The Cubs were not the only team that valued free-agent closer Craig Kimbrel enough to make him a three-year offer.



The Rays, the team with the lowest payroll in the majors, were the runner-up for Kimbrel, giving him a choice of two proposals, according to major-league sources. One of their offers was for two years, $31 million with a club option, while the other was for three years, $39 million, sources said.



The Cubs topped the latter mark, reaching agreement with Kimbrel on a three-year, $43 million contract Wednesday night with an option for a fourth year, pending a physical. But the Rays’ strong pursuit of Kimbrel provided two meaningful revelations:



First, Kimbrel’s regression during the 2018 regular season and shaky performance in the postseason did not deter Tampa Bay, which is widely regarded as one of the game’s most forward-thinking clubs.



The Rays, while unwilling to lose the 40th overall selection for signing Kimbrel...