Modeling performance in endurance sports

The computer programs developed and simulations carried out using the MATLAB programming language and platform prove to be useful for a better study of performance in athletes, particularly those specializing in long-distance running (marathon). Thus, in the article "Mathematical models for estimation and prediction of performance capacity in the 10 km EIFFAGE Dakar" published in 2019 in the Journal of Scientific Research at the University of Lomé, we were able to model and simulate performance variations in twenty-seven (27) athletes based on anthropometric and physiological variables. Principal component analysis allowed us to evaluate the main determining elements of performance among physiological, biomechanical, and anthropometric factors.

Ternary diagram showing the proportions of different phases of the stride within its duration, visualized in a chart for Senegalese athletes (o) and elite international athletes (▲).

This analysis primarily revealed that both actual and predicted best performances are dependent on the athlete's wingspan and %VMA (maximal aerobic velocity). The predictions of aerobic performance in trained endurance runners using the maximal aerobic velocity over a distance of 10 km based on physiological and anthropometric parameters exhibit a correlation of approximately 75-80%. However, Senegalese athletes specializing in long-distance running lag far behind those from countries like Ethiopia and Kenya [Billat et al., 2013]. The article aimed to mathematically translate the biomechanical characteristics of Senegalese athletes' running, such as impulse, suspension, and damping, in order to compare them with those of international Kenyan or Ethiopian athletes (Figure 8). This initial comparison helped determine the essential variables to improve for better performance. The results showed the need to increase the stride suspension time from 0.3 to 0.5 and reduce the damping time from 0.35 to 0.15.

Video analysis and trajectory modelling in Basketball

Extending this work on sport performance modelling to team sports and shooting mechanics, the article "Video analysis and mathematical reconstruction of three-point shot trajectories in Basketball: Validation through physical modeling", co-authored with El hadji Mamouthiam Diop and published in 2026 in the World Journal of Advanced Research and Reviews (WJARR), validates Kinovea - a free, open-source video analysis software - as a reliable, low-cost alternative to expensive motion-capture systems for shooting kinematics.

Eight U18 basketball players performed 34 three-point shots, tracked frame-by-frame to extract projection angle, initial velocity and maximum trajectory height, then reconstructed mathematically using classical projectile motion equations. Contrary to the traditional coaching emphasis on release angle, the study found that trajectory height was the main parameter discriminating successful from missed shots: successful shots reached a mean apex of 5.94 m versus 5.71 m for missed shots (23 cm difference), while projection angle and initial velocity showed no discriminating effect. This work illustrates how accessible video-analysis tools, classical mechanics and statistical modelling can be combined to generate practical, evidence-based recommendations for skill development in sport.

Trajectory height, not release angle, is what separates a made shot from a miss.