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Computer Simulations Assessing the Potential Performance Benefit of a Final Increase in Training During Pre-Event Taper

Thomas, Luc1; Mujika, Iñigo2; Busso, Thierry1

The Journal of Strength & Conditioning Research: September 2009 - Volume 23 - Issue 6 - p 1729-1736
doi: 10.1519/JSC.0b013e3181b3dfa1
Original Research

Thomas, L, Mujika, I, and Busso, T. Computer simulations assessing the potential performance benefit of a final increase in training during pre-event taper. J Strenth Cond Res 23(6): 1729-1736, 2009-A nonlinear model of training responses was utilized to test whether a 2-phase taper could be more effective than a traditional linear taper. Simulations were conducted using model parameters previously determined in 6 nonathletes trained on a cycle ergometer (non-ATH) and 7 elite swimmers trained in sport-specific conditions (ATH). Linear and 2-phase tapers were compared after a 28-day overload period at 120% of normal training. The 2-phase taper was assumed to be identical to the optimal linear taper, except for the final 3 days during which the training load was varied to maximize the final performance. The optimal linear taper was characterized by a mean training reduction by 32 ± 6% during 35 ± 6 days in non-ATH and by 49 ± 18% during 33 ± 16 days in ATH. The last 3 days of the 2-phase taper were characterized by a significant increase in training load by 23 ± 18% in non-ATH and 29 ± 42% in ATH (p < 0.005). The optimal taper characteristics were not statistically different between non-ATH and ATH. The maximal performance reached with the 2-phase taper was higher by 0.04 ± 0.02% in non-ATH and 0.01 ± 0.01% in ATH than with the optimal linear taper (p < 0.001). Positive and negative influences of training on performance were estimated as indicators of adaptation and fatigue, respectively. The negative influence was completely removed during both tapers, whereas the positive influence was slightly further enhanced during the 2-phase pattern. In conclusion, simulations showed that a 20 to 30% increase in training at the end of the taper, as compared to a prolonged reduction in training, allowed additional adaptations without compromising the removal of fatigue.

1Laboratory of Exercise Physiology, University of Saint-Etienne, France; and 2USP Araba Sport Clinic, Vitoria-Gasteiz, Basque Country, Spain

Address correspondence to Luc Thomas,

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The taper is a period of reduced training just before a competition with the aim of achieving peak performances at the right moment of the season. Although a well-designed reduction in training can improve performance by 0.5 to 6% (16), uncertainty exists about the optimization of the training during this critical period. These magnitudes of performance improvements were obtained with reductions in training load ranging from 50 to 90% during 4 to 35 days (16). A more recent meta-analysis focusing on competitive athletes suggested that the training volume should be decreased by 41 to 60% during the taper (3). The characteristics of an effective or optimal reduction in training appear variable and challenge both coaches and athletes in their preparations for high-level competitions. Nevertheless, there are some practical guidelines in regard to prescription of the taper, including the balance between training volume and intensity, and the form of the training reduction during the taper. The training intensity should be maintained at a level close to that of competition, and the training load (primarily the volume) should be reduced in a progressive form rather than in a single-step manner (3,16). One could even consider that the term “taper” implies a progressive reduction of the training load (2,11,12,14). Two forms of taper have been described in the literature: A simple step taper where the load is suddenly reduced and maintained at a low level thereafter, and a progressive form where the load is continually reduced according to a constant slope (linear taper) or a decay time constant (exponential taper). It is unclear whether more complex tapering strategies elicit better performances in trained athletes (3).

Theoretical studies based on computer simulations provide useful information on the optimal adjustment of taper characteristics (5,9,21,22). These simulations have primarily used a mathematical model of the training effects on performance first described by Banister et al. (1). Originally, the model described the individual responses to physical training in terms of adaptation and fatigue, assuming that performance is the balance between these 2 factors. Those responses depended on model parameters (constants), which were fitted for each participant from their actual response to a training program. Estimation of these parameters permitted the simulation of the responses to a training schedule other than that actually undertaken (13). This approach provided useful information on the optimal duration of the taper, typically between 2 and 4 weeks in competitive swimmers (15), and showed that a progressive reduction of training was more efficient than a step reduction (2). These derivations from the model proposed by Banister et al. (1) were questioned because this model implied that any training undertaken around 2 weeks before a competition would be detrimental for the performance (9). Indeed, the original model has a linear formulation that would provide an imperfect description of training-induced fatigue with a step change in training regimens (5,7).

