‘Listed on the Bills’ depth chart as the third-string tight end, Fine faces an uphill battle for playing time at that position. That hill became steeper recently when Fine injured the thumb on his left hand while making a tackle during a preseason game. Doctors told Fine he could miss up to five weeks. He’s not planning on being out that long. “Hopefully, it will be sooner than that,” Fine said. “I want to get back as fast as possible. It’s just a stinkin’ thumb. I can tough this out.”‘