An interesting article about distance covered per game in the EPL from 2006.

In 2005/06, the average EPL midfielder ran 11.49 kilometres per game. The average EPL centre-back covered 9.96 kilometres per game.

From the article, "the average distance covered by players in matches has changed little [between 2002 and 2006] but the amount done at top speed has almost doubled. What ProZone class as “high-intensity activities” — runs made by players at three-quarters of sprint pace or faster — have increased from 627 per team per match in 2002-03 to 1,209 in 2005-06, and the ground covered by players while sprinting has increased by 40% over four years. A sprint is classed as a run made at quicker than seven metres per second, equivalent to running 100m in a sharp 14 seconds."