Modeling and Prediction of Competitive Performance ...

European Journal of Sport Science, vol. 2, issue 2 Swimming and Neural Networks / 1 ©2002 by Human Kinetics Publishers and the European College of Sport Science

Modeling and Prediction of Competitive Performance in Swimming Upon Neural Networks Jürgen Edelmann-Nusser, Andreas Hohmann, andBerndHenneberg The purpose of the paper is to demonstrate that the performance of an elite female swimmer in the finals of the 200-m backstroke at the Olympic Games 2000 in Sydney can be predicted by means of the nonlinear mathematical method of artificial neural networks (Multi-Layer Perceptrons). The data consisted of the performance output of 19 competitions (200-m backstroke) prior to the Olympics and the training input data of the last 4 weeks prior to each competition. Multi-Layer Perceptrons with 10 input neurons, 2 hidden neuron, and 1 output neuron were used. Since the data of 19 competitions are insufficient to train such networks, the training input and competition data of another athlete were used in the training processes of the neural networks to pre-train the neural networks. The neural models were validated by the “leave-one-out” method, then the neural models were used to predict the Olympic competitive performance. The results show that the modeling was very precise; the error of the prediction was only 0.05 s, with a total swim time of 2:12.64 min:s. Key Words: swimming, forecasting, physiological adaptation, Multi-Layer Perceptron Key points: • The Olympic competitive performance of a single female elite swimmer is modeled very precisely using neural networks. • The problem of a small number of data sets is overcome by pre-training with data sets of another swimmer. • The results support a synergetic approach of training adaptation.

Introduction The analysis of training processes is one of the most important issues of training science with respect to assisting coaches in elite sports to monitor training and peak athletic performances in crucial competitions. The performance in swimming is closely connected to physiological adaptations that are induced by the athlete’s training program. Several studies focused on adaptation in swimming (1–5, 8, 12, Jürgen Edelmann-Nusser is with the Department of Sports Science at Otto-von-Guericke-University Magdeburg, 39104 Magdeburg, Germany. Andreas Hohmann is with the Department of Sports Science at the University of Potsdam, 14469 Potsdam, Germany. Bernd Henneberg, SC Magdeburg, Brandenburgerstr. 6, 39104 Magdeburg, Germany. 1

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14) are based on linear mathematical concepts like linear differential equations or regression analysis. But biological adaptation is a complex non-linear problem because the adaptation of a biological system leads to changes in the system itself— that is, the adaptive behavior can change. Further, it is commonly known that double training input does not lead to double performance output. Hence, linear models can only approximate the non-linear adaptive behavior in a very small range of the modeled performance output. The purpose of this paper is to demonstrate that the adaptive behavior of an elite female swimmer can be modeled by means of the non-linear mathematical method of artificial neural networks. The developed model was used to predict the competitive performance (200-m backstroke) at the Olympic Games in Sydney in 2000.

Methods Data Collection The training process lasted a total 95 weeks from week 01/1998 to week 39/2000. According to the system of Fry, Morton, and Keast (9), the training process was divided into different preparation macrocycles, including final competitions. The macrocycles consisted of 6–14 weeks (microcycles) of training preparation and 1–3 weeks of competitions. The data consisted of 19 competitive performances (200-m backstroke) and documented training loads in three zones of swim training intensity and two categories of dryland training. The three zones of training intensity were controlled by frequent lactate testing in the course of the training process. Table 1 shows the documented categories of training. For each week and each category, the training input was quantified according to the third column of Table 1. Table 1

Documented Categories of Training

Category of training

Abbreviation

Quantification

Compensation and maintenance aerobic endurance training at and slightly above the aerobic threshold (2–3 mmol/L blood lactate)

End I

Kilometers per week

Developmental and overload aerobic endurance training at and slightly above the anaerobic threshold ( 4–6 mmol/L blood lactate)

End II

Kilometers per week

Anaerobic power training, speed training, and competitions (6–20 mmol/L blood lactate)

