Modeled responses to training and taper in competitive swimmers : Medicine & Science in Sports & Exercise

Journal Logo

Applied Sciences: Physical Fitness and Performance

Modeled responses to training and taper in competitive swimmers


Author Information
Medicine & Science in Sports & Exercise 28(2):p 251-258, February 1996.
  • Free


This study investigated the effect of training on performance and assessed the response to taper in elite swimmers (N = 18), using a mathematical model that links training with performance and estimates the negative and positive influences of training, NI and PI. Variations in training, performance, NI, and PI were studied during 3-, 4-, and 6-wk tapers. The fit between modeled and actual performance was significant for 17 subjects; r2 ranged from 0.45 to 0.85, P < 0.05. Training was progressively reduced during tapers. Performance improved during the first two tapers: 2.90 ± 1.50% (P < 0.01) and 3.20 ± 1.70% (P < 0.01). Performance improvement in the third taper was not significant (1.81 ± 1.73%). NI was reduced during the first two tapers (P < 0.01 and P < 0.05, respectively), but not during the third. PI did not change significantly during tapers. Thus, the present results show that the model used is a valuable method to describe the effects of training on performance. Performance improvement during taper was attributed to a reduction in NI. PI did not improve with taper, but it was not compromised by the reduced training periods.

The most important goal for a coach and an athlete is to: 1) improve the physical, technical, and psychological abilities of the athlete to the upper limits to reach the highest possible levels of performance; 2) develop a precisely controlled training program to assure that the maximal performance is attained at the right moment of the season (i.e., at each point of a major competition). In competitive swimming, a systematic increase in the amount of training throughout a period is a general procedure in an attempt to achieve the first of the above mentioned goals. On the other hand, the most usual procedure followed to achieve the second goal is to reduce the amount of training during a variable period of time before the main competition. This reduction in training is known as tapering(10,11,14,15,19-20). Tapering attempts to reduce the physiological and psychological stress of daily training, but the line that separates the benefit of tapering from the negative effect of detraining has not been clearly established(18).

In 1975, Banister and colleagues (4) proposed a systems model of the effects of training as a method to study an athlete's response to training. The mathematical model generated estimated fatigue and fitness profiles from a training impulse computed from training in order to understand the fluctuation of athletic performance throughout periods of heavy training separated by periods of relative rest (taper). According to this model, the level of performance of an athlete at any time of the training process can be estimated from the difference between a negative function(fatigue) and a positive function (fitness), the result from each training bout and their accumulation. The training stimulus is quantified not only from the volume of training, but from its intensity as well(4). This model has been validated as a method of quantifying the training stimulus producing a physiological response to the training process in the organism (3,7).

In a somewhat different approach, fatigue and fitness indicators have been estimated from the combination of the two opposite components of the model(5,8). The negative influence of training on performance (fatigue indicator) and the positive influence of training on performance (fitness indicator) have been referred to as NI and PI, respectively (8).

The aim of the present study was to investigate the effect of training on performance in a group of elite swimmers and to assess the specific physical response of these swimmers to taper, by means of the above mentioned mathematical model and the estimated NI and PI profiles.



Eighteen highly trained national and international level swimmers were the subjects of this study (8 female, 10 male). Their mean (±SD) age, height, weight, and competition background were 20.3 ± 2.8 yr, 179.0± 8.2 cm, 67.5 ± 11.7 kg, and 11.9 ± 4.0 yr, respectively. Written informed consent was obtained from the subjects before entering the study. Each swimmer trained according to the program prescribed by the two team coaches, in which the authors of the present study did not interfere. The group mean number of measured performances during the season was 18 ± 3. Each swimmer's first performance, completed right after the summer break with a low level of motivation, was discounted. The level of performance was expressed as a percentage of the personal record achieved by each swimmer during the preceding season.

