And innings are taken into account, right? Since WAR is a cumulative stat.

And his ERA in innings 7-9 is lower than in innings 1-3 and 4-6 so those 7-9 innings helped his ERA, not hurt it.

Not exactly. With FIP, it hurts if he didn't try to strike every batter out. If he was told he was only going 7 innings, he'd probably have had more strikeouts. This is evidenced by the fact that he had a higher strikeout percentage in the 9th inning than in any other inning. His 8th inning was his worst inning in a lot of ways. So it would appear that he was saving something to close out games. If he had gone full out, knowing he was not expected to go deep into games, he would have had better FIP and a better ERA.

If WAR were a truly cumulative stat, you'd take into account all of the things I listed above because no replacement pitcher could, say, throw 7 consecutive complete games or three consecutive shutouts, or even approach the results Jack achieved in the late innings.There'd at least be a leverage component to the calculations, which there are for relief pitchers, but not for starting pitchers. But it definitely would be a difficult calculation, and would likely involve even more questionable assumptions than are already inherent in the calculations through things like ballpark effect and defense.

That Jack was so dominant in the 9th inning, brings up his 7-9 stats relatively. So you have to unpack that analysis a bit. Moreover, one of the reasons pitchers are taken out of games is to preserve them for the next game, and for the course of the season. Despite his freakish stamina, I have to believe that some of the runs he gave up in early innings were a result of having been overworked in previous games. Of course, there's no way of knowing for sure, but common sense and experience would say that's the case.

One problem with ERA is we assume that it means a pitcher averages a certain number of runs per nine innings pitched. That's true in a way, but not the 9 innings of any particular game. A more accurate statistic would show how many innings a pitcher averaged per start, and how many runs that pitcher averaged giving up per start. Then, if you want to get really into it, determine what innings the pitcher did not pitch, and how many runs an average bullpen from that league in that year would have given up in those games in those innings. I think Jack would come out looking really good if that's how we quantified run prevention.

Even though I think he could have had better "advanced" statistics if he had been used differently, I don't think it would have helped his teams win championships. The 1984 Tigers, 1991 Twins and 1992 Blue Jays relied on him to win games, but also pitch deep into games to that the bullpen could be used to assist weaker pitchers. That formula worked for the rotation, the bullpen and the teams he played on. And after all, his contributions to his teams is the main factor in whether he's a HOFer.