In 2003 Busso (4) proposed a nonlinear formulation to overcome some of the limitations of the early linear model. This nonlinear model was validated using data from 6 previously untrained subjects enrolled in a controlled training program on a cycle ergometer (4). This new formulation took into account the accumulation of fatigue with training on the assumption that the increase in fatigue induced by a given training session was dependent on the severity of prior training sessions. A training session following repeated demanding sessions would induce a greater fatigue than the same session included in a training period with lower training loads. The nonlinear model is consequently a better approach for the study of the responses to training, in particular the taper after a short period of overload training (4). Recent simulation studies took advantage of this new model to probe more extensively the factors that could influence the optimal taper characteristics (21,22). Characteristics of optimal step and progressive tapers were compared when following or not an overload training of a 20% step increase in normal training during 28 days. The highest performances were obtained with the progressive tapers (linear or exponential) after the overload period (21,22).

However, it is uncertain whether a progressive reduction in training is the most efficient tapering procedure. Only tapers with no changes in the variation in training load were compared. The nonlinear model could be used to simulate alternative tapering strategies with a break in the variation in training. Bosquet et al. (3) suggested an original taper in 2 phases involving a classical reduction in the training load, followed by a moderate increase during the last days of the taper. The aim of a so-called “2-phase taper” is to reduce the athlete's fatigue before reintroduction of more prolonged or intense efforts. The relevance of an increase in training load at the end of the taper is corroborated anecdotally by the progressive improvement in performance often observed in an athlete from the first round of a competition to the final. This assumption is consistent with the formulation of the nonlinear model proposed by Busso (4): Restoration of the tolerance to training occurs with a period of reduced training (17). A subject would respond more effectively to training at the end of the taper, which could contribute to improved performance. However, the capacity to respond more effectively could be lost in few days with significant training (17). We suggested that a final increase in training load during the taper should not last more than 3 days, in the hope of exceeding the gains in performance obtained with a classical progressive taper.

Therefore, the purpose of the study was to use a simulation procedure to determine whether a 2-phase taper could be more effective than a single-phase progressive taper. We assumed that the 2-phase taper was identical to the optimal linear taper, except for the last 3 days during which the training load was varied to maximize the final performance. We hypothesized that the highest performance would be elicited after a moderate increase in the training load during the final 3 days of the taper.

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Experimental Approach to the Problem

Our theoretical approach is summed up in Figure 1. The computer simulations of performance variations according to the taper pattern were done after (a) assuming the mathematical equation between systems input and output and (b) choosing the model parameters from previously published materials. In the present study, the individual responses to training were simulated using the model proposed by Busso (4). Two earlier reports provided useable parameters for a total number of 13 subjects (4,22): 6 nonathletic subjects enrolled in controlled laboratory setting (4) and 7 competitive swimmers in field training conditions (22). One subject from this last report (22) was not retained because the model parameters gave an optimal linear taper lasting only 3 days. We have pooled both groups despite differences in the participants' fitness and activity. First, each group's n size was not sufficient to reach a satisfactory statistical power. Second, the parameters determined from data of a controlled experiment had the advantage of being more precise than an observational study, whereas the swimmers' parameters allowed simulating responses representative of high-level athletes in real training conditions (8). Because the specific characteristics of both groups could interfere with the comparison between tapering strategies, this factor was included in the statistical analysis. Nevertheless, the goal of the computer simulations was only to determine whether it was theoretically possible to obtain a greater gain in performance than with an optimized single-phase progressive reduction in training. The simulation procedure enabled us to address this issue by achieving the following successive steps: For each participant represented by his or her own model parameters, (a) identification of the characteristics of the optimal linear taper, (b) identification of the characteristics of the 2-phase taper (i.e., determination of the optimal variation in training load during the last 3 days), and (c) comparison of the effectiveness of the optimal linear and 2-phase tapers, in terms of performance enhancements, training-induced adaptation, and fatigue changes.

Figure 1

Figure 1

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Individual Model Parameters Used for Simulations

Simulations were run independently for 13 sets of the nonlinear model parameters previously determined by Busso (4) and Thomas et al. (22). Each set of parameters was assumed to characterize the response to training of an individual. Consequently, 13 individuals were involved in the present study. We categorized them into 2 groups according to their training background: Either nonathletes (non-ATH) for the participants of the study of Busso (4) or athletes (ATH) for the participants of the study of Thomas et al. (22). The mean model parameters for both populations are presented in Table 1. The non-ATH group included 6 male untrained subjects before their enrollment in a 15-week laboratory experiment on a cycle ergometer (5). Their mean age was 32.7 ± 5.0 years and their maximal oxygen uptakes before and after the experimental training were, respectively, 42.9 ± 7.4 ml·min−1·kg−1 and 51.9 ± 9.0 ml·min−1·kg−1. Their criterion performance was their mean power during a 5-minute all-out exercise. The ATH group included 3 female and 4 male national and international-standard swimmers specialized in 100-m or 200-m events. Their training data were collected over 2 successive seasons in real training conditions (22). Their mean age and competition experience were 19.8 ± 2.5 years and 12.9 ± 3.0 years, respectively. Their personal record gave a mean international point score (IPS) for the 8 swimmers of 885 ± 21 (see Three swimmers had a score higher than 900, a benchmark criterion for swimmers of international caliber (19). Because no significant sex difference had been previously observed (22), the male and female subject data were combined. Written informed consent was obtained from the participants, and the experimental procedures were approved by the local Ethics Committee.