Quantification of the Training Stimulus

Application of the mathematical model described above requires a precise control of training, in order to quantify the training stimulus produced by volume and intensity of training. The total weekly training stimulus was determined as follows:

  1. Workouts in the water: a progressive test was performed in the early season for blood lactate concentration determination. During the test, each swimmer performed 200-m swims at a progressively increased percentage of his own best competition time in that distance, until exhaustion (failure to follow the required pace). Blood lactate concentration was determined from blood samples taken from a fingertip during the 1 min recovery periods separating the 200-m swims. According to the individual results obtained during this test, all the training performed in the water was divided into five intensity levels. Intensities I, II, and III represented swimming speeds inferior (≅2 mmol·1-1), equal (≅4 mmol·1-1), and slightly above (≅6 mmol·1-1) the onset of blood lactate accumulation, respectively. High intensity swimming that elicits blood lactate levels of ≅10 mmol·1-1 was defined as intensity IV and maximal intensity sprint swimming as intensity V. All season workouts were individually timed and each exercise categorized according to these intensity levels. Blood lactate testing was repeated several times during the season, and training intensity adjusted as the swimmer's lactate response was modified with training. The distance swum at each training intensity was associated with a stress index coefficient in order to weight the different physiological stress produced by each intensity. Blood lactate concentration seems to fairly reflect the physiological demands of different modes of exercise. Therefore, the blood lactate concentrations aimed during the different training sets were chosen as weighting coefficients for training intensity. Since sprint swimming is a very demanding mode of exercise as a result of which blood lactate is not accordingly increased, the corresponding lactate value for intensity V was estimated as 16 mmol·1-1. These lactate values were divided by two to make the stress index scale more easily manageable. The final weighting coefficients for the five training intensity levels were thus 1, 2, 3, 5, 8.
  2. Dryland workouts: to quantify the training stimulus of the dryland training sessions in the same training units as the workouts in the water, equivalent intensity ratings were estimated for the different types of dryland exercise. Since physiological indicators of dryland training intensity were not available, this was done on the basis of interviews and discussions with the coaches and athletes. On this basis, it was considered that a 1-h session was equivalent to 2 km of swimming. One-half of an average session was composed of low intensity warm-up and stretching exercise (equivalent to 1 km at intensity I), 25% of the session was composed of submaximal strength exercise (equivalent to 0.5 km at intensity IV) and 25% of maximal strength exercise (equivalent to 0.5 km at intensity V).

Thus, the total weekly training stimulus was computed as the sum of the number of kilometers swum at each training intensity, multiplied by their respective weighting coefficients, plus the amount of weekly dryland training equivalent: Equation

where W is the total weekly training stimulus, measured in arbitrary units. The weekly variations of the total training load for the entire group of swimmers are shown in Figure 1.

Fatigue and Fitness Indicators

In the systems model initially proposed by Banister et al.(4), the athlete is considered as a system in which the output is the performance, which reacts to a training stimulus considered as the systems input. The systems behavior is described by a transfer function composed of two antagonistic first order filters representing a fatiguing impulse and a fitness impulse, both calculated from the training impulse. This model relates mathematically the resulting performance to the amount of training as the difference between developing fatigue and fitness. In the present study, the model performance determined from the difference between the positive and negative functions at day n, ˆpn, was calculated from the successive training loads from the first day of the study to the day of performance (wi, with i varying from 1 to n - 1):Equation

The model performances were entirely defined with the following set of parameters: one positive and one negative multiplying factors, k1 and k2; one positive and one negative decay time constants, τ1 and τ2; and an additive term p*, which corresponded to an initial basic level of performance. The decay time constants are expressed in days. The other model parameters are expressed in arbitrary units depending on the units used in the quantification of the training load and performance. The model parameters are determined by fitting modeled performance to a real performance measured serially throughout the training program and by minimizing the residual sum of squares between them.

The time response of performance to a single training impulse and different variables derived from the model have been previously described(12). Fitz-Clarke et al. (12) defined as tn the critical time period before competition within which training has a negative effect on performance. tn, measured in days, is estimated by: Equation

tg has been defined as the time before competition about which training contributes maximally to performance on the day of competition(12). tg, measured in days, is computed as:Equation

The negative and the positive functions of the model have been associated with fatigue and fitness, respectively(1,3,7,17). Fatigue and fitness indicators have also been computed from the combined effects of both model functions on performance (5,8). These influence curves have been described in detail to determine the training program that would give the best performance at a target time (12). The influence of a training stimulus imposed at day i on performance at day n is calculated by the following equation: Equation

A negative value of I(i/n) indicates a negative influence of training on performance, whereas a positive value indicates a positive influence. The profile of the negative influence over the entire 44-wk training season was determined by calculating the sum of this negative influence, NIn, as follows: Equation

