The Patriots’ gamble paid off with T.J. Moe. The rookie slot receiver, who earned more guaranteed money than any of their undrafted free agents, cleared waivers and was placed on the Pats’ injured reserve list. He will not count against their 90-man roster. Moe tore his Achilles tendon last week, according to a source, and the Pats waived him Friday. Moe was subjected to waivers until 4 p.m. yesterday, but no one claimed him so the Pats were able to put him on IR. If the Patriots didn’t want to risk losing Moe, they could have waited until training camp to place him on IR without subjecting him to waivers. Instead, they made the gamble Friday in order to save a spot against the 90-man roster. This was how the Giants lost — and the Patriots gained — tight end Jake Ballard last year. Moe’s three-year contract included an $8,000 signing bonus and $22,000 in guaranteed base salary in 2013. That signified the level of competition for his services following April’s draft. Also, the Patriots re-signed rookie free agent offensive lineman R.J. Mattes. Mattes, 23, was originally signed May 13 out of North Carolina State before being released May 23.