1. Performance modelling and tapering
Iñigo Mujika
Department of Research and Development
ATHLETIC CLUB BILBAO

2. Mathematical modelling and systems theory
Athlete = System +
Fitness Σ
Performance
Training
Fatigue -
Banister & Fitz-Clarke J. Therm. Biol. 18: , 1993

3. Modelling the effects of training
Performance
Positive influence
Initial
Negative
Influence tn tg
Time
Training
Mujika et al. Med. Sci. Sports Exerc. 28: , 1996

4. Characterisation of a dynamical process? t
Input
Ouput
System .
Goodness-of-fit
Busso & Thomas Int. J. Sports Physiol. Perf. 1: , 2006

5. Modelling application in swimming
Performance (% PB)
105
100 95 90
Modeled Performance
Actual Performance 85 5 10 15 20 25 30 35 40 45
Positive Influence (PI)
Negative Influence (NI)
102 4
100 3 98 96 2 94 1 92 PI NI 90 5 10 15 20 25 30 35 40 45
Training Load (A.U. wk-1) .
120
100 80 60 40 20 5 10 15 20 25 30 35 40 45
Mujika et al.
Med. Sci. Sports Exerc. 28: , 1996
Weeks of Training

6. Mathematical modelling and taper duration
Performance
tg = 32 ± 12 days
tn = 12 ± 6 days tn tg
Time
Training
Mujika et al. Med. Sci. Sports Exerc. 28: , 1996

7. Modelling the effects of the taper92 93 94 95 96 97 98 99
100
Positive Influence (PI)
Early Season
Pre-Taper
Post-Taper T1 T2 ES
0,5
1,0
1,5
2,0
2,5
3,0
3,5 ** *
Negative Influence (NI) T1 T2 T3 ES T3
Mujika et al. Med. Sci. Sports Exerc. 28: , 1996

8. Varying adaptation profiles
Performance
Swimmer HR 14 38
Swimmer CJ 10 24
Time
Training

9. Limitations and model evolution
“The theoretical analysis based on the original model of Banister et al. (1975) is possibly flawed because of the underlying linear formulation. The response to a given training dose was independent of the accumulated fatigue with past training. This implies that the taper duration should be identical whatever the severity of the training preceding the taper ”
“This led us to propose a formulation of a new non-linear model. This non-linear model implied that the magnitude and duration of the fatigue produced by a given training dose increased with the repetition of exercise bouts, and was reversed when training was reduced (Busso, 2003)”
Thomas et al. J. Sports Sci. 26: , 2008

10. Prediction of system’s behaviour from previous observation
Model
&
Parameters ? t
Input
Ouput
Model
&
Parameters ? t
Input
Ouput
Busso & Thomas Int. J. Sports Physiol. Perf. 1: , 2006

11. Characteristics of the optimal simulated taper
Form of training reduction
Step
Linear
Exponential
Without OT
65.3
46.3*
54.7*$
% Reduction
With OT
67.4
43.1*
51.6*$
Duration
(days)
16.4
22.4
22.3*
39.1*
Without OT
With OT
25.4*
42.5*
Performance
(% Personal record)
101.1
101.4
101.5*
Without OT
With OT
*: different from Step; $: different from Linear
Thomas et al. J. Sports Sci. 26: , 2008

12. Effects of previous training on optimal taper characteristics
Without OT
With OT 1 2 3 4 5 6 *
Optimal Training Load
(Training Units)
Without OT
With OT 20 40 60 80
100
Optimal Reduction
(% Pre-Taper Training)
Without OT
With OT 5 10 15 20 25 30 *
Optimal Duration
(Days)
Without OT
With OT 1 2 3 4 5 **
Performance Improvement
(% Pre-Taper Performance)
Thomas et al. J. Sports Sci. 26: , 2008

13. Effects of optimal taper on NI, PI and performance
Pre
Post 1 2 3 4 5 *
Negative Influence 97 98 99
100
101
102
Positive Influence
Performance
(% Personal Record)
WITHOUT OT
Pre
Post 1 2 3 4 5 *
Negative Influence 97 98 99
100
101
102
Positive Influence
Performance
(% Personal Record)
WITH OT $
Thomas et al. J. Sports Sci. 26: , 2008

14. Changes in training load during optimal two-phase taper
Training Load (%NT) OT
120 NT
100
* $ 80 60 40 20 1 2 3 4 5 6
Weeks of Taper
Thomas et al. J. Strength Cond. Res. Submitted

15. Performance changes during optimal two-phase taper
Performance (%NT)
104 27 26 28 29 30
103,40
103,45
103,50
103,55
Days of Taper
Performance
Optimal linear taper
Optimal two-phase taper
103
102
101 NT
100 99 OT 98 97 96 1 2 3 4
Weeks of Taper
Thomas et al. J. Strength Cond. Res. Submitted

16. Conclusions

17. Conclusions
The available data on performance modelling confirm the relevance of the modelling approach in the study of individual responses to training and the optimisation of tapering strategies
Computer simulations based on mathematical modelling offer new prospects for further investigation into innovative tapering strategies and performance optimisation

18. (“Thank you very much!” in Basque Language)
ESKERRIK ASKO!
(“Thank you very much!” in Basque Language)