The assessment of competitive movement demands in team sports has traditionally relied upon global positioning system (GPS) analyses presented as fixed-time epochs (e.g., 5–40 min). More recently, presenting game data as a rolling average has become prevalent due to concerns over a loss of sampling resolution associated with the windowing of data over fixed periods. Accordingly, this study compared rolling average (ROLL) and fixed-time (FIXED) epochs for quantifying the peak movement demands of international rugby union match-play as a function of playing position. Elite players from three different squads (n = 119) were monitored using 10 Hz GPS during 36 matches played in the 2014–2017 seasons. Players categorised broadly as forwards and backs, and then by positional sub-group (FR: front row, SR: second row, BR: back row, HB: half back, MF: midfield, B3: back three) were monitored during match-play for peak values of high-speed running (>5 ms -1; HSR) and relative distance covered (mmin -1) over 60–300 s using two types of sample-epoch (ROLL, FIXED). Irrespective of the method used, as the epoch length increased, values for the intensity of running actions decreased (e.g., For the backs using the ROLL method, distance covered decreased from 177.4 ± 20.6 mmin -1 in the 60 s epoch to 107.5 ± 13.3 mmin -1 for the 300 s epoch). For the team as a whole, and irrespective of position, estimates of fixed effects indicated significant between-method differences across all time-points for both relative distance covered and HSR. Movement demands were underestimated consistently by FIXED versus ROLL with differences being most pronounced using 60 s epochs (95% CI HSR: -6.05 to -4.70 mmin -1, 95% CI distance: -18.45 to -16.43 mmin -1). For all HSR time epochs except one, all backs groups increased more (p < 0.01) from FIXED to ROLL than the forward groups. Linear mixed modelling of ROLL data highlighted that for HSR (except 60 s epoch), SR was the only group not significantly different to FR. For relative distance covered all other position groups were greater than the FR (p < 0.05). The FIXED method underestimated both relative distance (~11%) and HSR values (up to ~20%) compared to the ROLL method. These differences were exaggerated for the HSR variable in the backs position who covered the greatest HSR distance; highlighting important consideration for those implementing the FIXED method of analysis. The data provides coaches with a worst-case scenario reference on the running demands required for periods of 60–300 s in length. This information offers novel insight into game demands and can be used to inform the design of training games to increase specificity of preparation for the most demanding phases of matches.