0.82 /1.33). On the other hand, the average female rider in the sample was more variable in performance than the average male, though the true difference could be insubstantial (ratio, 1.21; likely range, 1.07 /1.37). Effect of cyclist’s ability. Within-cyclist variation for the faster subgroup of cyclists within each series was generally substantially less than that for the average cyclist. The only clear-cut difference was in the road races, where the difference between the subgroups was very large for both the World Cup and the Tour de France (ratio of CV of top eighth/all, 0.4; likely limits 0.3 /0.5). In the Kilo time trial, performance time of the top cyclists was probably substantially more variable than that of the slower cyclists (ratio of CV of top/bottom halves of the field, 1.6; likely limits, 0.9 /3.2). Effect of time between events. In the international timetrial series there was some evidence of greater
variability between the first and third races (CV, 2.2%; likely range, 1.5 /4.0%) than between consecutive races (mean CV, 1.4%; likely range, 1.1 / 2.3%). The Kilo showed a similar increase in variability between the first and third races (CV, 1.1%; likely range, 0.8 /1.8%) than between consecutive races (mean CV, 0.7%; likely range, 0.5 / 1.1%). Variability in the Kilo was also slightly higher between pairs of races between years (CV, 1.1%) than between pairs of races within a year (CV 1.0%, as shown in Table I). We observed no substantial increase in variability between mountain bike races separated by an increasing number of intervening races for either males (modeled ratio of CV of last/ first race, 1.14; likely range, 0.95 /1.36) or females (ratio, 1.11; likely range, 0.84 /1.47), though the likely range allows for the possibility of a substantial true increase in variability. Discussion The data presented here represent performances of some of the best cyclists in the world competing in top international road-race, time-trial and mountain-bike events. The Kilo time-trial data came from cyclists in US national competitions, but the top riders in this event would also be world-class athletes. The between-cyclist variations in performance time, representing the spread in rider ability, were smallest in World-cup and Tour road races, probably as a consequence of the effects of pack riding and because the cyclists in these races were professionals. The between-cyclist variation in the time-trial and mountain-bike series is probably larger as a consequence of the greater number of amateur cyclists competing in these events. In most cases the within-cyclist variation was larger for the average cyclist relative to the top subgroup of cyclists. The lower variability in performance of cyclists in the top subgroups is probably due to more consistent preparation and motivation of these athletes. Faster athletes in other sports also show less variability in performance than the slower athletes, probably for the same reasons (3,5). Our discussion will focus on the within-cyclist variation in the top subgroups, because this variation defines the smallest worthwhile change in performance for competitive athletes (Hopkins et al., 1999). The within-cyclist variation in performance of the top sub-groups ranges from /0.5% in road races through /2.5% in mountain biking. The uncertainty in the estimates (the width of the confidence intervals) is sufficiently low to conclude that the observed range is not simply a consequence of sampling error but instead reflects real differences in variability in cycling performance in different events. We will now identify and discuss the event-
Variation in cycling performance specific factors that we believe are responsible for the differences in variability. We will show that these factors also affect the ways in which our estimates can be used in studies of cycling performance and for monitoring the performance of individual cyclists. The factors are pack riding, pacing, environmental conditions, the relationship between a cyclist’s power and speed, technical demands, and crashes or mechanical problems. Pack or peloton riding is apparent in the clustering of finishing times in World Cup and Tour de France road races and in the mountain-bike races. The clustering of times is due to the practice of crediting cyclists with the same time when they cross the finishing line in a pack. Riders form packs in massstart races to benefit from ‘drafting’ (reduction of the braking effect of air resistance). In contrast, riders are not permitted to form packs in road time trials, so pack riding is probably the main reason why the within-cyclist variation in road races is much less than that in road time trials. Pack riding probably achieves this reduction by having an averaging effect on performance times of all riders in a pack, even though the number and composition of packs change during a race and between races. Crediting all riders in a pack with the same finishing time could also in principle contribute to a reduction in withincyclist variation. Cyclists are given the same finishing time when the gap between bikes in the pack at the finishing line is less than one second. In our experience such groups seldom contain more than 100 riders, so the distance between the first and last rider is unlikely to be more than /300 m. The resulting error in performance time for a road race of more than 200 km would therefore be less than 0.15%, which represents a negligible contribution to within-cyclist variation. The averaging effect of pack riding also reduces the effective sample size for our estimates of withincyclist variation, so the likely limits of the estimates for these races need to be more widely spaced than those shown in Table I. The effective sample size could be as small as the number of packs in each race, because the riders in a pack effectively act as a single unit. If we assume five packs in each race of the World Cup, the resulting likely limits for the within-cyclist variation of 1.1% for all the riders would be 0.9 /1.4%, which still represents enough precision to conclude that World Cup riders are amongst the least variable in performance. The within-cyclist variation for the Tour road races was substantially larger than that for the World Cup road races. Analysis of the different road-race stages of the Tour revealed that the larger variability was due to the inclusion of races over hilly and mountainous terrains, which are not generally a feature of World Cup races. The increase in varia-
