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According to Mike Monroe of the San Antonio Express News:
Re-exam of Kawhi Leonard's fractured 4th metacarpal (rt. hand) confirms simple fracture; in splint and out 3-4 weeks
— Mike Monroe (@Monroe_SA) January 23, 2014
Sometime at the end of February, the Spurs might have all three of their starters back as Tiago Splitter, Danny Green and now Kawhi are all expected to return towards the end of the yearly Rodeo Rode Trip.
UPDATE
An official injury update was released from the Spurs at 3:25 pm CST:
Spurs forward Kawhi Leonard underwent a CAT scan earlier today in San Antonio. Results confirmed he has a non-displaced fracture of the fourth metacarpal in his right hand. Leonard suffered the injury in the first half of the Spurs-Thunder game on Wednesday night. He is expected to be out three-to-four weeks.