Since the estimated performance at day n, ˆpn, is equal to the difference between the positive and the negative influence of training, the sum of the positive influence, PIn, is computed as:Equation

NI refers to the initial negative part of the fitness-fatigue difference of the influence curves previously mentioned. PI refers to the positive part of the curve after a crossover point when decaying fatigue first becomes smaller than decaying fitness from a single training bout (see Fig. 1 inreference 5). Indeed, NI is the negative contribution to performance of training performed until tn days before competition. PI, on the other hand, is the positive contribution to performance of training performed before tn days preceding competition. Thus, the indicators of fatigue and fitness used in the present study were respectively NI and PI, expressed in arbitrary units, the dimensions of which were the same as those used for performance (Fig. 2).


In an attempt to optimize the swimmers' performance during the championships, the three main competitions of the season, held on weeks 14, 29, and 44, were preceded by taper periods. Taper consisted of a progressive reduction of the amount of training The three taper periods lasted 3 wk, 4 wk, and 6 wk, respectively. The pattern of the training program during taper, as for the rest of the season, was prescribed by the team coaches and was not controlled by the authors of this study. To evaluate the response of the swimmers to the different tapering periods, the variations in the amount of training and the resulting variations in performance, as well as the modeled NI and PI, were specifically studied.

Statistical Analysis

Means and standard deviations or standard errors were calculated for all the variables. The statistical significance of the fit between actual performance and modeled performance was tested by an analysis of variance on the residual sum of squares. The level of significance of the fit was estimated from the F-test. Analysis of variance (ANOVA) and Scheffé's procedure were used to study the variations in training, NI, and PI during taper. The variations in performance were evaluated with a multiple paired t-test with Bonferonni's correction, since the low number of subjects with all the necessary performance measurements did not allow us to perform ANOVA. The acceptable level of statistical significance was set at P < 0.05.


Performance Fit and Model Parameters

The fit between the actual performance achieved by the swimmers at different moments of the season and the modeled performance was statistically significant for 17 subjects (P < 0.05), although it did not reach a level of significance in one case (P < 0.1). The r2 values of the fit ranged from 0.45 to 0.85. The mean (±SD) values of the different model parameters are shown in Table 1. Important differences among the subjects were observed. Indeed, the positive and negative time constants of decay, τ1 and τ2, ranged between 30 and 70 d and between 0 and 25 d, respectively; the k2/k1 ratio, where k1 and k2 are the positive and negative arbitrary multiplying factors, ranged from 0 to 13.34; the time period before competition within which training affects performance negatively, tn, ranged from 0 to 27 d, and the time before competition at which training is most beneficial to performance, tg, from 0 to 56 d. The results of the application of the mathematical model for one of the swimmers can be observed in Figure 3, where A shows the quality of the performance fit, B shows the NI and PI profiles, and C shows the weekly evolution of the training stimulus.


The amount of training was significantly reduced during all three tapers, compared with the pre-taper training values (Fig. 4). As shown in Table 2, significant reductions were observed in the weekly distance swum at intensities II, III, and IV during the first period of taper. During the second taper, the distance covered at each of the five levels of swimming intensity was reduced. During the third taper, on the other hand, the only significant reductions were observed at intensities III and IV. Individual swimming times before and after each period of taper are shown in Table 3. The first two tapers resulted in significant improvements in performance: 2.90 ± 1.50% (N = 17, P < 0.01) and 3.20 ± 1.70% (N = 15,P < 0.01), respectively (Fig. 5C). NI increased significantly from the early season to the beginning of the first taper (P < 0.001), but further increases during pre-taper training periods were nonsignificant. On the other hand, significant decrements in NI were observed during the first two tapers(Fig. 5B). PI increased significantly from the early season to the beginning of the first taper (P < 0.001) and from the beginning of the first taper to the beginning of the second (P< 0.05), but no significant variation was observed during any of the periods of taper (Fig. 5A).


