Broxton hasn't thrown as hard or missed as many bats the past two years as he did prior to his injury, succeeding this year thanks to a spike in his ground ball rate because of a little increased life on his fastball, which previously was flatter and thus easier to hit in the air. He's a depth guy for the Reds, who were a little left-handed in the back of their 'pen but didn't need a premium arm with Aroldis Chapman and Sean Marshall present.
In exchange for Broxton, the Kansas City Royals get right-hander J.C. Sulbaran, a possible back-end starter who's 90-94 mph with a plus changeup and some feel for a curveball. Born in Curacao, he has competed for the Netherlands in several international competitions, including the Beijing Olympics in 2008. He was also a high school teammate of Eric Hosmer. His fastball is true and his command is erratic, both of which hold him back as a potential starter, although with the potential for two above-average secondary pitches he could be an effective non-specialist reliever. He has whiffed more than a man per inning for Double-A Pensacola.
Left-hander Donnie Joseph is currently at Triple-A and is strictly a reliever, most likely a lefty specialist with a fastball/slider combination that has left-handed batters 7-for-54 against him this year with 24 punchouts and two extra-base hits across two levels. For Broxton, it's a solid return.
I'm surprised that the Cardinals gave up so quickly on 2010 first-rounder Zack Cox, although in their defense he has been awful this year as a 23-year-old in Triple-A, posting a .294 OBP; he hasn't drawn a walk since June 21, a span covering 25 games and exactly 100 at-bats. Cox has above-average raw power that has started to show up in games this year, although he still has a whole-field approach that unfortunately doesn't include working the count as much as it has to. He's fringy at third base with a plus arm but a slow lower half.
Is that too high of a price for a homer-prone right-handed reliever? I tend to think it is. Edward Mujica has switched to using a two-seamer more often this year to try to keep the ball in the park, without great success and at a cost of some swings and misses, and even with a splitter in his arsenal he has trouble with left-handed batters. He's marginally better than a replacement-level right-handed reliever and not someone I'd give up a decent, if clearly faded, prospect to acquire.