SAN DIEGO — A widely touted Border Patrol initiative to send migrants back to Mexico far from the points they are caught entering the U.S. illegally has one of the worst track records at discouraging people from trying again, according to a new study that offers a detailed assessment of how the agency’s new enforcement strategies are working.

The aim of the so-called lateral repatriations is to make it more difficult for migrants to reconnect with smugglers. The Congressional Research Service, drawing on previously unpublished Border Patrol data, found those migrants were among the most likely to get caught again.

The study, which was delivered to members of Congress earlier this month but not publicly released, also found that criminal prosecutions and placement in formal deportation proceedings appeared to be the most effective deterrents.

Nearly 102,000 arrests on the Mexican border were channeled to the Alien Transfer Exit Program during the 2012 fiscal year, which typically involves putting migrants caught in Arizona on buses to be sent back to Mexico hundreds of miles away at crossing points in Del Rio, Texas; Calexico, Calif.; and San Diego. The report says 24 percent of migrants who received such treatment during the 2012 fiscal year were caught again, compared to a recidivism rate of 17 percent overall along the border.

The gap was slightly wider in 2011, when 28 percent of crossers who were assigned lateral repatriation were caught again. That compared to an overall rate of 20 percent along the border.

The report does not explain why some return methods appeared to work better than others but noted that the Border Patrol looks at the history of each migrant before deciding which method would be the most successful.

Bryan Roberts, who held various positions as an analyst of border and immigration issues at Homeland Security, said smugglers may form alliances in distant cities to connect migrants with other guides. For example, a smuggler in Naco, Ariz., may call one in Brownsville, Texas, if his customer is bused there, to arrange another try.

“There’s an understanding (between the migrant and smuggler) that there will be multiple attempts,” said Roberts, now an economist at consulting firm Econometrica Inc.

Lateral repatriations performed better than simply turning migrants back to Mexico without any punishment. In those cases — which the Border Patrol still uses for children, medically ill and other rare cases — 27 percent were caught again last year. Operation Streamline, a commonly used tactic that allows U.S. Attorneys to impose jail time of up to six months, did well with a recidivism rate of 10 percent. It is used widely in Texas and Arizona, but not California.

Among those placed in formal deportation proceedings last year, only 4 percent were caught again. Migrants typically appear before an immigration judge, are made ineligible for a visa for at least five years and are threatened with criminal prosecution if they try again.

Another study, released by the Council on Foreign Relations, found the Border Patrol’s success rate at capturing immigrants may be lower than the agency says. A review of migrant surveys and Department of Homeland Security records suggests between 40 percent and 55 percent of illegal crossings result in capture. The Border Patrol estimated that 61 percent of illegal crossings resulted in capture in 2011, the latest year available.

Edward Alden, a senior fellow at the council, said the Border Patrol’s higher capture rate reflects the challenges of counting how many people get away, not any deliberate attempt to inflate its success. The council’s analysis of raw data from the other sources suggests that the Border Patrol may have a longer way to go to satisfy some lawmakers.

Under proposed legislation in the Senate, the Border Patrol would be required to show they are catching or turning back 90 percent of all border crossers. Measuring border security has emerged as a major theme and potential sticking point to immigration legislation. Tom Coburn, the ranking Republican on the Senate Homeland Security and Governmental Affairs Committee, said last week that the capture rate is “meaningless” without a firmer handle on how many crossers succeed.

The Border Patrol counts getaways largely by spotting footprints, broken twigs and other human traces along the 1,954-mile border with Mexico. Chief Mike Fisher said last week that the agency doesn’t know precisely how many succeed, which is why authorities are developing airborne radar and other technology.