The statistical significance of the performance fit confirms that the mathematical model used in the present study is a valuable method to describe the relationship between training and performance. In spite of the high number of subjects and the high performance level of the subjects used in the present study, the values of the different variables derived from the model were similar to those previously reported in the literature. Indeed, the mean value of 40 d for the positive time constant of decay, τ1, was close to those obtained in endurance trained athletes(1,3,9) and mildly active subjects(6,17). The mean value for τ2, the negative time constant of decay (≅12 d) was similar to those values obtained during strenuous endurance training programs(1,3,9,17). This indicates that the assumptions made for mildly active subjects(12,17) could be extended to other types of athletes (i.e., elite swimmers). In the present study, however, an important intersubject variability was observed in the model parameter values. This variability could be attributed to individual differences among subjects on the one hand (training program, training background, variability in the physical or psychological responses to training, etc.), and to a lack of precision of the model on the other hand. Indeed, the precision of the model does not seem to be high enough to explain the small variations in peak performance of elite competitive swimmers. Variations in the modeled performance of the present study accounted for 45-85% of the variations in the actual performance. The quantification of the training load used in this study for the application of the model was intended to take into account the multiple components of training by quantifying six water and dryland training variables. However, this method could be too general and imprecise, since it did not take into account a great deal of other training variables used by the coaches in their programs. Furthermore, in the present study, the model parameters were assumed to be constant during the entire follow-up period. This assumption could not account for a possible alteration in the responses to training occurring during a steep change in training intensity or during a long lasting period of intensive training. Training in itself might modify the response of an athlete to a training stress (2). Moreover, it has been shown by Banister (1) that actual performance does not correspond to the performance predicted from model parameters fitted later in the training process, and that the follow-up period should be divided into smaller periods lasting from 60 to 90 d, and the modeling process repeated in each of them. This technique implies a frequency of performance measurement that is difficult to attain when studying elite athletes like those of the present study.

Even though athletic performance grows and declines exponentially, performance values were linearized in the present study by referring the actual performance values to each swimmer's best performance of the previous season. The application of the model was also tested by expressing the actual performance on a logarithmic scale, as previously proposed by Morton et al.(17). Indeed, performance was also converted into a criterion score referred to: a) the personal best time and b) the world record on each swimming event. The model parameters (τ1, τ2, and the k2/k1 ratio) obtained with the application of the different performance scales were statistically analyzed, and no significant difference was observed as a result of this procedure. Thus, the simplest method was chosen and applied in the present study.

Two different ways of estimation of fatigue and fitness indicators have been described in the literature. In the original formulation of the model, the model performance was computed from the difference between two antagonistic functions (4). Banister's group assigned fatigue and fitness calculated from training respectively to negative and positive effects, which when summed produce a model output of performance(e.g., 3,12,17). The second method takes the time varying responses of performance to training into account, considering the initial decrease in performance as fatigue and the consequent recovery and supercompensation process as fitness. Fatigue and fitness indicators are thus computed from the combination of the two components of the model (5,8). To avoid confusion between these two kinds of fatigue and fitness indicators, it was considered preferable to limit the use of the terms fatigue and fitness to the two model components determined as in the original study (4). Thus, in the present study, negative and positive influences of training on performance were referred to as NI and PI, respectively. Different studies have shown the coherence of the model as a method to describe biological responses to training. Indeed, variations in iron status in five female distance runners(3), several serum enzyme activities in one runner(1), and hormonal adaptations in six elite weightlifters(7,8) have been shown to significantly correlate with modeled fatigue and fitness indicators obtained by both methods of computation. Studying the individual curves reflecting fatigue and fitness could thus provide valuable information for the understanding of the individual responses to training, and to develop individual adaptation profiles. Indeed, NI intends to synthesize all the physical variables contributing to shortand long-term fatigue, which affect performance in a negative way. On the other hand, variables contributing to enhance performance are synthesized in the function PI.

