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In limited time, Whitley has shown (so far) that he deserves a shot at a permanent spot in the starting rotation.
Chase Whitley is not a flashy prospect. His fastball is underwhelming, stuff and velocity-wise, and the only plus-pitch he really features is his changeup. That's all he has needed so far; Whitley has pitched to the tune of a 2.37 ERA and 2.27 FIP in 19 innings thus far. That's an extremely small sample; is it possible that this continues? Probably not.
Whitley has faced teams like the Cubs, Twins, and the Mets (and the Cardinals, too), so part of his success can be attributed to the fact that he faced three below-average offensive teams. He's also new to starting; he was converted from a full-time reliever just last season and has yet to be stretched out to the length associated with a starter as he has yet to pitch more than five innings in an outing. That doesn't mean he can't be successful over an extended period of time.
By all measures, Whitley's performance is not a total fluke. In terms of batted ball data, Whitley has not gotten lucky at all as he's had a BABIP of .339, a mark that is much higher than any mark he has had throughout his career. And while I won't say that this figure will regress to his minor league mean, it certainly is a good sign. He has not allowed a home run so far, so that will obviously come to an end. That doesn't mean he will become a home run machine, but I would expect them to pop up. Whitley's strikeout rate is stable at 7.11 K/9 and Steamer believes it will settle at around 6.9. His walk rate is relatively low at 1.42, and Steamer says it shoud land around 2.85-3.58.
What has also been working is his changeup and slider: Whitley has gotten a 16.5% Swinging Strike% and 68.8% GB% from his changeup. And while that actually is creating negative value from FanGraphs' pitch value metric, the fact that he is getting the swings and misses mean that that number will regress to a higher value. His slider, meanwhile, has induced a 29 wRC+ against and has gotten a 17.5% Swinging Strike% and 30.8% K%.
Chase Whitley has accumulated the third most fWAR (0.7) of any Yankee starter and it's no surprise given how he's pitched so far. Do I think he will continue to pitch at this pace? I highly doubt it. But with many of his peripherals stable (other than HR/FB%) and his plus-pitches working, it's clear that he will have some success at the Major League level. Considering that he is the eighth starting pitcher on the depth chart, the Yankees have to be happy about his performance thus far.
Whitley is not going to blow anybody away and he's not going to put up gaudy numbers, but he will be adequate. If the Yankees are lucky and he pitches to his abilities, I wouldn't be surprised if he pitched around 90 FIP-. While the Yankees thought they had a bounty of young pitching to fill out the back end of their rotation (Nova, Pineda, and Phelps), Whitley could be a dark horse in that race for a long-term spot.