The ability to predict running performance is of great interest for athletes and coaches. In fact, it is helpful not only for the prescription of training intensity during tempo runs but also to determine the optimal strategy during the race and to choose splitting times (5). The velocity associated with maximal oxygen uptake or with lactate threshold has been consistently used in this purpose (12). Unfortunately, their determination requires the completion of a maximal graded exercise test that is often difficult to schedule during a competition phase, although it is during this period that precision in intensity prescription is probably the most important.
A number of empirical and experimental observations suggest that predicting running performance in one distance from recent performances in shorter and/or longer distance is possible from the use of simple practical methods. A common approach consists in modeling the relationship between time and distance or velocity (1,14). Several models have been proposed in the literature (8-10,14,18), but the linear 2-parameter model (10) is generally considered as the most practical one. This model is represented by equation 1.
where D lim is the maximal distance (m) that could be run on oxygen reserves and the energy supplied by anaerobic metabolism; CV (critical velocity in m·min−1) is interpreted as the maximal rate of synthesis of these reserves by aerobic metabolism; TTE is the time to exhaustion (minutes); and ARC corresponds to the anaerobic running capacity (m), which represents the distance that may be run on oxygen reserves and the energy supplied by anaerobic metabolism (6). Predictive value of the linear 2-parameter model (10) is good for short-duration running events such as the 800 m (4), but weaker for events of longer duration when data are obtained by extrapolation (6). However, no study has tested the precision of predictions from the linear 2-parameter model (10) in middle-distance track events.
Another practical tool that allows one to estimate running performance at 1 event from running performances at 2 other events is the nomogram developed by Mercier et al. (11). This nomogram also provides a valid estimate of maximal oxygen uptake (16), which relies on the high correlation between maximal aerobic velocity, maximal oxygen uptake, and performance at the 3,000 m (11). Coquart et al. (5) have shown that the nomogram of Mercier et al. (11) provided valid estimations of long-distance running performance, but to date, data for middle-distance running performance are still lacking.
The purpose of the current study was therefore to test the validity and the precision of middle distance-running performance predictions by the nomogram and the linear distance-time model.
Experimental Approach to the Problem
All official running rankings of the French Athletics Federation for the men's 3,000; 5,000; and 10,000 m were scrutinized from 1996 to 2007. As the nomogram has been developed to predict the performance of heterogeneous runners, we have collected all performances regardless of runners' performance level. These performances are accessible on the website of the French Athletics Federation to everybody. Performances of male runners (age range: 21-50 years) who competed over the 3 distances within a 12-month period were recorded.
The performances of 100 runners were likewise considered. The 3,000-; 5,000-; and 10,000-m performances were 8.23 ± 0.24 minutes (range: 7.56-8.70 minutes), 14.20 ± 0.44 minutes (range: 13.05-15.16 minutes), and 29.86 ± 1.09 minutes (range: 27.02-32.60 minutes). These performances in the 3,000; 5,000; and 10,000 m represented, respectively, 86 ± 3, 86 ± 3, and 84 ± 4% of the current world outdoor records (i.e., 7.21 minutes by Daniel Komen in 1996; 12.37 minutes by Kenenisa Bekele in 2004; and 26.18 minutes by Kenenisa Bekele in 2005).
For the 3 distances, performances were predicted individually using the linear 2-parameter model (10) and the nomogram of Mercier et al. (11). In the first method, the distance-time relationship was modeled using the linear 2-parameter model (10). Two running performances were plotted, equation 1 being used to determine the third performance. For example, a runner covering the 3,000 m in 8 minutes and the 5,000 m in 14 minutes has a VC = (5,000 − 3,000)/(14 − 8) of 333 m·min−1, and ARC of 333 m. Therefore, he should be able to run the 10,000 m in TTE = (10,000 − 333)/333 = 29 minutes 00 seconds.
To predict performance from the nomogram of Mercier et al. (11) (Figure 1), the intersection point between the line connecting the 2 actual performances and the vertical axis of the desired distance was noticed. This intersection point provided the predicted performance value. As an example, a runner covering the 3,000 m in 8 minutes and the 5,000 m in 14 minutes should be able to run the 10,000 m in approximately 29 minutes 55 seconds.
