When it comes to projecting pitchers into their older years, there's often a survivor bias that needs to be eliminated. If I were to try to project to see how a 30 year old pitcher will perform at 40, that projection will definitely have to be deflated due to the fact that most pitchers never reach there. But when one is projecting 39 to 40, that whole perspective changes. I'm incredibly fascinated by older pitchers in the past 20 years: pitchers like Randy Johnson, Greg Maddux, Kevin Brown, Kenny Rogers, and Bartolo Colon. As these pitchers have aged they've been able to become so much more efficient in their mechanics, smarter with their pitch selection, and have been able to provide value with a diminished velocity. Hiroki Kuroda is interesting much in the same way, but even more so because there's no age 25-30 data to see what his peak would have been in the United States. But nonetheless, it's obvious that Kuroda is a smart, efficient, and consistent pitcher. Projection systems have him performing at about a 3.50-3.75 FIP/2.50-3.0 fWAR clip. I've decided to run my own rough estimate as well, an estimate based off of historical comparisons.
To pick these historical comparisons, I chose pitchers who played age 38 and 39 seasons some time from 1990-2013. I eliminated any pitchers who played in their age 38 but not their age 39 not seasons; I didn't have to worry about survivor bias because we know for a fact that Kuroda will be playing in his age 39 season. I then took their context-neutral stats--IP, FIP, xFIP, and fWAR, and figured out the percent change over the season. This is obviously a small sample as there were only 23 pitchers, but it's certainly telling of a general trend among older pitchers. Pitchers in this sample saw a 3.25% drop in IP, a 2.14% increase in ERA, a 1.77% increase in FIP, a 27.4% increase in xFIP, and surprisingly, a 4.67% increase in fWAR. Those last two are kind of strange, and that's just an example of how small the sample is. But a couple of things do pop out: Kuroda's innings will drop, most likely by a couple of starts; he will allow more runs, but probably by only a marginal increase; and, his fWAR will still probably decrease regardless of these results.
So what is the most likely outcome? Given his historical comparisons and his previous numbers, I would expect him to pitch 175-195 IP, record a ~3.40-3.60 ERA, a 3.60-3.80 FIP, and an fWAR around 3. That's certainly nothing to scoff at, and I don't foresee a sudden halt in his performance. There have been questions about whether he'll have the steam to push through the second half of the season, and that will be key in terms of his innings total. But if Joe Girardi does not rely too heavily on him (hopefully the offense helps), then I don't see 190 IP being out of the question. Of course, we all have to expect something within two standard deviations of his true talent level--that means he could be a ~3 fWAR as projection, or he could be within ~1.7 fWAR. There's certainly a great deal of randomness involved, but one thing is for sure: pitchers do not get to 39 in MLB on luck. They're usually the best pitchers and usually have avoided serious injuries across their careers. There are definitely questions in the Yankee roster, but I would not consider Hiroki Kuroda one of them.