Table 1

Table 1

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Modeling Procedures

The mathematical model proposed by Busso in 2003 (4) was applied to compute the performance, ascribed to model output, from the training doses, ascribed to model input. The model is based on a transfer function composed of 2 antagonistic first-order filters representing the positive and negative training effects on performance, according to the following impulse response: k 1.e−t/ τ 1 - k 2(t).e−t/ τ 2. The performance is defined as the balance between the 2 opposite effects, where the level depends on which effect predominates at each specific time point. Both effects are supposed to vary in a similar way after a training dose (i.e., an immediate increase proportional to the volume of training), followed by an exponential decrease during the intervening period between 2 training impulses. The parameters k 1 and k 2 are gain terms corresponding to weighting factors for the initial increase of the positive and negative effects, respectively; τ 1 and τ 2 are decay time constants and determine the speed of the subsequent reduction. A high τ indicates a slow reduction and vice versa.

Contrary to the initial model of Banister et al. (1), the gain term for the negative component k 2 is not time invariant but is assumed to vary over time with training doses according to an impulse response (k 3.e−t/ τ 3). This extension from earlier model formulations implies that a given session will result in greater fatigue after an intensification of training and requires a longer time to recover. Therefore, the nonlinear model includes 5 constant parameters: 2 gain terms (k 1 and k 3) and 3 decay time constants (τ 1, τ 2, τ 3), which characterize the individual athlete's response to training. These model parameters are individually determined by fitting the modeled performances to the actual performances.

The performance p(t) is estimated by the convolution product of the training doses w(t) with the impulse response added to the basic level of performance noted p*. The training w(t) is considered a discrete function (i.e., a series of impulses each day, wi on day i). The convolution product is computed as a summation in which model performance P^n on day n is estimated by mathematical recursion from the series of wi. P^n is estimated as follows:

The value of k 2 at day i is estimated by mathematical recursion using a first-order filter:

Adaptations and fatigue were estimated with the positive and the negative influences of training on performance, computed from the combined effects of both model functions on performance (6). The amount of training on day i had an effect on performance on day n quantified by:

The values of the positive and negative influences on day n (PIn and NIn, respectively) were estimated from the sum of influences of each past training amount depending on whether the result was positive or negative:

Model performance on day n was also the difference between PIn and NIn.

The outcomes from the nonlinear model showed an inverted-U relationship between daily training amounts and performance (4). This model is based on the assumption that performance could be stabilized at a maximal level for an optimal daily training, assuming sufficient training to reach a steady state. Optimal daily training (ODT) is computed from the model parameters as follows:

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Training Simulations

All the training simulations were composed of 3 successive periods of daily training: A normal training period followed by an overload training period and finally a taper (Figure 2). In line with our previous studies (21,22), normal training was set to optimal daily training for non-ATH and to the mean training load of the 40 weeks with the highest training loads over the 2 studied seasons for ATH. In both cases, normal training was assumed to be long enough to stabilize performance. Overload training was then characterized by a 20% step increase in training load during 28 days. The taper started with a training load set to the normal training level. The first days of the taper could not be considered as an overload period, in contrast to the period when the load was progressively reduced from the overload training level (21,22). Afterward, 2 tapering patterns were produced: Either a linear taper with a constant linear reduction in the training load, or an alternative strategy, termed 2-phase taper, in which the training load varied linearly in a 2-phase sequence. The slope of the training reduction in the linear taper was variable in degree and duration to determine its optimal characteristics for maximizing performance.

Figure 2

Figure 2

The overall duration of the 2-phase taper was set to the duration of the optimal linear taper, assuming that the second phase of the 2-phase strategy extended over the last 3 days. During the first phase of the 2-phase strategy, training was identical to the optimal linear taper (same slope of the training reduction). During the second phase, the training load was free to vary linearly and could decrease (with the same slope or not), remain stable, or increase. This approach assumed that only the variation in training load, which maximized the performance at the end of the taper, was used for the analysis. To compare the responses to training of the 2 groups of participants, training load and performance were standardized and expressed as a percentage of their respective level during normal training (%NT).