Standard statistical methods were used for the calculation of means and SDs. Normal Gaussian distribution of the data was verified by the Shapiro-Wilk test and homogeneity of variance by the Levene test. Because the data sets did not pass the test for normality, a Wilcoxon matched pairs test was used to compare actual and predicted performance at the 3,000; 5,000; and 10,000 m. The magnitude of the difference was assessed by the effect size (ES). The Cohen scale was used for interpretation. The magnitude of the difference was considered as trivial (ES < 0.2), small (0.2 ≤ ES < 0.5), moderate (0.5 ≤ ES < 0.8), and large (ES ≥ 0.8). The level of association between actual and predicted performances was verified with the Spearman rank order correlation. We considered a correlation over 0.90 as very high, between 0.70 and 0.89 as high, and between 0.50 and 0.69 as moderate (15). The bias and 95% limits of agreement (LoAs) were computed according to the method of Bland and Altman (2). The normality of the distribution of the differences between actual and predicted performances was verified with the Shapiro-Wilk test and homoscedasticity with a modified Levene test. Thereafter, we tested the null hypothesis that the bias was not different from zero with a t-test for dependant measures. Statistical significance was set at p ≤ 0.05, and all analyses were performed with Statistica (release 6.0, Statsoft, Tulsa, OR).
Mean values and SD of critical velocity and anaerobic running capacity are presented in Table 1.
The linear 2-parameter model (10) overestimated the actual performances for each distance (p < 0.05; Table 2). Effect size was large, small, and moderate for the 3,000; 5,000; and 10,000 m, respectively (Table 2). Predicted performances were significantly correlated with the actual ones (p < 0.01; r > 0.46; Table 2 and Figure 2). In 95 of 100 new predictions, the difference between actual and predicted performances would be less or equal to 18 ± 19, −13 ± 13, and 44 ± 47 seconds, on the 3,000-; 5,000-; and 10,000-m performances (Table 2 and Figure 2). The LoAs represented 15.5, 6.2, and 10.6% of the mean of actual and predicted performances on each distance.
When compared with actual performance, predictions from the nomogram (11) were significantly lower for the 3,000 m (p = 0.001; ES = −0.25). We found no significant difference for the 5,000 and 10,000 m (Table 2). Significant correlations were observed for each distance (p < 0.01; r > 0.48; Table 2 and Figure 3). The bias and LoAs are shown in Figure 3. In 95 of 100 new predictions, the difference between actual and predicted performances would be less or equal to 5 ± 16 seconds, −1 ± 14 seconds, and 1 second ± 1 minute 33 seconds for the 3,000; 5,000; and 10,000 m, respectively (Table 2 and Figure 3). The LoAs represented 12.8, 6.9, and 20.8% of the mean of actual and predicted performances on each distance.
The purpose of the current study was to test the validity and the precision of middle distance-running performance predictions by the nomogram and the linear distance-time model. Our main finding was that both approaches could be considered as valid and accurate provided performance is obtained by interpolation, not by extrapolation.
As reported in Table 2, the difference between actual and predicted performances was consistently lower for the nomogram, whatever the distance. The magnitude of this difference was considered as small if not trivial, although it was occasionally large when performance was estimated from the linear distance-time model. A first examination of our results therefore suggests that (regardless of runners' performance level) the nomogram should be preferred to estimate middle distance-running performance. This would be however an oversimplification. In fact, a closer reading of the results presented in Table 2 shows that the correlation between actual and predicted performances is generally moderate when performance is obtained by extrapolation (i.e., for the 3,000 and the 10,000 m), whatever the method, whereas it is high (almost very high) when obtained by interpolation. The same observation is true for the precision of predictions, because the 95% LoAs vary from 10 to 20% when performance is extrapolated, whereas it is only 6.2-6.9% when performance is obtained by interpolation. When combining all statistical measures that should be accounted to assess the validity of the nomogram or the linear distance-time model to predict middle distance-running performance, it appears that their respective predictions can be considered as valid and accurate provided performance is obtained by interpolation (i.e., 5,000 m), but not when it is obtained by extrapolation. The lower bias between actual and predicted performances in the 5,000 m, although 95% LoAs can be considered as similar, gives a slight practical advantage to the nomogram when compared with the linear distance-time model, particularly if we consider that it also provides valid estimates of maximum oxygen uptake and aerobic endurance (16). It does not mean however that the linear distance-time model should be forgotten.
