Ask five coaches what "establish the run" means.
You get five answers. They are different claims, and they need different data. A quarter of a million plays, 18 columns each, can test two of them.
Where the research stands
On the first meaning: a Bates College study (Shea and Quenzel) of 429 games tied at halftime from 1994 to 2012 found no late payoff from first-half running. On play-action: Ben Baldwin (Football Outsiders, 2018) and Josh Hermsmeyer (FiveThirtyEight, 2019) found that the fake works whatever a team's run volume or run success before it. On the last meaning: winning causes running, because teams that are ahead run to use the clock, and the episode page shows how far the whole-game number moves once the halftime score is held close.
The agent rules on the first meaning. Its policy asks for the comparison that could prove it wrong: the first half only, in games within 3 points at halftime. Change the filters yourself and watch the answer move.