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Encarnacion throwing to Lind instead of Overbay: disaster?

There has been much discussion lately around these here parts about whether to bring back Edwin Encarnacion (which is now a moot point, since we just resigned him) and what to do with him in 2011. Since E5 has always played third base (>600 GP in his career, and only 2 at any other position - both first base), the assumption was that he will continue to play there. This no longer seems to necessarily be the case, but it's certainly still a possibility.

More speculation has centred on the Blue Jays' first base position in 2011. The presumption was that Adam Lind, formerly an outfielder and DH who was a second team All America first baseman at the University of South Alabama, would be converted into a first baseman under the tutelage of our great infield coach Brian Butterfield. In anticipation of this, Lind was played at first 11 times last year and he generally underwhelmed in his limited action. 

Given E5's seeming entrenchedness at the hot corner and his poor defense both when playing in Cincinnati and last year, some have questioned whether Lind should be the one to man first base and be responsible for tracking down E5's errant throws. These naysayers explain that E5's seeming improvement over the course of last season was an aberration, that Lyle Overbay's glove was responsible for significantly moderating the effects of E5's arm, and that the downgrade to Lind would be devastating to the team. They suggest that the Jays should look for a player, via free agency or trade, with more experience at first base (e.g. Derrek Lee or Carlos Pena) as an offseason priority rather than stick with the Lind plan.

Others (including myself) feel differently. I believe that first base, as it is the least demanding defensive position, can be fairly easily learned by most reasonably athletic people. Given that such players as Jason Giambi, Adam Dunn, and Carlos Delgado have capably played first base in the past, I figure Lind could be coached up to be at least as good (or bad) as these guys and probably even a little bit better.

Unfortunately, such debates can go on ad nauseum, since they are largely subjective in nature. So, I decided to run an analysis and determine how detrimental the change from Overbay to Lind at first base would be to the Blue Jays if Edwin Encarnacion were to play a full season at third base.

Read on after the jump...

First, I needed to determine just how bad a thrower E5 truly is. For this, I used fangraphs' statistics. For the purposes of this analysis I also assumed that E5's aggregate 2010 statistics represent his true skill level with Lyle Overbay as his first baseman.

Edwin played in 95 games last year, all at third base, and was responsible for 174 assists and 11 throwing errors according to fangraphs. These are 11 throws from Edwin that even the sainted Overbay could not corral and turn into outs. This represents a rate of 16.8 throws per throwing error. It also represents 1.95 throws per game.

Extrapolated over a full season (for which I used 160 games), this rate represents 18.5 errors, which is rounded up to 19. A full season would also see 311.6 total throws from E5, rounded up to 312.

Now, let's assume Overbay had not been at first base in 2010, but Lind had been. Let's further estimate that Lind's inferior skill changes E5's error rate from 1 error per 16.8 throws to 1 error per 10 throws. To me, this seems like significantly more of a decrease in throws-per-error than is likely to actually happen, but for the sake of argument we will go with it. If E5 made 1 error per 10 throws in his extrapolated full season (312 throws), he would make 31.2 errors, or 32 errors. Lind can be blamed for 13 of these errors (32 with Lind - the 19 with Overbay).

Next, I laid out all 24 outs-and-base-runners situations that can occur in baseball (e.g. 0 out, man on 2nd; 1 out, 0 on; 2 out, bases loaded, etc.). I then figured out what would happen in each situation if a ball was hit to E5 and he made an out. For example, if the situation is 0 on and 0 out, the "no error" situation would be 0 on and 1 out; if the situation was runner on second, 1 out, the "no error" situation would be runner on second, 2 out. I assumed that runners would not be advancing on "no error" situations. Either way, runners advancing in "no error" situations would be the same if Overbay or Lind was at first base, so that doesn't figure into this analysis anyway.

I then figured out what would happen in all 24 situations if E5 made a throwing error. This is a little trickier. Sometimes runners get an extra base due to an error, but most times they don't. Most times when a third baseman misthrows to first base, the throw either pulls the first baseman off the bag causing the runner to be safe or bounces in the dirt causing the first baseman to not catch it, but the ball stays around him and runners do not advance. For this analysis, I assumed that 2/3 of the time, runners do not advance an extra base on an E5 throwing error (i.e. the batter stays at first and all runners on base advance only 1 base on the play) and that 1/3 of the time, the batter and all runners on base get an extra base (i.e. batter goes to second, all runners advance two bases). Again, I think this is a high estimate for how often runners get an extra base, but let's go with it.

Once I had figured out each of these results I went to http://1.bp.blogspot.com/_AtlVw4SMQfg/TP3N2JARj2I/AAAAAAAAAPA/mn3cuZSf98M/s1600/baseout-states-%25282010-12-08%2529.png to find Baseball Prospectus' run expectancy values for each runner-and-out situation. Using the weighted average of the error situations (2/3 no advancement, 1/3 runners get an extra base) subtracting the run expectancies from the non-error outcomes, I could figure out the relative value of an E5 throwing error in each situation.

Finally, though, not every base-and-out scenario is equally common. Every inning starts out with none on and none out, but only rarely do teams load the bases with 0 out. For this, I went to the book "The Baseball Economist" who lays out the frequencies of all base-and-out scenarios. I also assumed that errors from E5 are randomly distributed, so he has equal chance of making an error in a given no-on-no-out situation as in a given bases-loaded situation.

I multiplied the frequency of the original scenario by the difference in run expectancy caused by the error (taking into account any runs that score as a result of the error on that play) and then summed all of these values to determine the average run expectancy difference created by an E5 throwing error, which worked out to 0.746 runs per error. Multiplied by the 13 additional errors Lind is assumed to have caused, this works out to 9.7 runs over a season, or just under 1 win.

Note that this is pretty much a worst-case scenario, since I can't imagine Lind will be bad enough at first to increase E5's error rate by 40% over last season [(16.8-10)/16.8].

Now, as always, the tough part is making sense of this data. To me, this demonstrates that first base defense isn't all that important, and that E5 throwing to Lind is probably not as terrible a result as some people fear. Lind's probably-improved bat over Overbay should make up for whatever glove-based deficiencies he has and then some. Certainly, it does not warrant going after and possibly overpaying for Derrek Lee's supposedly superior defense but inferior bat and ignoring other potential signings, like Manny Ramirez, over fears of Lind at 1B.

Others might see things another way, and I leave that to the comments to hash out.

Note that I have all the numbers and calculations on a spreadsheet, but I decided not to post everything in all its math-y glory since it would take up a lot of space and probably fry some peoples' brains with lots of numbers and charts and stuff. I figured it was easier to get my point across by describing my methods, quoting my sources and showing the results. If people want the numbers I used, I can post it separately or send it in private messages.

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