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Statistical Analysis

Mean, standard deviation, and standard error were calculated for the selected variables. Our goal was to compare the benefits from linear and 2-phase tapers. Because the model parameters came from subjects with different training activity and background, this factor was also included in the statistical analysis. The differences between the 2 tapers were thus compared using analysis of variance (ANOVA) with 2 factors (ATH vs. non-ATH and linear versus 2-phase tapers or first vs. second phase of the 2-phase taper). The acceptable level of statistical significance was set at p < 0.05. The statistical power values calculated at the n sizes used was greater than 0.97 for the comparisons between the 2 types of tapers and lower than 0.5 for the comparisons between ATH and non-ATH.

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The duration of the optimal linear taper was 35 ± 6 days in non-ATH and 33 ± 16 days in ATH. The 2-phase taper was set to have the same duration. The other taper characteristics that yielded the highest performances according to the 2 studied patterns (linear or 2-phase) and the participants' training background (non-ATH or ATH) are shown in Table 2. No substantial differences were found between non-ATH and ATH. Conversely, the mean training reduction and the final load were substantially higher with the optimal 2-phase taper than the optimal linear taper.

Table 2

Table 2

To ascertain that the training load increased during the last 3 days of the optimal 2-phase taper, the final load was compared with the load of the 3 previous days. The optimal variation in the training load during the final 3 days of the 2-phase taper was an increase from 66 ± 13 to 83 ± 23% of normal training in non-ATH and 35 ± 32 to 49 ± 46% of normal training in ATH (Figure 2). This increase in training load was statistically significant in the whole group (p < 0.005) without an interaction effect. In 2 participants (1 in each group), the training load continued to decrease during the last 3 days of the 2-phase taper but less quickly than during the first phase and during the linear taper.

The changes in performance during the 3 periods of training are shown for 2 participants (Figure 3). For the whole groups, the performance decreased during overload period by 2.2 ± 0.7% in non-ATH and 1.4 ± 0.9% in ATH. During the optimal linear taper, the performance increased from the end of overload training by 4.4 ± 2.5% in non-ATH and 4.0 ± 2.6% in ATH (p < 0.0001). The maximal performance reached with the optimal 2-phase taper was higher by 0.04 ± 0.02% in non-ATH and 0.01 ± 0.01% in ATH than with the optimal linear taper (p < 0.001). This slight difference was explained by a higher increase in the positive influence during the 2-phase taper than during the linear taper, given that the negative influence was removed completely in each participant at the end of both tapers.

Figure 3

Figure 3

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The present model study showed that the last 3 days of the taper were optimized with a 20 to 30% increase in training load. Compared to a traditional linear taper, such a 2-phase taper allowed additional adaptations without compromising the removal of fatigue. Although the performance benefit is questionable, a final increase in training load during the taper may have practical implications for athletes and coaches in the lead-up to competitions.

The first 2 steps of the investigation were to determine the optimal characteristics of the linear and the 2-phase tapers. The training load, irrespective of the type of taper, should be reduced by ∼30% in non-ATH and ∼50% in ATH over a period lasting slightly more than a month. The mean training reduction in ATH was in accordance with the range of 41 to 60% recommended from a recent meta-analysis of experimental data in competitive athletes (3). The ∼30% reduction in non-ATH, who had trained on cycle ergometers, is consistent with the enlarged range of 21 to 60% proposed specifically for cycling from the same meta-analysis (3). Notably, the duration of the taper was twice as long as that suggested from the meta-analysis by Bosquet et al. (3). However, empirical data on the effectiveness of long 4-week tapers are yet to be fully investigated (3). The duration of the optimal linear taper after a 4-week overload period was 2 weeks shorter if the taper began at the level of normal training, rather than overload training, as computed in previous studies in both groups of participants (21,22).

The weak statistical power for the comparison between ATH and non-ATH did not enable us to draw conclusions about differences in the characteristics of the optimal tapers and the performance changes. It is likely that the number of subjects and the large interindividual variability observed in ATH could explain this finding. This variability could be attributed partly to the imprecision of the data on field training and performances required to determine the model parameters compared with data derived in a controlled laboratory setting (22). In addition, the difficulties to collect data in such a population prevent the determination of model parameters in a large and homogeneous group of high-level athletes. Nevertheless, the parameters determined from data on elite athletes in the field are necessary for having model outputs representative of the responses to training of this type of population (8). Moreover, non-ATH and ATH were not tested in the same sport (cycling and swimming, respectively). This difference is likely to hamper the comparison in the responses to training between the 2 groups, given that the dynamics of the taper are specific to the activities (3).