End III

Kilometers per week

Dryland strength training

Strength h

Hours of training

Dryland general conditioning training

Conditioning h

Hours of training

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The competitive performances in the 200-m backstroke events were transformed according to the pointage system of the Ligue Européenne de Natation into LEN-points. Therefore, we used the LEN-point table for 1997–2000 that reaches from 1 to 1200 points, and where the actual World Record (e.g., in the female 200-m backstroke: 2:06.62 min:s) serves as a reference value of 1000 points. Data Analysis Three analyses were conducted: • The first analysis determined the influence of the 2-week taper phase prior to the 19 competitions (model A, see Figure 1). The function of the taper is to allow the athlete to recover from the high training loads before and to peak his performance. • The second analysis determined the influence of the high load training phase 3 and 4 weeks prior to the 19 competitions (model B, see Figure 1). This “crash” cycle normally contains very intense and exhaustive training, and functions to create a state of slight overreaching (14) in the athlete. That state of transient fatigue allows the athlete to reach an accumulated, and thus optimal, supercompensation after the later taper. • The third analysis resulted in an overall model to determine the influence of a 4-week phase prior to the 19 competitions (overall model). For models A and B, Multi-Layer Perceptrons consisting of 10 input neurons, 2 hidden neurons, and 1 output neuron were used (see Figure 2). Ten input neurons were necessary to account for 2 weeks with each of 5 training loads for both models. The overall model was computed as the mean of models A and B. To train the Multi-Layer Perceptron of Figure 2 at least 40 data sets each consisting of one competitive performance and the accompanying 10 training loads of 2 weeks are necessary. But only 19 were available; therefore, data of a second athlete were used: For a second elite female swimmer (400-m freestyle) who is no longer active, 28 equivalent data sets were available. These data sets were used to pre-train the neural networks. The training parameters of the neural nets are shown in Table 2.

Figure 1 — Temporal relationships of models A, B, and competition. Both models are used to compute the competitive performance on the basis of the training input of 2 weeks. Hence, for each model, we compiled 19 data sets, each consisting of 10 training loads of 2 weeks and 1 competitive performance.

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Figure 2 — Multi-Layer Perceptron with 10 input neurons, 2 hidden neurons, and 1 output neuron (circles: neurons; lines: connections between the neurons). Corresponding to the data, each input neuron represents one documented training load of 1 week. For model A, i substitutes 1 and ii substitutes 2; for model B, i substitutes 3 and ii substitutes 4. Since the competitive performance shall be computed, the output layer consists of one neuron that represents the competitive performance.

Table 2

Training Parameters of the Multi-Layer-Perceptrons

Variable

Model A

Model B

Transfer function, input layer Transfer function, hidden layer

Linear Tanh (hyperbolic tangent function) Linear 10,000 5000

Linear Tanh (hyperbolic tangent function) Linear 10,000 1000

Randomized [–0.1 . . . +0.1] 0.1 0.999999 Randomized

Randomized [–0.1 . . . +0.1] 0.1 0.999999 Randomized

Transfer function, output layer Total number of training steps Pre-training, number of training steps Initialization of synapses Learning rate Decay of learning rate (per step) Presentation of training data sets

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Validation All three models were validated by the “leave-one-out” procedure (see Figure 3). The procedure used 18 of the 19 data sets of the participant in the Olympic games to train the network. Hence, during pre-training, 46 data sets (28 + 18) were used; after pre-training, 18 data sets were used. The athlete’s training input of the remaining data set is used to “predict”/model the competitive performance of this data set. Afterwards the “predicted”/modeled competitive performance is compared with the real competitive performance, and the error is computed (error = modeled performance – real performance). This procedure was used for each data set and each model—that is, 2 3 19 modeled performances were computed to validate the neural models. Then the overall model was computed as the mean value of the corresponding modeled performances of model A and model B. Table 3 shows the mean error and standard deviation of the modeled performances in this procedure. Finally, the results of Table 3 were compared to the results of multiple linear regression analyses. According to the leave-one-out method, multiple linear regression analyses were used to compute each of the 19 competition performances for model A as well as model B. Eighteen of the 19 data sets were used to compute the coefficients of the equation of Figure 4. Each time, the coefficients were used to compute the 19th competition performance. Then the overall model was computed as the mean value of the corresponding modeled performances of model A and model B. Table 4 shows the mean error and standard deviation of the modeled performances upon multiple linear regression analysis. It is evident that the results derived from the

Figure 3 — “Leave-one-out” procedure. For model A as well as model B, 19 runs were performed, with each model “predicting” the 19 competitive performances.

