My Issue With wOBA, Linear Weights, Runs Created, etc... Part I

My Issue With wOBA, Linear Weights, Runs Created, etc... Part I
Note: I'm not thinking that this is like, breaking news. I'd be pretty surprised if the guys who made these statistics didn't already know this. Having said that, many people using them don't, and I think the point is still a valid one.These statisitics are on a per-plate-appearance basis. I think this is from tradition more than anything else, developed originally (over a long period of time and with many intermediaries) from old statistics like batting average. Batting verage, of course, has At Bats in its denominator, which really doesn't make sense at all - why should walks and hit by pitch and the like be ignored? So newer, better statistics like on-base-percentage, using plate appearances (or some variation thereupon) in the denominator were developed. And this is a clear improvement. And then most of the advanced statistics are somehow based off of this. But the problem is that games don't last a fixed number of plate appearances. They last a fixed number of outs. So if two teams have he same wOBA, we should expect the one with the higher On-Base Percentage to get more plate appearances and thus score more runs. For confirmation, let's look at two teams with basically identical wOBA.

Team one has the following stats:
BB 1458
H 1279
1B 934
2B 222
HR 123
AB 5659
PA 7078
wOBA 0.339854479

Team two has these stats:
BB 373
H 1513
1B 934
2B 345
HR 234
AB 5532
PA 5865
wOBA 0.339856777

So we can see that the two teams have nearly identical wOBA, with the second one having an infinitessimally better offense by that metric. But the first team gets on base at a .387 clip, whilst the second only gets on at a .322 rate. And my calculations by the homogeneous model show that the first team will score 5.59 runs per game, whilst the second will score only 5.37, for a difference of just over 4%. Now some of this is down to the weights on wOBA not being tuned for the exact run environments of these teams, but further, similar research with smaller increments from rael teams further confirms my findings here.Now, a couple of caveats to this. First off, I want to say that I'm picking on wOBA here because, of these metrics, I like it the best, not because there are any problems with it. And I do think it's a pretty good and useful metric. The other metrics listed here, or any that are calculated on a per-PA basis, will all eshibit the same flaw of undervaluing OBP. The second caveat is that there is some appeal to measuring things on a per-PA basis over the more-accurate-for-a-team per-out (I use per-inning, but that's just a factor of 3 off from the same thing) basis. Basically, this is tied up with wanting to evaluate players. You want to get rate stats for individual players that are based on the number of chances they get, and it's the team's OBP, not the individual's, that controls how many chances that hitter gets. Of course, the individual has some control over the team's OBP (roughly 1/9th, but not exactly), so any per-PA metric is still going to have some of the error. Ideally what you want to do to measure the player is to have the team's performance with that player and measure it against the same team's performance when you replace that player with the alternative.