Linear weights

[redbuck]

Don't know if this is common knowledge or not, but linear weights isn't so complex after all:

Linear weights:

1.40 HR
1.09 3B
.78 2B
.47 1B
.33 BB

= values for each type of hit

which more or less equals in terms of ratios

4.5 HR
3.5 3B
2.5 2B
1.5 1B
1 BB

All it is is (times on base / 2) + total bases + walks ... at least in terms of ratios and getting the feel for the player's ability

And that can be derived from OPS. It all adds up.

Sorry if this is old information.

[pizzacutter]

Well, that depends on whom you ask. The weights will be determined a great deal by the run environment, which will vary from year to year and era to era. But I'll grant you those values for the moment.

However, I think you meant to type "(hits/2) + TB + BB"

Your original formula would assign BB a value of 1.5, which contradicts your previously stated value of 1.

The formula could simplify to (H + 2TB + 2BB) / 2 or, alternately (H + BB + TB + TB + BB)/2.

H + BB is the beginning of a numerator for OBP, (if we ignore HBP, XI, and ROE), and TB is the numerator for slugging percentage. The problem is that OBP has a denominator of plate appearances and SLG has a denominator of AB. Even if we assume that PA = AB + BB (again, ignoring HBP, XI, ROE, and SF), that's still a pretty messy formula that you're leaving yourself with.

We could probably get something in that formula to equal OPS if we tortured it long enough, but I don't know that it would be helpful in terms of a quick and dirty estimator. Someone tell me if my algebra is off.

[redbuck]

Yeah. You're right on the walks. And of course I'm trying to keep it simple so not factoring in complexities like HBP etc.

If you add walks to slugging avg. to get the same denominator as with on base %, then you'd get:

((Times on base) + (Total bases + walks)) / PA

which would be:

(H + BB + TB + BB) / PA

or

((2 x BB) + (2 x 1B) + (3 x 2B) + (4 x 3B) + (5 x HR)) / PA

This presents two major issues because walks would count the same as singles, and instead of adding 0.5 bases per each type of hit it's adding an entire base.

We did, after all, add walks in just to get equal denominators so that's a pretty reconcilable change to make to this, but then how to deal with the difference between the weights for each type of hit? I'm assuming that OPS is overstating the value of getting on base rather than Linear Weights understating.