How valuable would this closer be?

I've had the thought now of what if somehow there was a pitcher that every time he came into the game, he let up 1 run, never anymore, never any less, how valuable would he be?

He only can pitch 1 inning like a normal reliever and also has to take rest and breaks between appearance.

My thought is he would very valuable, as if you are winning my more than 1 in the 9th, him being available guarantees the win.

Ive asked others and they say that he wouldn't be on the level of mason Miller or jhoan Duran, which I understand due to them giving up very little runs.

So im coming to reddit to get more opinions.

Im writing at 3am in the morning since I cant sleep, any spelling or grammar errors, I apologize.