Log5 vs. Strat-O-Matic

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

where P_B is the hitter’s average, P_P is the average allowed by the pitcher and P_L is the league average. P_B,P is the probability (or average) that the player will get a hit against the pitcher.

 

The Strat-O-Matic (SM) game works by rolling dice. Half the time you have to look at the batter's card and half the time the pitcher's card (determined by the dice).  The hitter and pitcher cards have rows and columns and you know where to look for the result from the dice.

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)

.230 batters vs. .230 pitcher) -.004

.230 batters vs. .330 pitcher) .005

.330 batters vs. .230 pitcher)  .005

.330 batters vs. .330 pitcher)-.006

 

So 90% of the cases would differ by no more than -.006. Now what about the most extreme cases? Here the highest and lowest averages for the batters and pitchers from 1980:

 

Batters

George Brett .390

Kiko Garcia .199

 

Pitchers

Ed Figueroa .364

Mike Norris .209

Below are the predicted averages for the 4 cases using Strato and Log5

Brett vs. Figueroa) Strato .485, Log5 .499

Brett vs. Norris) Strato .330, Log5 .315

Garcia vs. Figueroa) Strato .294, Log5 .279

Garcia vs. Norris) Strato .139, Log5 .151

So even at those extremes, there is not that much difference.

Another season I looked at was the 1996 NL.  Here are the extremes in AVG for all players and pitchers who had 300+ PAs or 300+ batters faced.

 

Batters

Jim Eisenreich .361

Rey Sanchez .211

 

Pitchers

Chris Hammond .315

Trevor Hoffman .161

Mel Rojas .193

 

The reason I put in Rojas is that Hoffman's season is a bit of an outlier (and Rojas had the next lowest average allowed). It is the 16th lowest average allowed in the Stathead data base for pitchers with 300+ batters faced. They have only 33 seasons of .170 or lower. So Hoffman 1996 is an unusual case.

 

Below are the predicted averages for the 6 cases using Strato and Log5. The NL batting average in 1996 was .262.

 

Eisenreich vs. Hammond) Strato .414, Log5 .422
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

 

These are generally pretty close except for  Eisenreich vs. Hoffman where there is a .026 difference between Strato and Log5. But again, it was an unusual season for Hoffman. The differences we observe are in the same range as for the extremes in the 1980 AL. So it is likely that a large % of the match ups in the 1996 NL would have very little difference between Strato and Log5.