Tuesday, May 10, 2016

LWR Component Deflators and Replacement Hitters’ Batting Lines

Last time, I explained how we could use Linear Weight Ratio, an offensive metric developed by Tango Tiger, as a shortcut in finding a variable which I call the “component deflator” and symbolized as “a”.

Last time I focused on its application to park adjustments, but that’s not necessary. In fact, the component deflator can be applied generally to any situation in which you’d like to know what across the board percentage change in mutually exclusive offensive events would you have to see in order to alter run scoring by some scalar (assuming you are willing to accept that the linear weight values stay constant, which is certainly an assumption that must be applied with care).

So there are any number of questions that this kind of approach can address. One that I will consider in this piece is “What would a replacement-level hitter’s batting line look like?" First a few caveats, though. As Tango has pointed out, there really is no such thing as a replacement-level hitter. A replacement player is a replacement player because his overall contribution, offense and defense, is at a level so as to have no marginal value. Thinking about it in terms of a replacement level hitter only confuses the issue.

However, the analytical structure of assuming that replacement level players are average in the field, and thus calculating their value as their offensive contribution above a “replacement” performer specific to their position plus their defensive contribution above an average performer at their position can be a useful approximation. It is the structure used by a number of approaches, including Pete Palmer’s TPR (which is above average, but the same principle holds), Keith Woolner’s VORP, and the RAR figures I post here at the end of each season. I am not claiming that this approach is optimal or superior to the others, only that if applied with caution it can be a useful model of player value.

For the sake of this post, let’s just assume that we are going to use a model where a replacement level player hits at some percentage of the league average. Then, if we’d like to know what his batting line might look like, we can use the component deflator approach. The good thing is that we don’t have to worry so much about the fact that we have static linear weights, since we are now applying the process to individuals for whom we’d like to hold the weights constant (ignoring the Theoretical Team arguments). So that caveat is loosened in this application.

Of course, this approach carries some of its own caveats with it: one is that we are again developing a model in which all events are equally deflated. It might actually be that replacement level hitters tend to not be as deficient in BA as one might expect. Or maybe teams are willing to trade BA for power in a replacement level hitter. This is a specific model with specific assumptions, and it is not necessarily reality.

Anyway, if we define R as the percentage of league average (or positional average or anything else if you’d like), then we can just plug it into one of the formulas from last time, and carry out the rest of the calculations as explained in that post:

New LWR = ((LWR/s' + x)*R - x)*s'

In my RAR estimates, I assume that a replacement player’s R/O is 73% of the positional average, where the positional average is figured by taking the overall league average times a long-term offensive positional adjustment. The positional adjustments I use are (note: you can tell how long ago I wrote this by the use of 2008 league totals):

C = .89, 1B/DH = 1.19, 2B = .93, 3B = 1.01, SS = .86, LF/RF = 1.12, CF = 1.02

Combining these adjustments, the LWR component deflator procedure, and the overall 2008 MLB offensive averages, here is the offensive output expected from a replacement player at each position:

How do these numbers look to you? My impression is that the batting averages are too low; teams may resort to replacement level players at 73% of league R/O, but they may be those that trade secondary skills for BA points of equivalent value. (assuming that players of this profile even exist in reality)

Anyway, you don’t have to take any of this too seriously, and I’ve already stated that the assumptions and admitted they may not model reality, so I’m not going to spend too much time justifying the results. Instead, I have another potentially amusing if not completely realistic application.

Namely, it is to take the initial statistics of a real hitter, and maintaining the proportional relationships between his positive events, projecting what his line would look like at a different level of productivity. For example, what would a replacement level hitter with Barry Bonds’ bizarre 2004 proportional relationships look like?

In this case, I’ll assume that a replacement player would have a 3.50 RG. Bonds’ 2004 line comes out to a 18.26 RG, so our “R” will be 3.5/18.26 = 19.2%. This line results:

The bizarro Bonds would hit just .140, but would still manage to put up a .416 secondary average. Of course, such a player would never really exist, but if he did, his offensive value would be about the same as the other replacement level guys above.

Let’s look at Tony Gwynn, 1994 to see what this would look like for a very good singles-type hitter:

And we could try going the other way. What would Mario Mendoza, superstar look like? Here’s the transformation from Mendoza’ career line to a 8 RG:

In order to turn Mendoza’s no-secondary skills profile into an all-time upper echelon great, you have to allow him to hit .400, and increase all of his positive rates by 81%.

This translation approach falls squarely under the category of "toy"; please don’t get the impression that I’m elevating it to any greater pedestal.