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Has Statistical Analysis Changed the EPL?

Here's Arsene Wenger, via Duncan White  in the Telgraph:

“What the statistics have done, is that they have kicked out of the game all the players who cannot run. Suddenly the English level is much higher. You play against a team and you know it.”Where Wenger has really noticed the improvement in the Premier League’s middle-ranking teams has been at the end of games. Over the years, he had grown used to watching the opposition fade dramatically at the end of games as chasing Arsenal’s passes left them exhausted. Now teams can play at high intensity right up to the whistle.

“Before you would play a team and know that in the last 20 minutes they would be dead,” he said. “That does not exist anymore. The physical demands are very, very high and that provokes of course an adjustment of the mental. You must find somewhere else to make the difference.”

All clubs now have access to ProZone data, in which they can track to quite a sophisticated degree not just how far players run in games but the types of runs they are making. The fitter players are the better they will be able to concentrate and therefore make fewer errors.

The testable implication is a decline in the number of late, game-deciding goals scored by the bigger, previously fitter clubs.  And perhaps a tendency for their rivals to pull it off themselves.  What's the evidence on that?