Calculated Metrics

Learn how calculated metrics are derived and how to interpret them in a force-velocity profile.

F₀ and v₀

The main output of a force/velocity profiles are the two numbers $F_0$ and $v_0$. Together, they describe the physical abilities of the runner:

• F₀ (Force Intercept): $F_0$ represents the theoretical maximal horizontal force the athlete could produce when starting from rest (i.e., at zero velocity). This value reflects the athlete’s force-producing capability.

• v₀ (Velocity Intercept): $v_0$ is the theoretical maximum sprinting speed that the athlete could achieve if the force output dropped to zero. Although no athlete actually reaches $v_0$, it serves as a benchmark for their speed potential.

These two values, together with the athlete's body weight and height, can then be used to calculate all the remaining metrics.

Max Speed Unloaded

While $v_0$ is a measurement of speed capacity, it does not represent what the person could actually achieve.

A better value is the estimated max unloaded speed which is calculated by adding the effects of air resistance. This value represents a speed that the runner is expected to be able to reach.

Power

Max Power (Pmax): Greatest power (product of force and speed) a sprinter can generate during the acceleration phase. It reflects overall explosiveness, with higher values indicating better sprint performance.

Relative Max Power: Max power adjusted/normalized to body weight, which allows for a better and more fair comparison between athletes of relative explosiveness.

Acceleration

Tau (𝜏): Defined as the time taken to reach 63% of the top speed ($v_0$). A smaller $\tau$ means the athlete accelerates to a significant portion of their top speed more quickly, indicating a more explosive start, while a larger $\tau$ suggests a more gradual build-up of speed.

This is a relative acceleration measurement and as such can be hard to compare between individuals in a team. To get an absolute measurement of acceleration ability, the various prediction tables can be used (e.g. time to 5 m).

Ratio of Force

RF Max (Maximum Ratio of Force): Is the push aimed the right way? This measurement represents how much of a sprinter’s total force (percentage) is directed horizontally during the start of a sprint. A greater $RF_{max}$ means better and more effective force application for explosive horizontal acceleration. Thus, this is an indirect measurement of early acceleration ability based on Newton´s second law ($F = ma$). Maximum ratio of force — "is the push aimed the right way?"

Every step produces one total force vector into the ground. Part of it holds the athlete up; part of it drives them forwards. RFmax is the biggest share that goes forwards, measured around the first step. This is the closest thing in the profile to a technique score, and it is why two athletes with identical strength can accelerate very differently. Caution: higher is not infinitely better (some vertical force is mandatory just to fight gravity).

DRF (Decrease in Ratio of Force): How long can they keep pushing? This measurement is the rate at which a sprinter’s ability to apply horizontal force drops as they gain speed. A lower DRF means the athlete is better able to maintain a horizontal force application during acceleration. Based on Newton´s second law ($F = ma$), this becomes an indirect measurement of acceleration ability.

As speed climbs, the ability to angle force forwards decreases. DRF is the rate of that decrease. The flatter it is (closer to zero), the longer the athlete can keep meaningfully accelerating. DRF describes distance to peak velocity. Team-sport athletes typically top out around 25–30 m. National-level 100 m sprinters keep accelerating to 40–50 m. World-class sprinters reach 50–80 m — and record DRF values near −6.4%, the flattest measured in humans.