Yeah, I have a lot of trouble with statistics! I'm sure you're much better at them than I am.
You seriously are bringing up that WAR is calculated differently for pitchers? Such insight! The problem is that it is not calculated differently for closers than it is for starters. Which is why Rivera's WAR is so feeble compared to tons of starting pitchers. Which is just one reason why WAR is a weak statistic. Not awful, but with flaws, as is the case with almost any summary statistic. WAR's particular weakness, in my opinion, is that it does not take the context of the game into account. If a player singles in two runs in the bottom of the tenth with two outs for a come from behind win in extra innings, that counts no more than a single hit in the top of the ninth with nobody on and a 10 run difference between the two teams. WAR for pitchers was developed for starters and applied to closers. It shouldn't be. Plus, WAR is a cumulative statistic, not averaged out for years, or games in the case of closers, played. And of course, there actually is not a single thing called WAR; there are a whole bunch of different versions of it.
The way this plays out for closers as being bogus is that if a team is up by three runs in the ninth and the closer gives up three singles and two earned runs, but still wins the game, he is penalized for the three singles and the earned runs a certain amount. If, on another occasion, he comes in with his team up one run, and he gives up three singles and two earned runs and loses the game, it's all counted the same. But in one situation, he merely gave up two meaningless runs; in the other situation, he blew the save. WAR doesn't care. It thinks the two situations are identical. Apparently you do, too. I don't.
When I bring in my closer, I want him to successfully close the game. Apparently you just want to tally singles and the like. That's why you believe in WAR instead of saves. Go right ahead. I'll take the closer who closes.