The third step of the study was to evaluate the potential benefits of a 2-phase taper compared to a linear taper. We observed that after a prolonged decrease in the training load, a moderate increase during the last 3 days of the taper elicited higher performances than a constant linear training reduction throughout the taper in ATH and non-ATH. The computation of the positive and negative influences of training on performance, as indicators of positive adaptations and fatigue, respectively, shed light on the greater effectiveness of a 2-phase pattern in comparison with a linear strategy. The gains in performance during a linear taper preceded by overload period have been essentially explained by a removal of the fatigue, associated to a light increase in the positive adaptations to training, primarily attributable to the delayed adaptations induced by overload training (22). The present results show that the optimal 2-phase taper would not preclude the fatigue dissipation, even though the training loads during the final 3 days were higher than in the linear taper. Conversely, the short increase in the training load in the lead-up to competition would allow the positive adaptations to exceed their maximal level attained with the linear taper. From a mathematical standpoint, these results imply that a 3-day period of moderate increase in the training load would maintain the gain term for the negative component of the model, k 2, at a low level. After a prolonged period of reduced training, a subject could complete an appreciable amount of training having only a positive impact on performance, eliciting the better performances obtained with a 2-phase design. However, a too-large increase in the training load or over a too-long period would increase k 2 excessively, which would have a detrimental effect on performance.

Maximal performances obtained with the optimal 2-phase and linear tapers were similar. Compared to the linear design, the 2-phase strategy provided further performance benefits averaging 0.01% in ATH and 0.04% in non-ATH, which corresponds to 6 to 25 milliseconds for a 60-second event. It is unusual when these magnitudes of performance enhancements allow an athlete to reach a better ranking (10,18). However, these low performance benefits were expected because the 2 studied tapers only differed in the final 3 days and the linear taper was already optimized. The lower performance benefits obtained with the 2-phase taper in ATH than in non-ATH are also consistent with the common idea that athletes would have a reduced margin for performance improvement. Notably, the present theoretical results point out that innovative tapering strategies may be potentially at least as effective as the traditional progressive tapers. It is noteworthy that during both tapers performance increased by more than 4% in ATH and non-ATH, as compared to the end of overload period.

The effectiveness of the 2-phase taper could be improved with manipulation of key variables of training prescription. First, the 2-phase taper may not necessarily be optimal because only the second phase was optimized. The 2 phases could be manipulated to determine precisely their characteristics (training loads level and duration), which maximize performance. Second, the present enhancements in performance only ensued from the alteration of the training amount (intensity, volume, or both). Associated changes in the content of the training sessions could increase the benefits of the 2-phase taper-for instance, by completing work more specific to the competition requirements during the final increase in training. Unfortunately, this type of change cannot be considered by the modeling procedure because the required quantification of the training aggregates all the various training components and does not account for their specific effect on performance (20). These limitations emphasize that the conclusions drawn about an innovative training strategy using the modeling should be tested experimentally (8,20). Nevertheless, the present simulations provided arguments for a new strategy for the pre-event taper. This point highlighted the interest of a model approach to overcome the difficulties that might be met with the experimental protocols required for the investigation of the optimal taper. Another interest of our study is that it gives directions for future potential experimentations. For example, the mere preservation of the performance at a high level despite a 3-day period with a significant training dose could have implications for training programming, particularly for competitions with multiple rounds over several days. The successive qualifying rounds could act as the final increase in the training load before the final round. Other practical implications relate to sports with weekly competitions (e.g., team sports), but specific investigations are needed to optimize training programs in such activities requiring an athlete to repeatedly perform at their best.

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Practical Applications

Two successive phases in the variation in the training load could provide further performance benefits compared to a constant linear reduction through the taper. Whatever the practice level, the training load should be decreased initially and then, during the last 3 days of the taper, progressively increased until 50 to 80% of the normal training level. This tapering design would allow an individual to profit maximally from the training undertaken during the taper by maximizing the adaptations to training without compromising the removal of the fatigue. According to the present theoretical results, the performance benefits obtained with such a tapering strategy were nonetheless very small if compared to the common linear taper. But the fact that a moderate increase in training at the end of taper was not detrimental to performance should be considered when preparing for competitions with multiple rounds over several days. The present study also offers new prospects for further investigation into the performance optimization, suggesting that innovative tapering strategies can be at least as efficient as the traditional tapers.

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The authors gratefully acknowledge Prof. David Pyne for his critical reading of the manuscript and his valuable editorial assistance.

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recovery; modeling; overreaching; training program

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