I probably overthink here because I use a closer on both my teams, and they're my third best RPs, The save situation is one I classify as low leverage, Ninth inning, three outs, starting with no one on base. Frankly, any schmuck can do it, once you get rid of the real life mythology of balls and charisma.
On one team my closer is an RP with the third best splits who can't throw a lot of innings. On the other team he's a lefty with a great first pitch and a poor second pitch. I set them for ninth inning, save situation only. The better RPs get the 7th and 8th innings, but the low leverage spot goes to the closer. Probably overthinking it, but this way I save the better guys for more 7th and 8th innings by not overusing them in the 9th. (I'm also one of these guys who bats the pitcher 8th and my best hitter in the 2 hole.) And in the case my closers come up against the other team's best hitters, well, I'm taking my chances with them anyway