Tapering intends to maximize sports performance by reducing the amount of training before competition. The duration of the taper should be long enough to minimize the stressing effects of training, while avoiding the fall into detraining (18). In other words, tapering must allow the elimination of fatigue without compromising fitness. The duration of the taper would thus depend on such factors as previous training, fatigue, and fitness levels or degree of the training reduction. The critical time frame for recovery from the fatiguing effects of training can be determined from the model parameters. The model structure leads to consider that only training done before tn days before competition has a positive effect on performance at the time of competition, whereas training within tn days before competition contributes more to fatigue than it does to fitness(12,17). tn would thus be the optimal period of total cessation of training before competition. However, competitive athletes generally continue to train until the very day of competition. Considering that tg is the time before competition necessary to reach a maximal benefit from training (12), the optimal duration of an active taper would be included between tn and tg, between 12 ± 6 and 32 ± 12 d for the present group of swimmers. However, the above mentioned assumptions were made either upon theoretical bases or by studying mildly active subjects. In the present study, the swimmers tapered for 21, 28 and 42 d, and swimming performance improved by ≅3% during the first two periods of taper, while nonsignificant improvements were observed during the third one. These values were similar to those reported for competitive swimmers in previous studies(10,11,15). Improvements in performance during taper could be related to enhanced recovery processes in response to the reductions in the amount of training(13,15,18). These improvements have been partly attributed to improved muscular power, which seems to be enhanced during taper as a result of recovery(10,13-15,18,19). As the present formulation of the model integrates all the positive influences on performance into one single function, the interpretation of any variation in the fitness indicator is very limited. Therefore, the specific influence of the different factors affecting performance (e.g., muscular power) cannot be studied separately.

The nonsignificant improvement in performance achieved during the third taper could be explained by a low pre-taper training level and a high pre-taper performance level. This observations are justified by the fact that most of the swimmers were regularly participating in different meetings held at that time of the season, for which reasonably high levels of performance were required. Also, a reduced training period of 6 wk seems inordinately long compared with tapers normally reported for competitive swimmers(10,13,20,21). Furthermore, a lower number of subjects with pre- and post-taper performances could have affected the statistical analysis.

When the variations in NI and PI were studied during taper, NI appeared as the major performance determining parameter. The analysis of variance of NI showed that it reached its peak level by the beginning of the first taper. Then, an alternate steep decrease and then increment occurred during taper and high volume training periods, respectively. A significant reduction in the level of NI was observed during the first two tapers. A large reduction in NI also occurred during the last taper of the season, but it did not reach the level of statistical significance. PI, on the other hand, followed a very different pattern. The peak PI level was reached by the end of the first taper. It then remained at a high stable level until the end of the season, but no further significant increases of this parameter occurred. However, slight nonsignificant improvements were achieved until the end of the second taper. Furthermore, the PI level was not significantly increased nor reduced during any of the three taper periods. Therefore, it could be suggested that during taper, improvements in performance were mainly due to significant reductions in the levels of NI, rather than to the nonsignificant variations in PI. In other words, it seems that even though PI was high enough to achieve a high performance level without tapering, the elevated levels of NI prevented the swimmers from performing at their best.

In conclusion, the mathematical model used in this study permitted to relate swimming training with performance. Estimations of individual profiles of the negative and positive influences of training on performance could be helpful in studying specific physiological reactions of the swimmers to a particular training stimulus. The present study showed that 3- and 4-wk tapers, consisting of a progressive reduction in the training load, resulted in ≅3% improvements in the swimmers' competition times. This enhancement in performance was attributed to a reduction in the negative influence of training during taper. The positive influence of training did not improve with taper, but it was not compromised by the reduced training periods either.

Figure 1-Weekly training load for the entire group of swimmers during the 44 wk of the training season. The values are means ± SE; T.U. = training unit.
Figure 2-Schematic representation of the negative influence (NI) and the positive influence of training on performance (PI) after training bout. NI represents an initial decay in performance and PI a phase of supercompensation.
Figure 3-Application of the model in one of the subjects: A) fit between modeled and actual performance; B) NI and PI profiles; C) Weekly amount of training. NI and PI are expressed in the same type of unit as that used for performance. T.U. = training unit.
Figure 4-Mean (±SE) training loads during the 4 wk preceding each taper and during each taper; *** and ** denote significant differences between pre-taper and taper values (:
P < 0.001 and P < 0.01, respectively). T.U. = training unit.
Figure 5-Early season (E.S.), pre-taper, and post-taper means(±SE) of: A) positive influence of training on performance (NI); B) negative influence of training on performance (PI); C) actual performance;** and * denote significant differences between pre-taper and post-taper values (P < 0.01 and P < 0.05, respectively). NI and PI are expressed in the same type of unit as that used for performance; T.U. = training unit.


