These decisions are always going to be a little arbitrary. No matter what you're going to wind up with a fuzzy number anyway, and to make matters worse it's going to be taken out to the thousandth place because tradition dictates.

OBP is how often a player doesn't make an out

OBP was clearly designed to measure how often a player earned not making the out. You and Allan Roth have different ideas about how to measure "earning" the base. Doubtless Roth did know about the limitations of measuring all hits as hits, all errors as non-hits, etc., but considered H+BB+HBP to be the best possible compromise, and perhaps an easier one to pitch to management.

Well, it's a lousy compromise in some ways of course. What about great batted balls that meet better plays, like you said? What about poor reads that lead to a ball landing in the grass when it should've landed in leather?

But it's nice to pretend a hit's an earned hit, or whatever. It makes the game look tidier than it actually is.

As far as errors go, one thing this is going to do is inflate the OBP of players from previous generations, when errors were more frequent. But that's okay really, because all cross-generational comparisons are built on foundations of sand anyway. Even league-adjusted stats.

I am confused, by the way, by how easily you accept that an error is "not a hit" in the context of batting average. It's such an arbitrary call that you may as well do the same for OBP. Just say it's not a "time on base." It makes no more or less sense.

And anyway, batting average was intended to do more or less the same thing as OBP, it was just an earlier stab at it. It was not designed to fall short.

Catcher's inteference is an incredibly odd one, because not only is it not counted towards OBP, it's not counted against it either.

Why would it count against it? The batter often didn't do anything that would have made an out. What if the catcher's interference occurs on a swinging strike on a 1-0 count?

So obviously it can't count against your OBP. The remaining question is why it wouldn't count for it. And clearly Roth and other statisticians believed that catcher's interference was not a repeatable "skill" (or proclivity) in the sense that, say, getting hit by a pitch is. And who can blame him? As rare as it is today, it was so much rarer back then.

Comparing recent years to some years during Roth's time in Brooklyn:

Still only happens every few thousand plate appearances, but that still makes it an order of magnitude more common than in Roth's time.

Anyway, Ellsbury showed that it is a repeatable thing, but even the best at drawing XI would only get a .004 bump, or about one base every 57 games for him. Well, maybe it should be there. It would hardly affect any lines at all, but no matter. The five active leaders in PA have batted a combined 49,282 times without reaching on a single catcher's interference. (That's Pujols, Cabrera, Canó, Molina, and Votto.)

You may as well ask about sac bunts, too. They're left off as managerial decisions: you've been told not to try to reach base. The trouble is, most people run out their bunts anyway. I mean, Ichiro bunted quite a lot with runners on first and he always tried for a hit himself--and often got one. So if he reached his OBP would go up, and if he made an out his OBP would stay the same. Bit odd.

It's muddied waters, because often of course managers don't expect bunters to reach. Pitchers, for example.

And if sac bunts are sort of 'out of a hitter's hands,' well so are intentional walks. In fact those aren't even looked at when calculating wRC+, WAR, etc., those models just assume you would have done as well in those PAs as you did in the others. (Probably a little unfair, as you're more likely to have a platoon advantage when IBBed than otherwise.)

I mean, there will also be quibbles. We're pulling a thread here, which is that BA and OBP are foggy appromixations, and that's true even if you add in ROE, whatever. What about the great plays, still? The robbed home runs, the diving catches, the throw from the knees at deep short?

We're getting closer to demonstrating the talents of a player with Statcast measurements (xOBP etc), which doubtless need a good deal of refining still.