In 2016 there were 13 states in which both campaigns bought advertising or the final election result was within two percentage points on election day. In these so-called battleground states, 47.5 million out of 72.4 million eligible citizens voted, or 65.6%

But in the non-battleground states in 2016, 89.2 million out of 158.2 eligible citizens voted, or 56.4%. So when the campaigns advertised, opened local offices, tried to get out the vote, they drove participation up from 56.4% to 65.6%, an increase of 16.3%. 

An increase in voting of 16.3% when the campaigns seek the votes: a big number.