1. Banister, E. W. Modeling elite athletic performance. In:Physiological Testing of Elite Athletes, H. J. Green, J. D. McDougal, and H. Wenger (Eds.). Champaign, IL: Human Kinetics Publishers, 1991, pp. 403-424.
2. Banister, E. W. and T. W. Calvert. Planning for future performance: implications for long term training. Can. J. Appl. Sport Sci. 5:170-176, 1980.
3. Banister, E. W. and C. L. Hamilton. Variations in iron status with fatigue modelled from training in female distance runners.Eur. J. Appl. Physiol. 54:16-23, 1985.
4. Banister, E. W., T. W. Calvert, M. V. Savage, and T. Bach. A systems model of training for athletic performance. Aust. J. Sports Med. 7:57-61, 1975.
5. Busso, T., R. Candau, and J. R. Lacour. Fatigue and fitness modelled from the effects of training on performance. Eur. J. Appl. Physiol. 69:50-54, 1994.
6. Busso, T., C. Carasso, and J. R. Lacour. Adequacy of a systems structure in the modeling of training effects on performance.J. Appl. Physiol. 71:2044-2049, 1991.
7. Busso, T., K. Hakkinen, A. Pakarinen, ET AL. A systems model of training responses and its relationships to hormonal responses in elite weight-lifters. Eur. J. Appl. Physiol. 61:48-54, 1990.
8. Busso, T., K. Hakkinen, A. Pakarinen, H. Kauhanen, P. V. Komi, and J. R. Lacour. Hormonal adaptations and modelled responses in elite weightlifters during 6 weeks of training. Eur. J. Appl. Physiol. 64:381-386, 1992.
9. Calvert, T. W., E. W. Banister, M. V. Savage, and T. Bach. A systems model of the effects of training on physical performance.IEEE Trans. Syst. Man. Cybernet. 6:94-102, 1976.
10. Costill, D. L., D. S. King, R. Thomas, and M. Hargreaves. Effects of reduced training on muscular power in swimmers.Phys. Sportsmed. 13:94-101, 1985.
11. Costill, D. L., R. Thomas, R. A. Robergs, D. Pascoe, C. Lambert, S. Barr, and W. J. Fink. Adaptations to swimming training: influence of training volume. Med. Sci. Sports Exerc. 23:371-377, 1991.
12. Fitz-Clarke, J. R., R. H. Morton, and E. W. Banister. Optimizing athletic performance by influence curves. J. Appl. Physiol. 71:1151-1158, 1991.
13. Houmard, J. A. Impact of reduced training on performance in endurance athletes. Sports Med. 12:380-393, 1991.
14. Houmard, J. A. and R. A. Johns. Effects of taper on swim performance: practical implications. Sports Med. 17:224-232, 1994.
15. Johns, R. A., J. A. Houmard, R. W. Kobe, T. Hortobagyi, N. J. Bruno, J. M. Wells, and M. H. Shinebarger. Effects of taper on swim power, stroke distance and performance. Med. Sci. Sports Exerc. 24:1141-1146, 1992.
16. Morton, R. H. The quantitative periodization of athletic training: a model study. Sports Med. 3:19-28, 1991.
    17. Morton, R. H., J. R. Fitz-Clarke, and E. W. Banister. Modeling human performance in running. J. Appl. Physiol. 69:1171-1177, 1990.
    18. Neufer, P. D. The effect of detraining and reduced training on the physiological adaptations to aerobic exercise training.Sports Med. 8:302-321, 1989.
    19. Sheply, B., J. D. MacDougall, N. Cipriano, J. R. Sutton, M. A. Tarnopolsky, and G. Coates. Physiological effects of tapering in highly trained athletes. J. Appl. Physiol. 72:706-711, 1992.
    20. Van Handel, P. J., A. Katz, J. P. Troup, J. T. Daniels, and P. W. Bradley. Oxygen consumption and blood lactic acid response to training and taper. In: Swimming Science V, B. E. Ungerechts, K. Wilke, and K. Reischle (Eds.). Champaign, IL: Human Kinetics, 1988, pp. 269-275.
    21. Yamamoto, Y., Y. Mutoh, and M. Miyashita. Hematological and biochemical indices during the tapering period of competitive swimmers. In: Swimming Science V, B. E. Ungerechts, K. Wilke and K. Reischle(Eds.). Champaign, IL: Human Kinetics, 1988, pp. 243-249.


    ©1996The American College of Sports Medicine