Bullpen: Bobby Parnell, David Hernandez, Bruce Rondon, Luke Hochevar, Cory Gearrin.
The list doesn't even include New York Mets star Matt Harvey, who is still recovering from elbow surgery last October.
Is there a reason so many pitchers seem vulnerable to elbow injuries right now? Tampa Bay Rays manager Joe Maddon has a theory.
''Sometimes you have to look underneath the surface and I tend to agree it has a lot to do with youth sports and travel teams and multiple travel teams and kids pitching to win when they're really young and throwing too many pitches,'' Maddon said. ''I think the more recent epidemic curiously might be tied to what they're doing before they even get here professionally.''
Maddon and the Rays are hoping for the best after Moore went on the 15-day disabled list Tuesday. If that's all the time the left-hander misses, the Rays should consider themselves fortunate.
It was not immediately clear if he would need surgery, but Tampa Bay fans are obviously bracing for the possibility.
Here are five things to watch around the majors this week.
MARQUEE MATCHUP: Texas sends Yu Darvish to the mound Wednesday night against Seattle's Felix Hernandez in an early duel between AL West aces. Darvish and Hernandez have combined to strike out 45 with only four walks so far this season. Darvish has not allowed a run in 15 innings.
OFF AND RUNNING: The Milwaukee Brewers have won nine in a row, and although it's far too early to proclaim them NL Central favorites, they'll have a chance to open up a nice lead if they can keep this streak going. Second-place St. Louis visits Milwaukee for a three-game series that starts Monday, and the Brewers are already three games ahead of the Cardinals. Carlos Gomez, Ryan Braun and Aramis Ramirez are swinging the bats well for the Brewers.
CASHING IN: San Diego right-hander Andrew Cashner was once known for throwing 100 mph, but the tall Texan now favors movement over velocity, particularly with his sinker. After striking out 11 in a one-hitter against Detroit on Friday, Cashner takes the mound again Wednesday night against Colorado.
DIVISION RIVALS: Detroit edged Cleveland by one game to win the AL Central last year, with the Indians settling for a wild card. The Tigers took the division on the strength of a 15-4 head-to-head record against the Indians. The teams meet this week for the first time in 2014, when Detroit hosts a three-game series starting Tuesday.
SLUGGING SOX: The Chicago White Sox have scored 80 runs in their first 13 games, with Cuban newcomer Jose Abreu boosting a lineup that already included Adam Dunn and Alexei Ramirez. Star left-hander Chris Sale has already received 15 runs of support this year. He received 76 runs in 30 starts last season, when he posted a 3.07 ERA but went only 11-14.
STAT OF THE WEEK: Kansas City went without a home run in its first seven games before Alex Gordon finally went deep Wednesday. Does this tell us anything about how the Royals will fare the rest of the way?
Well, in 2013, there were eight teams that went at least seven games without a homer at some point during the season, according to STATS. The bad news for Kansas City? Only one of those teams - the St. Louis Cardinals - made the postseason.
Gordon's homer is still the only one of the year for the Royals.