Lately, more agents correspond with a decrease in apprehensions and removals.
The Senate debate over immigration reform, as in the House, increasingly hinges on a desire from Republicans to "tighten" border security, by which they mean the border with Mexico. To that end, a new version of the Senate proposal that's advancing today would nearly double the number of border patrol agents to 40,000. But in recent years, more agents have corresponded only with a decrease in apprehensions and removals.
Customs and Border Protection has a document that outlines the number of agents in each of three zones over the past twenty years. Over that time, the vast, vast majority of agents have been dedicated to the "Southwest Border Sectors" — the one in need of tightening. Even as the number of agents has risen dramatically, that ratio has been maintained.
The agency of which Customs and Border Protection is a part compiles its own statistics which show how well those agents are doing. And the numbers aren't great. The most recent year for which data is available is 2011. From 1993 to that year, the number of apprehensions (people caught illegally crossing the border), removals (deportations), and returns (people sent back informally) have largely declined as the number of agents has risen.