Recently, Gamelin et al. (7) have compared 5 mathematical models, based on the relationship between time and distance or velocity, to determine which provides the most accurate prediction during 1-hour running events. This study revealed that the 3-parameter model proposed by Morton (13) was the only model for which the prediction was not significantly different from actual performance (p > 0.05; ES = 0.31). This result has also been confirmed by Bosquet et al. (4) in the 800-m running performance (p > 0.05; ES = 0.00). Although it is less accessible, because 3-5 performances are required to obtain parameter estimates, additional data are needed to determine whether the nomogram is more accurate than more complex critical velocity models like the 3-parameter model of Morton (13).
Another potential interest of the linear distance-time model is the estimation of ARC. This second parameter is usually defined as the distance that may be run on oxygen reserves and the energy supplied by anaerobic metabolism (6). If we assume that anaerobic stores are completely used during each event, then ARC allows determining their respective anaerobic contribution. For example, our ARC of 460, 334, and 238 m would suggest that the 3,000; 5,000; and 10,000 m are 15.3, 6.7, and 2.4% anaerobic, respectively. This information may be relevant to determine the weight of anaerobic work in the training program. However, it should be kept in mind that the validity, reliability, and practical usefulness of ARC has been questioned in several studies (3-4,17).
The results of the present study are confined by a major assumption, which is the equivalence between performances. Considering that some events may have been performed in different meteorological conditions (e.g., environmental temperature, altitude, or humidity), opposition fields, or race profiles (flat or hilly), it is possible that the supposed equivalence between these performances was not strictly true. In this case, the precision in the predictions (not only from the linear 2-parameter model  but also from the Mercier et al. nomogram ) may have been decreased. Another potential limit is that, according to Mercier et al. (11), the predictions can be reached only if runners are trained specifically on each distance. It is possible that some runners included in the current study ran the 10,000 m without a specific preparation, or inversely that some 10,000-m runners participated in 3,000 or 5,000 m as preparatory races without being prepared for them or giving their maximum. This possible bias undoubtedly contributed to increase the LoAs we observed in this study.
Athletes and coaches need field measures that may provide them with accurate estimates of performance. The nomogram and the linear distance-time model offer this possibility. Unless performance is obtained by extrapolation, our results show that estimates from these tools can be considered as valid and accurate. The easier use of the nomogram (no calculation to perform), added to a slightly higher accuracy and the possibility to obtain valid estimates of maximum oxygen uptake and aerobic endurance, provides it with a practical advantage. In fact, knowing the required maximum oxygen uptake and aerobic endurance for a given performance and actual values of the athlete, it is easier not only to choose goals and optimize periodization of the season but also to monitor improvement in these performance determinants. Moreover, having an accurate idea of an athlete's performance capability at one distance allows one not only to prescribe realistic training intensities during tempo runs, but also to determine the optimal strategy during the race. It should be kept in mind that the accuracy of performance prediction, either from the nomogram or from the linear distance-time model, may be improved by choosing 2 performances that are not too distant one from each other, that are performed in similar or at least comparable conditions, and for which athletes have been prepared.
Research relating to this manuscript was not funded by a grant support. However, the authors gratefully acknowledge Pr Berthoin Serge (Laboratory of Human Movement Studies, Faculty of Sports Sciences and Physical Education, University of Lille 2) and Dr. Dekerle Jeanne (Chelsea School Research Centre, University of Brighton) for their expert advices in the writing of the manuscript.
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Keywords:© 2010 National Strength and Conditioning Association
runner; time to exhaustion; estimation; validity; linear 2-parameter model