The aims of this study were to: a) examine the relationships between high-intensity distances covered above generic and relative speed thresholds in English Premier League (EPL) matches across two consecutive seasons and b) analyze the effects of playing position and team possession. Sixteen elite male soccer players (seven defenders, six midfielders and three forwards) participated in this study (age 27.8 ± 3.5 years, height 183.7 ± 5.4 cm, body mass 83.9 ± 7.1 kg). An Optical Tracking System was used to collect the following variables: total distance covered; high-speed running distance (HSRD) (> 5.5 m/s); high-intensity running distance (HIRD) (5.5-7 m/s); sprint distance (> 7 m/s); total distance covered above Maximal Aerobic Speed (MAS); distance covered > 85% peak speed (PS); and distance > 30% Anaerobic Speed Reserve (ASR). All measures were analyzed as whole match totals and as distances covered in the periods of the team in possession (TIP), opponent team in possession (OTIP), and ball out of play (BOP). Analysis by position based on defenders, midfielders and forwards was also performed. Distance > 30% ASR was almost perfectly correlated with HSRD (r = 0.98), while distances > MAS were highly correlated with both HIRD (r = 0.91) and HSRD (r = 0.91), and distance > 85% PS were highly correlated with SD (r = 0.70). Although the generic and relative speed thresholds show almost perfect correlation, the differences between HSRD, HIRD and distance > MAS indicate that players may be exposed to more HIRD when using relative thresholds.