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bility during the hilly stages of the Tour is probably a consequence of riders forming smaller and more widely spaced packs, because drafting has less benefit at the slower speeds of these stages. Withincyclist variation in the Tour may also be larger than that in the World Cup because of the effects of cumulative fatigue on individual riders. As the Tour progresses, any differences in fatigue between riders, caused by variation in an individual’s effort on each stage, would contribute to increased overall variability in performance, whereas riders in the World Cup presumably enter each race with little fatigue from previous competitions or training. Performance in the mountain-bike series was even more variable than that in the hilly and mountainous stages of the Tour, probably because there was even less pack riding in mountain-bike races. At the slower speeds of mountain biking there is little benefit from drafting behind other riders, so any packs are small. Pack riding cannot be the only factor affecting variation in a cyclist’s performance, because there is no pack riding in the Kilo, yet reproducibility of performance in this event was comparable with that in the road races. An important difference between the Kilo and all other events is pacing. In our experience, cyclists in the Kilo make an all-out effort throughout the race, whereas in the other events the cyclist tries to select an optimum pace, taking into account the duration of the event and the perception of current state of fitness. Error in self-selection of pace could therefore account for the larger withincyclist variability in road time trials, where there is no pack riding, and in the mountain-bike races, where pack riding probably has a minor or negligible effect. Changes in environmental conditions (such as wind direction and speed) between cyclists during the course of a race could also account for the larger within-cyclist variability in the road time trials than in the Kilo. Environmental conditions will have little effect in the Kilo, because it is held in the more stable conditions of a velodrome. Another characteristic that could help explain the difference in variation between the Kilo, road time trials, and mountain-bike races is the power-speed relationship for each of these events. The relationship between a cyclist’s power and speed determines the way in which variation in the cyclist’s fitness (ability to generate power) contributes to variation in the cyclist’s performance time. The cyclist develops power to overcome the combined effects of inertia, air resistance, rolling resistance, and gravity (when climbing any undulations or hills). Each of these effects is a function of speed, and each contributes a different and unknown amount in the Kilo, road time trials, and mountain-bike races. A change in a
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C. D. Paton & W. G. Hopkins
cyclist’s ability to develop power from race to race will therefore produce different but unknown changes in performance time in each of these three events. Technical demands, crashes, and mechanical problems are the remaining event-specific factors that could affect a cyclist’s variability in performance. We believe these factors will have a substantial effect only in mountain biking. In our experience, the slow speed of mountain-bike races (less than half that of the other events) is due at least in part to the fact that cyclists negotiate technically difficult sections of the course using substantially less power than they have at their disposal for the race overall. As a result, any variation in fitness from race to race will tend to have less effect on within-cyclist variation in performance time. On the other hand, courses that differ in technical demand will favor different cyclists, thereby increasing the within-cyclist variability. Time lost through crashes and mechanical problems will affect different riders in different races and thereby also increase within-cyclist variability. These problems appear to be more frequent in mountain biking than in other events. They will also have more impact in mountain biking, because riders in these events are allowed no outside support to repair punctures or other mechanical problems. One of the aims of the present study was to use the within-athlete variability in cycling performance time to estimate the smallest worthwhile change in performance for a top competitive cyclist. Statistical simulations of the effect of changes in performance on the medal prospects of top athletes have shown that the smallest worthwhile change is about half the within-athlete variation in performance between competitions (Hopkins et al., 1999). Two assumptions are implicit in these simulations: athletes compete as independent individuals, and athletes attempt to perform their best in each race. Cycling races in which pack riding plays a substantial role in determining performance time violate both these assumptions, because cyclists in a pack are not independent, and because team tactics can dictate the effort of team members. We therefore cannot draw any conclusions about the smallest worthwhile change in performance time for an individual cyclist in road races. On the other hand, cyclists in a Kilo or road time trial perform independently of each other, and any interdependence of cyclists in a mountainbike race arising from pack riding is probably negligible. We also think that most riders in the top subgroups of these races are unlikely to give less than their best effort, for example by using a race as a hard training session. The smallest worthwhile change in performance time for a top cyclist is therefore /0.5% in the Kilo, /0.6% in road time trials, and /1.2% in mountain-bike races.
