The maximum running speed that a football player can attain during match play has become one of the most popular variables to assess a player’s physical talent. However, the influence of a player’s maximum running speed on football performance has not yet been properly investigated. The aim of this study was to determine the influence of a player’s peak/maximum running speed on the team’s ranking position at the end of a national league. A second aim was to investigate differences in maximum running speed among playing positions. To fulfil this aim, the peak/maximum running speeds of 475 male professional football players were recorded for 38 fixtures of the Spanish first-division league (LaLiga) from the 2017–2018 season (7838 data points). Players’ peak running speeds in each match were assessed with a validated multicamera tracking system and associated software (Mediacoach®). Players’ maximum running speed was established as the fastest running speed they attained during the entire season. Most players (53.5% of the total) had a maximum running speed in the range of 32.0–33.9 km/h, with only three players (0.6%) with a maximum running speed of over 35.0 km/h. Overall, forwards were faster than defenders and both types of players were faster than midfielders (33.03 ± 1.35 > 32.72 ± 1.32 > 32.08 ± 1.63 km/h; p < 0.001). There was no association between teams’ maximum running speed and ranking position at the end of the league (r = −0.356, p = 0.135). The correlations between teams’ maximum speeds and ranking position were low for defenders (r = −0.334, p = 0.163), midfielders (r = 0.125, p = 0.610), and forwards (r = −0.065, p = 0.791). As a result, the variance in the ranking position at the end of the season explained by a team’s maximum speed was of only 7.5%. Finally, as an average for all teams, players’ peak running speeds remained stable at ~30.7 ± 0.6 km/h throughout the whole season. These results suggest that successful and less successful football teams have squads with players able to obtain similar maximum running speeds during match play throughout the season. Hence, players’ maximum running speeds have a poor association with the team’s ranking position at the end of the Spanish professional national league.