Click here to read the Wikipedia article on Log5. I will compare the batting average we expect a hitter to get vs. a pitcher from the tabletop baseball game Strat-O-Matic to what Log5 predicts.
Log5 is a formula that estimates the winning pct one team will have against another. For example if team A has .700 winning pct while team B has a .600 pct (and they each played in the same league and played a large number of games), what winning pct would team A have against team B?
It can also be used to estimate what batting average a player will have against a pitcher if we know the hitter's average, the average the pitcher allowed and the league average. That formula is
Suppose the league average is .270. A .300 hitter is facing a pitcher who allowed a .300 average. The hitter has to have an average higher than .300 on his card since that is how he does against the whole league and the average pitcher allows a .270 average. This pitcher is worse than average, so the hitter should do even better than he normally does.
As far as I can tell, what SM does is give the batter's card a .330 average. Since he was 30 pints better than the league average, we add that to .300 to get .330. So that means that if he faced a league average pitcher all the time (one who allows a .270 average), he would end up batting .300 since half the time he would hit .330 and the other half .270 (since the game is set up to be on the hitter's card half the time and the pitcher's card half the time). The pitcher who allows a .300 average would have a .330 card. So this hitter would hit .330 against this pitcher.
I don't know if either Log% or Strat-O-Matic take into account that hitters don't face pitchers on their own team (and vice-versa). If the league average is .270 and your team's pitchers allowed a .260 average, then the average pitcher you faced will be a little above .270. Also, I don't know if either method takes into account unbalanced schedules. You play a disproportionate share of games against your own division. A batter might face a group of pitchers whose composite average allowed does not match the overall league average. I don't know how much difference any of this makes.
I created two tables of all the predicted batting averages, one using the Strat-O-Matic method (Table 1) and the other using the Log5 method (Table 2) for a league with a .270 batting average. Batting averages for the hitters and pitchers both ranged from .150 to .390 in increments of .010. The averages allowed by the pitchers are read going across and for the batters they are read going down (it looks like it actually does not matter who gets rows and who gets columns).Click here to see those tables.
There is also a third table that shows the differences (Strato minus Log5). That is Table 3
Table 1 for Strato shows that if a .250 hitter faced a pitcher who allowed a .200 average, he would bat .180. Log5 says he would bat .184. So the difference is -.004. That is shown in Table 3.
There are a total of 625 cases. In 419 of them, the difference between Strato and Log5 is .010 or less. Those cases are in bold red in Table 3. There are 50 cases where the difference is .025 or more. Those are in bold green in Table 3.
So it looks like in almost two-thirds of the cases, Strato and Log5 differ by no more than .010. In less than 10% of the cases do they differ by .025 or more.
The 1980 AL season had a league average of .269. There were 134 players with 300+ PAs. 121 of them had averages between .230 and .330 (90%). There 112 pitchers who faced 300+ batters and 102 of them were between .230 & .330 (91%). Data from Stathead.
The numbers below show the difference in batting average expected in the 4 cases of the endpoints of these brackets facing each other in terms (Strato minus Log5)
Eisenreich vs. Rojas) Strato .292, Log5 .276
Eisenreich vs. Hoffman) Strato .260, Log5 .234
Sanchez vs. Hammond) Strato .264, Log5 .257
Sanchez vs. Rojas) Strato .142, Log5 .153
Sanchez vs. Hoffman) Strato .110, Log5 .126