The number of half-marathon runners has increased steadily over the past ten years. As an example, in the United States the number has doubled in just a decade, reaching two million in 2013. Similarly, in Europe, it is estimated that there are around 50 million people who are regular long-distance runners (Scheerder et al., 2015). Furthermore, in Spain more than 300 half-marathon races are held annually, with an important number of runners. As a result, an increasing number of amateur runners train assiduously to finish the races and improve their personal race times. It is very helpful for them to know their ideal paces or speeds for training and competition. Accordingly, identifying these values in advance is an objective necessity, for both the athletes and their coaches.

The physiological variables related to performance have been previously described (Ramsbottom et al., 1987). In the case of long-distance runners, those variables obtained in the incremental laboratory tests, essentially maximal oxygen consumption (VO₂max) and its related variables, have been very useful for observing the adaptations produced by training (Legaz Arrese et al., 2006), and to predict performance in competition (Foster, 1983). Additional laboratory tests and associated variables have been proposed that may be determinants of long-duration aerobic performance. Thus, the finish time in cross-country races has been associated with a high percentage of oxygen consumption (Loftin et al., 2007), as well as with blood lactate accumulation (Loftin et al., 2007), lactate threshold (Mujika et al., 2000), ventilatory threshold, or race economy (speed reached for a given oxygen consumption) (Amann et al., 2004; Saunders et al., 2004; Lucia et al., 2006; Støren et al., 2008; Santos-Concejero et al., 2017). However, it appears that the maximal speed achieved in the laboratory tests is the variable most closely associated with sports performance, regardless of the duration of the test (Noakes et al., 1990; Knechtle et al., 2011a; Ronconi and Alvero-Cruz, 2011).

Despite conclusions from previous research, most of the participants in these studies were elite or high-level athletes, and studies that focus specifically on the half-marathon are lacking (Tanaka et al., 1984; Weyand et al., 1994; Roecker et al., 1998). Those studies carried out in amateur runners described the following as the main predictors of final test performance: kilometers per week, number of weeks of training for each event, body mass index, resting heart rate (Campbell, 1985), anaerobic threshold and vVO₂max (Roecker et al., 1998), anthropometric variables (Knechtle et al., 2011a, b, 2014), or fat percentage combined with average running speed during training (Knechtle et al., 2014). However, almost all the models used in these studies involve some form laboratory assessment, and are, therefore, hardly applicable in most of the amateur population.

The usefulness of field tests (Penry et al., 2011; Alvero-Cruz et al., 2017) for the assessment of the physiological construct of aerobic condition has shown great variability with respect to laboratory tests, although their validity in predicting the construct of final race performance has been poorly addressed in the literature. It should be noted that there is a paradox between the high reliability and low ecological validity of laboratory assessments and the low reliability and high validity of the methods used in field tests (Reilly et al., 2009; Galbraith et al., 2014; Llodio et al., 2016). The Cooper test, given its simplicity of application and low cost, has traditionally been widely used to estimate maximal oxygen consumption (Cooper, 1968), but its ability to predict constructs associated with sports performance in long-distance runners, such as half-marathon runners (Grant et al., 1995), has never been evaluated. Therefore, the objective of this study was to compare the predictive ability of half-marathon race time between two models derived from: (a) variables obtained in treadmill tests and (b) the Cooper test.

The characteristics of the participants are shown in Table 1. All were older than 30 years of age, and their body mass index values and fat mass percentage indicated that they did not have excess adiposity.

Table 2 presents the data on the laboratory variables. The mean HR max at the end of the treadmill test was 181 ± 14 bpm and the heart rate of the Cooper test of 177 ± 13 bpm without significant differences (P = 0.47). Respiratory exchange ratio values at the end of exercise confirm maximal effort.

To the best of our knowledge, this is the only study that has evaluated and compared the ability to predict race time in the half-marathon by means of a graded exercise test in the laboratory and a Cooper test. In this work, we have identified variables associated with race time in the half-marathon through both laboratory assessment and the Cooper test. In the literature, there were several studies on different performance determinants in middle- and long-distance runners, such as anthropometric variables (Arrese and Ostáriz, 2006; Knechtle et al., 2010, 2014; Friedrich et al., 2014), variables related to training load (Ramsbottom et al., 1987; Knechtle et al., 2011a; Balsalobre-Fernández et al., 2014) as well as physiological variables (Roecker et al., 1998; Reilly et al., 2009; Rabadán et al., 2011; Ronconi and Alvero-Cruz, 2011; Gómez-Molina et al., 2017; Støa et al., 2010), which have associations with half-marathon performance.

Our results reveal that the variables from both the laboratory and the Cooper test enable significant models to be obtained for the prediction of half-marathon race time. In addition, we found that the regression model from the distance covered in the Cooper test has a better predictive value. According to results of this study, the model developed from the distance covered in the Cooper test, would explain 87.3% of the total variance of half-marathon race time in recreational runners. The laboratory model that combines vVO2max and body weight would explain 76.95% of the total variance. The variables included in our models find partial similarities with other published studies. With respect to anthropometric variables, the skinfolds of the lower limbs, anterior thigh and medial calf are associated with performance in runners of 1500 and 10000 m (Arrese and Ostáriz, 2006). Rüst et al. (2011) found that race time in the half marathon in amateur runners was associated with BMI and average training speed. Similar results are also found in relation to BMI (Friedrich et al., 2014) and sum of six skinfolds with race time in half-marathon (Gómez-Molina et al., 2017) in male runners. Other authors have linked the fat mass percentage with performance in half- marathon (Knechtle et al., 2014).