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neural networks (see Table 3) are much better. After this validation, the Olympic competitive performance was predicted. For model A, a neural network was trained for 5000 training steps with all 19 data sets of the Olympic participant and 28 data sets of the other swimmer (pretraining). Then the neural network was trained with the 19 data sets of the Olympic participant for the 5000 remaining training steps (main-training). Next, the Olympic competitive performance was predicted on the basis of the training loads of the taper phase before the Olympic competition (prediction of model A). For model B, a neural network was trained for 1000 training steps with all 19 data sets of the Olympic participant and 28 data sets of the other swimmer (pretraining). Then the neural network was trained with the 19 data sets of the Olympic participant for the 9000 remaining training steps (main-training). Next, the Olympic

Table 3 Mean Error and Standard Deviations of the Error of the Modeling of the 19 Competitive Performances (LEN-Points) Upon Neural Networks

Variable Mean error Standard deviation

Model A: “taper cycle”

Model B: “crash cycle”

Overall model

14.78 15.76

20.16 17.73

12.02 15.82

Note. The mean error of 12.02 of the overall model is equivalent to differences of +0.62 s or –0.61 s in the mean time of all nineteen 200-m backstroke races of 2:12.94 min:s.

Figure 4 — Linear equation to compute competitive performance. For model A, i substitutes 1 and ii substitutes 2; for model B, i substitutes 3 and ii substitutes 4. Table 4 Mean Error and Standard Deviations of the Error of the Modeling of the 19 Competitive Performances (LEN-Points) Upon Multiple Linear Regression Analyses

Variable Mean error Standard deviation

Model A: “taper cycle”

Model B: “crash cycle”

Overall model

39.55 29.93

37.22 25.72

34.19 18.72

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Figure 5 — Comparison of the real competitive performances, the modeled performances (overall model), and the prediction of the Olympic competitive performance. The error of the prediction is 1.24 points and 0.05 s.

competitive performance was predicted on the basis of the training loads of the crash cycle before the Olympic competition (prediction of model B). In the final step, the prediction of the overall model was computed as the mean value of the prediction of model A and the prediction of model B.

Results Figure 5 compares real competitive performances and modeled competitive performances of the overall model. The overall model predicted an Olympic competitive performance of 2:12.59 min:s (871.24 LEN-points), while the real competitive performance was 2:12.64 min:s (870 LEN-points).

Discussion The results demonstrate that neural networks are excellent at modeling and predicting competitive performances on the basis of training data. The problem, of neural networks generally requiring many data sets for training, was overcome by using data sets of another athlete. But this was only possible because the documented training loads were the same for both athletes. It is necessary that the adaptive behavior of both athletes is similar. We assumed this, but we did not know it before the modeling; hence, there is no guarantee that such modeling and prediction can be done with data sets of any other athletes. The validation procedure must be conducted for each athlete and, for each set of results, one must decide whether the neural network is a good or poor model of the adaptive behavior of the athlete. To establish a good model, it may also be necessary to change some of the training parameters (see Table 2). Currently, however, there are no rules for changing these parameters, apart from trial and error. A good model is not only able to predict competitive performance; it may also be used to calculate a simulation of the prospective performance responses of the athlete under the influence of a slightly changed structure of training loads. Thus, after some training analysis, the trained neural network allows the coach to simulate

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the effects of certain modifications of the training program on the competitive performance of the athlete. This makes the planning and monitoring of a training process more effective. To investigate the applicability and limitations of neural networks to model and predict competitive performances, we used Multi-Layer Perceptrons (Figure 2) to model 28 competitive performances of another athlete who was no longer active (see 6). This neural modeling resulted in a mean value of the error of 12.8 LENpoints. As this is very close to the mean error of 12.02 LEN-points in Table 3, we can assume that our modeling would be successful for other athletes, provided there are at least 40 data sets and the documented categories of training are comparable. To reduce mean error, more information about the training process (i.e., more documented categories of training as shown in Table 1) is necessary. But increasing the number of categories in Table 1 means also increasing the number of input neurons in Figure 2: A sixth category increases the number of input neurons to 12 and would require at least 50 data sets for the training of the net. Another way to decrease the error is to increase the number of neurons in the hidden layer, but this requires many more data sets. For instance, a third neuron in the hidden layer would require at least 60 data sets. (The minimum number of data sets is about double the number of connections between neurons.) More single case studies using larger data sets are necessary to gain experience about this method. The accurate results of the neural modeling compared with the poor results of the linear regression analysis emphasizes a very important aspect of training science: The adaptive behavior of the system athlete is quite a complex, non-linear problem. This supports a synergetic approach of training adaptation. The synergetic approach is to be seen as a metaphor for the adaptive behavior of the system athlete in which the athlete enters a certain stable state of performance (the attractor) in a self-organized way under the influence of the training load as a control parameter. To analyze the synergetic behavior of a complex dynamic system, tools are needed that predict what states of the system are more or less likely to occur. This question is precisely addressed through neural networks, because neural networks are computing devices that are able to recognize or distinguish different kinds of input and output patterns of the behavior of interest. Hence, from a synergetic point of view, a successful neural modeling may be (but is not required to be) interpreted as a representation of deviations of the different states of the system from equi-probability, in our case the identification of stable states of the athletic performance (see 7, pp. 211-12). This synergetic point of view is a very interesting, but still-hypothetical, aspect of neural modeling a competitive performance, because the non-linear dynamical systems perspective is rapidly emerging as one of the dominant metatheories in the natural sciences (10, 11), and there is reason to think that it will provide integrative understanding in training science as well.

