In 1968, Gates Brown hit .450 as a pinch hitter and .370 in total with an OPS of 1.12. Yet, Brown did not register in the year end MVP voting. His AL record 107 pinch hits did not garner in Hall of Fame ballots in his name. Neither did they for Lenny Harris whose 207 career pinch hits leads the majors. Why not? These contributions, while noteworthy and taking place often in pressure-packed situations, reflect a small number of contributions relative to full-time position players.
Yet, Mariano Rivera's will certainly enter Cooperstown. He also finished second, third (3 times), and fifth in AL Cy Young voting while pitching less than 3-4 times less than starting pitchers. Let me make clear -- Rivera is terrific, and has pitched incredibly well for a long time. But ... Gates Brown. In the year that Rivera finished second in the voting, the next four players pitched 2.5-3 times as many innings -- not exactly a Gates Brown to Carl Yastrzemski comparison but in that direction. In 2010, Roy Halladay pitched 4 times more innings than Rivera.
Fixation on the incremental effect (a per nine innings stat like ERA or ERA+) rather than total impact on wins promotes this kind of elevation of a player beyond his contribution. Of course, Rivera's career "Wins above Replacement" value places him second among active pitchers and 64th all time. This figure is influenced by his longevity (which should matter), but also by the fact that even enhanced performance measures, such as WAR, suffer an apples-to-oranges problem. It's really an extrapolation problem -- Rivera's ERA as a starter would not be as low as JC Bradbury clarifies in his book, The Baseball Economist (JC also has other, more technical issues with WAR).
Beyond player valuation measurement and debate, I wonder (as others have) about the under-use of players like Rivera by managers. In the simplest economic terms, managers try to maximize wins based on using resources at their disposal. Simple models like this work surprisingly well in many situations, but they don't capture all interesting behavior. The complexity of managerial tasks leads them toward systems and templates (heuristics) that have worked for others. Tony LaRussa's success in using Dennis Eckersley as a 9th-inning-only "closer" prompted a whole era of copy-cat managers. The ability to get batters out in high pressure situations is different and more valuable than outs with the game likely in or out of hand. Yet, as many others have noted, the 9th inning may not be the most pressure-packed relief situation. Sometimes, key outs arise in the 7th or 8th. Pre-Eckersley, managers used their best relief pitcher in these settings and for longer outings, depending on the situation. Bruce Sutter and other relievers in his era pitched 100-125 innings per year. Rivera, as "setup guy" pitched over 10o innings but only 60 to 80 in his closer role.
Who would think using Michael Jordan as 6th man would be optimal? If playing only limited minutes in the 2nd and 4th quarter, his per-minute numbers could have been astronomical. Also, he could have been around and fresh for the key shot at the end of the game. The flaws in such a managerial strategy leap out. I don't want to draw the analogy too far. Some pitchers due to mechanics or other factors may not be as well suited to starting roles. LaRussa may have thought in terms of extending an aging pitcher's career in using Eckersley the way that he did.