The predictive model of this author explains only 44% of the race time, which can be explained by the wide limits of concordance in the prediction of race time (±25 min) and the great heterogeneity of the study sample. In our study, the only anthropometric variable that predicts race time is body weight.

Training load variables have traditionally been associated with performance in the half marathon. These include average training speed, previous experience, distance per week, hours per week, and daily training time (Friedrich et al., 2014). In the last of these studies, associations were found with the average training speed (r = −0.77 and r = −0.58, for women and men, respectively), with fat mass percentage and the average training speed as predictors. Despite the previous evidence, no training variables were introduced into our models, which must indicate the strong dependence of training on the variability of the test result.

The dependent variables in the laboratory prediction model explain 77% of the variance. vVO2max corresponds to around 72% and body weight to 5%. Similar aspects are those presented by Knechtle et al. (2014) who, in a recent study, found predictive models of race time in the half marathon based on body weight and average training speed as predictor variables, but explaining only 44% of the race time. The results of our research provide much more accurate equations, with a coefficient of determination of 0.873 for the equation derived from the Cooper test and 0.77 for the equation derived with body weight and vVO2max.

This group of researchers (Knechtle et al., 2014) sought to improve the prediction with new equations, introducing other independent variables into the model, such as the percentage of fat mass, obtaining an R² of only 0.42 for the men and 0.68 for women. These coefficients are still low compared to those of our study. These authors also failed to measure VO₂max and the maximum speed reached in the maximal graded test. They additionally analyze the accuracy of the prediction model using the limits of agreement (LA) between the actual value and the value predicted with the new equation. The LA of the study are very broad, between −25.6 and 24 min, with a proportional error as the race time increases. In our study, the LA for the equation derived from the distance covered in the Cooper test are from −7.4 to 7.5 min with no proportional error (P < 0.05).

The laboratory tests allowed us to obtain multiple variables, all of them well controlled and generally very reproducible. Maximal oxygen uptake is normally a good predictor of performance in long-distance runners (Hagan et al., 1981). However, this variable was not significant in either of our prediction models. Another factor that has frequently been associated with performance in runners is the maximum speed attained (vVO₂max) in the incremental exercise test in the laboratory (Roecker et al., 1998). In our study, vVO2max was also a predictor in the laboratory model. This is likely due to race intensity in the half marathon being close to maximal oxygen consumption or maximum aerobic speed. Race time in the half marathon is not always explained by the absolute value of VO₂max and is often best explained by the fractional use of VO₂max, corresponding to a running speed, usually of a submaximal character and therefore to a submaximal VO₂ value.

Nevertheless, Williams and Nute (1983) studied the physiological demands of half-marathon runners finding similarities in the physiological values of this study, in terms of the race times and VO₂max values of the athletes. This study evaluated four runners and the variables that related to performance were VO₂max and estimated speed at a concentration of 4 mmol/L of lactate, although they later verified that the average lactate values were 5.65 ± 1.42 mmol/L, which would confirm values close to VO₂max.

Other studies such as that by Rabadán (Rabadán et al., 2011) analyze in the laboratory the physiological determinants of middle- and long-distance runners, finding that VO₂max, VO₂VT2 and vVT2 are variables that characterize these athletes. The strength of variables such as VT2 is that they are very reproducible parameters and therefore very useful in predicting and evaluating changes based on training. They can also help differentiate the performance of middle- and long-distance runners. In the present study, these values were not found to be predictors of performance.

The present study described the predictive ability of finish time in the half-marathon races using variables obtained in the Cooper test and in laboratory evaluations, with a higher predictive ability found in the former. In addition to the Cooper test being statistically more powerful than the treadmill laboratory test, its main strength is that it does not require laboratory technology and can be introduced into the daily training routine to provide a relatively valid prediction of race time.

The high predictive power of distance covered in Cooper test suggest that athletes and coaches should give attention to control of training paces and as a tool for selecting adequate competition strategies in half-marathon. Altogether, these results may guarantee a high degree of applicability for predicting half-marathon time in recreational male runners for its great reproducibility.

The datasets generated for this study are available on request to the corresponding author.

The studies involving human participants were reviewed and approved by the protocol used in this study was approved by the Ethics Committee of the University of Málaga (2013-EMEFYDE-005) and was in accordance with the Declaration of Helsinki. The patients/participants provided their written informed consent to participate in this study.

JA-C, MG, and EC conceived and designed the study. JA-C collected the data. JA-C, MG, EC, and FA analyzed and interpreted the data, and drafted the manuscript. JA-C, MG, EC, FA, PN, TR, and BK revised the manuscript and approved the final version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.