Modeling the relationship between athletic performance and training has been a major topic of sports science research since the 1970s. The idea is that an athlete's performance on a given date is explained by all the training completed beforehand.
From this viewpoint, if P*t denotes performance on date t and Xi*,*j the volume of type i training completed on day j (where, of course, 1 ≤ j ≤ t), then we seek a function f* such that:
P*t = f* (X1,1… X1,*t*‒1, X2,1… X2,*t*‒1… X*k*,1… X*k*,*t*‒1) + *εt where k is the number of different types of training and εt* represents the influence of uncontrolled random factors on performance.
This type of problem, known as a time-series problem, is widely studied in economics, for example when analyzing stock prices. Such models are high-dimensional and involve many parameters, which remain statistically viable because there are thousands of observations (hourly stock prices over several months). In sport, however, there are few observations of an athlete's performance, so the models are more limited…
Banister's model
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