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3. Busso T, Häkkinen K, Pakarinen A, Carasso C, Lacour J-R, Komi PV, Kauhanen H. 1990. A systems model of training responses and its relationship to hormonal responses in elite weight lifters. Eur J Appl Physiol 61:48-54. 4. Busso T, Denis C, Bonnefroy R, Geyssant A, Lacour JR. 1997. Modelling of adaptations to physical training by using a recursive least squares algorithm. J Appl Physiol 5:168593. 5. Chatard JC, Mujika IT. 1999. Training load and performance in swimming. In: Keskinen KL, Komi PV, Hollander AP, editors. Biomechanics and medicine in swimming VIII. Jyväskylä: University Press (Gummerus Printing). p. 429-34. 6. Edelmann-Nusser J, Hohmann A, Henneberg B. 2001. Modellierung von Wettkampfleistung im Schwimmen mittels neuronaler Netze. In: Perl J, editor. Sport und informatik VIII. Cologne: Sport und Buch Strauss. p. 11-20. 7. Eiser JR. 1994. Toward a dynamic conception of attitude consistency and change. In: Vallacher RR, Nowak A, editors. Dynamical systems in social psychology. San Diego, CA: Academic Press. p. 197-218. 8. Fitz-Clarke JR, Morton RH, Banister, EW. 1991. Optimizing athletic performance by influence curves. J Appl Physiol 71:1151-58. 9. Fry AC, Morton RH, Keast D. 1991. Overtraining in athletes: an update. Sports Medicine 12:32-65. 10. Haken H. 1983. Synergetics. An introduction. Nonequilibrium phase transitions in physics, chemistry and biology. Berlin: Springer. 11. Haken H. 1995. Erfolgsgeheimnisse der natur. Reinbek bei Hamburg: RoRoRo. 12. Hohmann A. 1992. Analysis of delayed training effects in the preparation of the westGerman water polo team for the Olympic games 1988. In: MacLaren D, Reilly T, Lees A, editors. Swimming science VI. London: E & F Spon. p. 213-17. 13. Hooper SL, Mackinnon LT. 1999. Monitoring regeneration in elite swimmers. In: Lehmann M, Foster C, Gastmann U, Kaizer H, Steinacker JM, editors. Overload, performance, incompetence and regeneration in sport. New York: Kluwer Academic Plenum. p. 139-48. 14. Kreider RB, Fry AC, O’Toole ML. 1998. Overtraining in sports: terms definitions, and prevalence. In: Kreider RB, Fry AC, O’Toole ML, editors. Overtraining in sport. Champaign, IL: Human Kinetics. p. vii-ix. 15. Mujika IT, Busso T, Geyssant A, Chatard JC, Lacoste L, Barale F. 1996. Modeling the effects of training in competitive swimming. In: Troup JP, Hollander AP, Strasse D, Trappe SW, Cappaert JM, Trappe TA, editors. Biomechanics and medicine in swimming VII. London: E&F Spon. p. 221-28.

Acknowledgment This study was funded by the Federal Institute of Sports Science (Bundesinstitut für Sportwissenschaft; reference no.: VF 0407/16/02/2000), Bonn, Germany.

About the Authors Dr. Jürgen Edelmann-Nusser studied sports science and electrical engineering. He worked at the University of Stuttgart in the Department of Sports Science (1995– 1998) and at the Department of Parallel and Distributed High Performance Systems

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(1998–1999). In Magdeburg, his main fields of research are computer science in sports and sports equipment. Prof. Dr. Andreas Hohmann is with the Institute of Sport Science in the University of Potsdam, Germany. He was a assistant coach of the German water-polo national team at the Olympic Games 1988 in Seoul. Today, he is a member of the scientific advisory board for the German Swimming Federation. Bernd Henneberg is a coach at SC Magdeburg and assistant coach of the German national swim team.