These estimates of smallest worthwhile changes in performance time are useful thresholds for interpreting the magnitude of performance changes in studies of groups of cyclists or when monitoring individual cyclists, but only when the measure of performance is time in simulated or real competitions. The estimates are not thresholds for changes in power in laboratory tests, because the relationships between change in power in laboratory tests and change in performance time in the various events are not known. Further research is needed to establish these relationships. The research will involve monitoring athletes with mobile ergometers during repeated real or simulated competitions to estimate the relationship between change in performance time and change in mean power. In the case of the Kilo and road time trials, the relationship will automatically give the desired estimate for the threshold change in laboratory-test power, if one assumes that any change in a cyclist’s mean power in a laboratory test will be the same as the change in mean power in an upcoming competition. For example, if changes in performance time in the Kilo turn out to be 0.4 / the change in mean power in the Kilo, and the smallest worthwhile change in performance time in the Kilo is 0.5% (a result from the present study), then the smallest worthwhile change in laboratory-test power is 0.5/0.4 /1.25%. In the case of mountain-bike races, the computation will involve averaging the power for non-technical (high-intensity) segments of the race, because it is only in these segments that changes in the athlete’s fitness can affect performance time. The relationship between performance time and mean power will vary with the technical demands of different courses. The estimated thresholds for change in laboratory-test power will also represent benchmarks for assessing the utility of a laboratory test for monitoring changes in performance. If the error of measurement of a test is substantially greater than the threshold change, the researcher or practitioner will need a large sample size or multiple retests to make confident assertions about small changes in performance (Hopkins, 2000). Key points: . For events in which cyclists compete independently, variation in performance time from race to race determines the smallest change in performance affecting the athlete’s chances of winning. . Performance time of top cyclists from race to race varies typically by 0.4 /2.6%, depending on the type of event. . The smallest worthwhile changes in performance time ( /0.5 / typical variation) are /
Variation in cycling performance 0.5% in the Kilo, /0.6% in road time trials, and /1.2% in mountain-bike races. . Pack riding precludes estimation of the smallest worthwhile change in performance time in road races.
References Hopkins, W.G. (2000). Measures of reliability in sports medicine and science. Sports Med , 30 , 1 /15.
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Hopkins, W.G., Hawley, J.A., & Burke, L.M. (1999). Design and analysis of research on sport performance enhancement. Med Sci Sports Exerc , 31 , 472 /485. Hopkins, W.G., & Hewson, D.J. (2001). Variability of competitive performance of distance runners. Med Sci Sports Exerc , 33 , 1588 /1592. Paton, C.D., & Hopkins, W.G. (2001). Tests of cycling performance. Sports Med , 31 , 489 /496. Stewart, A.M., & Hopkins, W.G. (2000). Consistency of swimming performance within and between competitions. Med Sci Sports Exerc , 32 , 997 /1001.
