But these days, on the field at least, so do the Boston Red Sox.
Boston completed a four-game sweep of the Angels on Sunday, beating them 7-0 before 35,107 at Angel Stadium behind a brilliant performance from former Angels ace John Lackey.
The Red Sox have taken 13 of 14 from the Angels since the start of the 2010 season and outscored them 20-5 in this series.
"Those guys took it to us," said Angels Manager Mike Scioscia, who met with the team after it was shut out for the second consecutive game and told his players to mentally move past the sweep.
The Angels (12-10) have dropped four in a row after winning 11 of 14. It's also their first four-game home sweep since 2005 against Seattle.
"You have to stay positive," Angels outfielder Torii Hunter said. "It's April. It's early."
The Red Sox (10-11) have won a season-high five in a row and eight of nine after starting the season 2-10.
Before this series, the Red Sox were 1-7 in road games.
"I don't remember the last time a team came in with all their pitchers just on a hot streak," Hunter said. "It's just not possible."
The Red Sox have had nine consecutive games in which their starting pitcher has given up fewer than three runs and pitched at least five innings.
That ties the longest such streak in franchise history, set in 1946.
Lackey (2-2) gave up six hits and struck out six in eight scoreless innings Sunday.
The right-hander who spent eight seasons with the Angels, winning Game 7 of the 2002 World Series as a rookie, improved to 4-0 against his former team after signing with Boston in 2009.
The game was briefly delayed because of rain, but that didn't delay Boston's hot start.
As a capper, outfielder Carl Crawford hit a two-run home run in the sixth inning to right-center field, his first homer in a Red Sox uniform.
Angels starter Matt Palmer (1-1) threw five-plus innings and gave up six hits and four runs.
Is there something to these losses to the Red Sox?
"Obviously they've gotten their share of wins in the last year and coming into this year, but two years ago it was reversed," Scioscia said.
"I don't think it has much to do with a rivalry."
Judging by how one-sided these matchups have been recently, it's not much of a rivalry, either.