So a few days ago, someone (Stephen M, I believe) asked in a thread here whether there was a way to determine whether arm or range was more important for fielding the third base position.
This is both just a potentially-interesting and quirky thing to look into, as well as something of minor relevance to the Braves going forward, as it pertains to Jose Peraza and his future with the club. Of the many narratives this season have been both the controversial Chris Johnson extension and his oft-maligned performance on both sides of the ball, as well as the emergence and prowess of Tommy La Stella, that inhuman hitting machine. With all those going around, there's been a fair bit of talk about whether Peraza could possibly stick at third base, though I realize that this is far from the only solution. After all, he could be tried in center, or Tommy La Stella could be moved. (However, I think people that are already proclaiming that TLS is not the longterm solution at second for the team are a bit premature. Let the kid play at least one full season before we determine who can and can't be a longterm solution... After all, it's not like major league teams have franchise players all over the diamond; you're lucky if you can get a couple to play together for a half-decade at that.)
Anyway, back to the topic at hand: there's no real way, as far as I know, to gather publicly-available, outcome-based stats on different defensive aptitudes. While UZR and DRS both have components that speak somewhat to defensive outcomes, such as "double play runs saved" or "outfield arm runs saved," there aren't very many of these tracked and as such it's difficult to really use these defensive metrics to look at arm versus range for infielders. (Disclaimer: while "range runs" is indeed tracked by UZR, I don't use it below to maintain an apples-to-apples comparison.)
Instead, what I used to answer this question is somewhat flimsier, but still pretty fun and relatively accurate on average: the Fans' Scouting Report (FSR) data available via Fangraphs. These data are crowdsourced player defensive ratings on a 1-100 scale for many different types of defensive aptitudes, and there's at least a decent sample size of fan ratings for most players available on Fangraphs.
So, here's what I did: I looked at the available FSR data for all third basemen from 2001 to 2014 with at least 1,000 innings played at the position, which yielded a list of 88 players, from Aaron Miles to Wilson Betemit (sorry, there are no third basemen in this sample with Y or Z first names). Because of the nature of the FSR data, regulars tend to be rated far more than fill-ins or backups, and as such, the average number of ratings for a player in this sample is 124. It's not great, but it's not exactly one random guy's opinion driving these data for a given player (though some younger guys, like Nolan Arenado, only have a handful of ratings so far).
FSR data contain an "arm strength" category, which really captures that particular aspect of defending. However, there's no specific "range" variable; instead, I created an index by taking the straight average of the "instincts, first step, and speed" variables. All 88 players are mapped below, with quadrants specifying the different relationships between the range index I created and arm strength included as well.
The thick red/green lines are the medians of the datasets, the thinner lines are the 25th and 75th percentiles. Naturally, most of the FSR data clusters in the middle; there are only a few statues with cannons and/or slick-fielding noodly-armed guys in the data, and those are really the guys of interest to look at...
So basically we've got four guys that are really bad at moving, but have relative cannons, and six guys that I've highlighted that have no real arm but can scoot around the hot corner. (I removed the 25th/75th percentile lines to reduce clutter a bit.) Also, as a disclaimer, I used a slightly-different method to identify the ten guys I highlighted that was a little more rigorous than eyeballing the chart, but it's not really relevant to the analysis. Just in case you were wondering why Maicer Izturis is highlighted but the dot he partly overlaps with (Jerry Hairston Jr.) isn't.
So now that we've identified these guys, the real question is whether defensive metrics are going to be skewed towards one group or the other, or whether they're terrible for both groups, and so forth. Now, if you've been paying attention to relative defensive ranks over the last few years, these results won't surprise you much, but try not to spoil it for the rest of the audience:
Noodly-armed guys are in green, statues are in red, and the list is sorted by average UZR and DRS over 150 games from best to worst. As you can see, all the noodles are at the top, and the statues are at the bottom. So while not an unassailable conclusion arrived at by top-notch statistical reasoning, it doesn't look like having a weak arm is really that much of a death sentence for third base, especially when compared to the alternative.
It's interesting that a lot of the ten players highlighted above are multi-positional players. Part of this might be that third base is kind of an unloved position in many cases, where your "infielder that didn't pan out at short or second" is relegated. Nick Punto is a utility infielder that's played all over the infield and puts up ridiculous defensive metrics at third while his second base ratings are fairly weak; Counsell and Vizquel were shortstops that slid over to provide help at third in their twilight periods.
In conclusion, if the Braves need to play a guy with a relatively weak arm at third, I don't think it'll do that much damage to the team defensively. Lots of players have been able to provide good defensive value at third, even with poor arms. And if we can get some confirmation on how Peraza's arm compares to late-career Craig Counsell or Omar Vizquel, or even how it compares to Bonifacio's noodly appendage right now, that should maybe give us a better sense of potential projections for his defense at third.
Side note: you might be wondering where CJ is on the scatterplots above. He's right below the "e" in "Aramis Ramirez." Which is pretty awful, but not as awful as you might think. Certainly not as bad as Aaron Miles, who was apparently a light-hitting utility infielder that couldn't field. (Miles is that dot all by his lonesome in the bottom left-hand corner.)