Catapult Metabolic Power parameters draw on published scientific works by Manetti et al. (2002) and Osgnach et al. (2010) who documented methodology of estimating the energy demands of acceleration/deceleration events.

The original authors use a fifth order polynomial to relate energy cost to the slope (see publications).

Acceleration is calculated by differentiating the GPS velocity measurements before applying smoothing. This smoothing is given in equation 11 of the Osgnach et al. (2010) publication, in which a 186-point filter of unknown characteristics. At catapult we use a discrete Gaussian filter with a width of 1s.

Accelerations exceeding 1g are excluded and assumed to be due to GPS errors.

The equivalent slope is the ratio of the forward acceleration in g over the 1g downward acceleration. This is the assumption being used in the Osgnach paper; that forward acceleration is roughly equivalent to walking up a slope of this gradient:

**ES** = a/1

The equivalent mass ratio is the combined forward and downward acceleration over the downward acceleration:

**EM** = (a² + 1² )/1

From these are calculated the metabolic power, including a scaling factor of 1.29 to account for the extra energy required for the grass surface: P = CESEMv1.29 (W/kg)

The total distance is calculated by a simple integration of the velocities:

**TD** = vdt (m)

The equivalent distance represents the how much extra ground would be covered if the total energy (including accelerations) was expended purely in continuous running. It is calculated by integrating velocity weighted by a scaling index that represents the total power to constant velocity power:

**ED** = v(CES.EM)/Cdt (m)

Because total distance calculated from velocity may be slightly different to the odometer calculated from the positions, we normalize the equivalent distance so that it can be compared to the odometer:

**EDnormalized** = ED/TDodometer (m)

The equivalent distance index is just a ratio representation of the equivalent distance compared to the actual total distance. It is computed over a period interval.

**EDI** = ED/TD

### For the range of parameters available in the catapult OpenField software please see the ‘Parameters’ section of the OpenField Cloud settings menu.

**References:**

Minetti, Alberto E; Moia, Christian; Roi; Giulio S; Susta, Davide; Ferretti, Guido. "Energy cost of walking and running at extreme uphill and downhill slopes". in J Appl Physiol. Vol 93, pp 1039-1046. 2002.

Osgnach, Cristian; Poser, Stefano; Bernardini, Riccardo; Rinaldo, Roberto; Di Prampero, Pietro Enrico. "Energy Cost and Metabolic Power in Elite Soccer: A New Match Analysis Approach". in Medicine & Science in Sports & Exercise. pp 170-178. 2009.

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