UPDATE: Please to disregard this for now. I've discovered an issue with the IDs in the zone rating database. I'm working on fixing the issue, but until then, this is fraught with issues. My sincerest apologies for the error.
I’ve been doing a lot of thinking about replacement level and positional adjustments recently; about the only thing I learned from that was that Gary Gaetti was the biggest free agent bargain of the past 20 years. That’s not very useful, I know.
But it got me thinking about the relative value of different positions. Consider this table, based off of Chris Dial’s excellent work:
Lemme ‘splain – LG_ZR is the average zone rating (plays divided by chances) at the position. [I derived those values from SG’s zone rating database; everything else in the table is straight from Dial.] ZR_CH is the average number of chances in a season at the position. ZR_RUNS is the average value in runs at the position.
Each of those measures different things; Zone Rating itself measures the difficulty of making a play. Chances and runs, on the other hand measures leverage of that skill. Tango has done some great work in this area in the past, but at the runs level. That's fine for measuring value, but I'm going to look at it from a different perspective.
Right now, all I have is data for players who were at both second and short for the same team in the same season. (Well, at least, that's all the data I've looked at and processed.) Here’s the data, if you're interested.
Here's what I did - I took a weighted average of each player's numbers (plays made and chances) at each position, using the number of chances as the weight. For all players, the number of chances used as the weight comes from the position where the player had the fewest number of chances. Then, I calculated zone rating from the weighted averages. (From here on out, when I say average I'm referring to a weighted average, except for the league average.)
The average zone rating of a shortstop in our sample pool is .836, compared to .843 for the league. So the players that play both positions tend to be below-average shortstops. Makes sense, right? For second basemen, it's .827, compared to .825 for league. So second basemen who play shortstop are (slightly) above-average second basemen, according to our sample. Again, this makes sense, but the difference is small enough that it's probably not worth considering.
Now, here's the conclusion that doesn't seem to make sense on the face of it: players in our sample pool are making more plays per opportunity at shortstop, compared to second base. All this means is that, for a shortstop, it's easier to make a play on a ball at short than it is to make a play on a ball at second.
There is a selective sampling issue here: the players in our pool, by and large, have the physical tools to play shortstop; there are many second basemen who don't posses those tools, which largely comes down to arm strength. From any of the available data - zone rating, Retrosheet play-by-play, etc. - it's, as far as I can tell, impossible to tell who those players are. [We do have that data available from Tango's Fan Scouting Report. That's the next obvious avenue of approach for studying this issue.]
I also split my sample into two groups - players that played mostly at shortstop and players that played mostly at second base. There wasn't a large difference between the two groups that I noticed.
The difference between the average second baseman playing shortstop (which is pretty close to the average second baseman overall) is about four plays or three runs over a full season. Again - this is for players who teams selected based on their ability to play shortstop. The difference between our shortstops-at-second and the league second baseman was only one play; bear in mind that these are below-average shortstops to begin with.
My hunch is that the best way to do a conversion factor for a player, assuming that he's able to play shortstop at all, is to use a multiplier to convert plays per chance between positions. I'll have to look into that - and, again, the next step is to look at physical tools using the Fan's Scouting Report.