The Cy Young Award almost always goes to a starting pitcher and it almost always should. Starting pitchers can end up throwing over 100 more innings than most heavily-used relievers. In the process, they do other things that relievers do not (some of which may not actually have any value): throwing a wider pallet of pitches, sticking to a more rigorous schedule, "setting the tone for the game," bunting.
So there's a perfectly valid reason that only 9 relievers have won the award across both leagues, out of the 103 all-time winners (including 1956-'66, when it went to the best pitcher in the majors).
If you look at how Chapman stacks up against (who I've circled as) the Top 5 Cy Young contenders in the NL, he's a fringe candidate based on counting states and accumulated value. That's incredibly impressive on its own. (Strasburg is going to hit his innings limit and there are a few more names that could easily be added here for comparison, but you get the idea.)
That IP sticks out like a sore thumb -- not to mention the fact that he's competing against his own teammate, which raises all kinds of voting complications.
The argument for Chapman has to lean heavily basis of rate stats, talent level and the marginal value of his performances in important game situations - with bonus points for helping lift a contending team into the playoffs. There may be some performances down the road that give his case the shot in the arm that he doesn't need.
This is murkier territory, but saying "Aroldis Chapman is the best pitcher in the NL" - or at least most dominant - meets the smell test. The Rolaids Relief award doesn't quite cut it.
Here's how Chapman stacks up using rate stats. It's a little cartoonish:
Of course, Chapman still runs afoul of the fact that he's a reliever. And Craig Kimbrel (who Chapman has narrowly beat in all the above, except FIP) has been almost as dominant. From a statistical standpoint, you'd have to go a little further and pump up the value of being a shut-down reliever, pitching in high-leverage situations, to bridge the innings gap. You'd also have to take Kimbrel along for the ride.
Chapman leads the league in Shut Downs (# of times a reliever improves a team's chances of winning a game), though he has a slightly worse shut-down to melt-down ratio than Craig Kimbrel. He also leads relievers in WPA/LI. WPA/LI removes leverage from win expectancy. It's another way to compare relievers by removing the accidents of when they entered the game.
Here's how Chapman and Kimbrel compare. Higher numbers are better for all these metrics, except meltdowns ("MD").
Pretty close, though Chapman looks better in pretty much all the top-line rate stats (above).
One interesting side-note is that Johny Cueto is right behind Chapman in WPA and leads the NL in WPA/LI. We'll have to get to him in a later post. Regardless of what you think of the "total value" vs. "total dominance" argument for evaluating players, the Reds probably have the best chance in franchise history this season to bring home a Cy Young Award.