Rodriguez earned his 58th save this season when he finished out Los Angeles' 5-2 win over Seattle on Saturday night. Thigpen posted 57 saves for Chicago in 1990.
"Only a handful of major league relievers understand what it takes to reach the 50-save mark," Thigpen wrote. "Your record-setting season is an accomplishment you should treasure this year for and for years into the future. I am certain your record for saves will stand for many, many seasons to come."
Thigpen, who now manages the White Sox's rookie league affiliate in Bristol, Va., wrote that Dave Righetti sent him a congratulatory note after breaking the record the former Yankees reliever set.
"I wanted to continue that tradition with a note of my own to you," Thigpen wrote.
He closed the letter, which the White Sox distributed to the media, by writing, "I wish you continued success this season and with your outstanding career."
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