Two steps and tangos: a look at pivots

First, an aside.  You are probably expecting an article on run estimation. I was expecting to provide you with (yet another) one. The hang-up was all in getting my linear weights values to reconcile with actual run scoring totals. It’s not that I didn’t – oh, if only that was it. No, I got the linear weights values to reconcile, and without simply forcing them, but naturally. This simply was not accompanied with any ideas as to why the method I used worked. (I discovered it totally by accident.)

Since in fairness to you (and me!) I really don’t want to throw things out there that I can’t comfortably explain, or at least suggest an avenue of study, I’m going to table the run estimation articles until I can sort out some of the peculiarities I’m discovering the more I work with zero-baseline run expectancy tables. The good news is that it doesn’t impact the BaseRun formula I published in the comments, so that’s a small comfort.

In the meantime, though, I didn’t want to leave you all alone without an article one Friday morning. So hopefully you’ll indulge me in a little discussion of defensive stats – and I mean the really basic stuff, not the super-advanced UZR and PMR or what Brian’s talking about, but the official defensive statistics: the putout, assist, error and double play.

Because if you look at the official fielding stats of all players (except catchers), that’s all you’re ever going to get. And prior to the Retrosheet years (as well as many other years for leagues other than MLB), official fielding stats are all we may ever have. So it probably behooves us to see what we can do with them.

So let’s start off by looking at the official definitions. I’ll go ahead and note that they’re long, much longer than you would expect at first blush. I’ll go ahead and summarize them here, but I do suggest you take the time to go peruse them at some point.

  • A player is awarded a putout whenever he records an out on a batter – either by catching a ball on the fly, tagging the runner or through the forceout. Oh, and a catcher gets a putout every time a batter strikes out, because that makes sense somehow.
  • A player is awarded with an assist if he handles the ball on a play when a putout is made by another fielder. I do not want you to place too much importance on the word “handles the ball,” if you bat down a ball on the infield by diving for it and another player throws out a runner, you can get an assist.
  • An error is awarded whenever the official scorer fears that someone might notice that they’re actually paying him to watch a baseball game and so wants to look like he’s doing something.
  • A double play is awarded whenever a fielder records an assist or putout on a double play, or whenever he would have if not for the first baseman some other player making an error.

Official fielding statistics simply expressed as totals – either by player or team – isn’t very instructive. Bill James explains in the “New Bill James Historical Abstract”:

Traditional fielding analysis often fails because the fielding statistics of a good team are not very much different from the fielding statistics of a poor team. This is not true of pitching or hitting.

Fielding evaluation is based primarily on three factors: range, double plays and fielding percentage. The “range” number, on the team level, is constrained by the fact that each team makes only 27 outs per game, regardless of how good their fielders are.

Double plays are no constrained by a boundary, but there is a problem there, too, which is that

1. Bad teams (and bad defensive teams) have more opponents on base than good teams.

2. The more opponents you have on base, the more chances you have to turn a double play.

So bad teams, on the average, don’t turn fewer double plays than good teams – in fact, they turn a few more.

James’ answer to these issues, and many others, was fielding Win Shares. I’d love to go through them point-by-point sometime, but that’s constrained by both my available time and my understanding of the system.

What brought all this up, you may be wondering by now, was a discussion on Baseball Fever about the relative difficulty of different defensive positions. And the question arose: which is more valuable, a second baseman or a shortstop?

Take your time thinking about it.

The argument arose that second basemen are as valuable defensively in an absolute sense, because they make more plays than the shortstop. And, if your definition of plays is based upon putouts and assists, this is entirely true, if a bit counterintuitive.

This is a look at the batted ball distribution for grounders in the Retrosheet era, for those years where we have hit location data:


To explain. LOC is location, based upon the Project Scoresheet zone system. I combined the available zones by depth – we’re interested in the left to right distribution of chances, not necessarily whether the fielder was playing shallow or deep when he fielded it. (That is relevant to a lot of things, but for now it would be a distraction.) And I combined zones 1 and 2 into zone 0, because they don’t add much to the discussion.

BIP is ground balls hit in that zone, BIP_OUT is the number of outs recorded. The next four columns reflect how often a fielder fields the ball, and then the number of times an out was recorded when that fielder fielded the ball. Finally, we look at the percentage of BIP_OUTS recorded by each fielder in that zone. We do that to assign zones of responsibility – essentially we award a fielder that percentage of the ground balls in that zone as his responsibility. So we can see that shortstops field more balls and record more outs, largely because they have more balls hit to them. They actually convert fewer of their chances into outs than second basemen, but thanks to their larger number of chances record more outs.

To put a face on the data, look at this chart – it’s a density plot of where ground ball hits – not outs, simply hits – were recorded during this season. (It’s taken from the batted ball locations recorded by the Gameday application.)


You can see where the outfielders tend to play as the most distinguishing feature. But note on the diamond, the dark band running along the third base line. More infield singles are hit to the shortstop and the third baseman than to the second and first basemen. Partly that’s because more of everything is hit to the left field side, at least on the ground. But it’s also because of the longer throw over to first to get the runner out.

So why, then, are second basemen awarded more plays by the official scorer? Because of the double play. The pivot man in a conventional three man double play is awarded both a putout and an assist.

This shows up in what I like to call “secondary assists,” where a player is awarded an assist on a ball he didn’t field:


The left-hand column is a reflection of who fielded the ball (FLD_CD 0 usually represents plays without a ball in play, like a strikeout, caught stealing or home run, but it seems like it also represents missing data sometimes). Then we look at what other players were awarded an assist on the play. (The parser I use to process Retrosheet event logs goes up to ten assists on one play!) Second basemen run away with this category, having 91,536 secondary assists. The other three infield positions rack up 94,464 secondary assists between them.

If we really want to look at how well a player pivots, we want to know precisely how many pivot chances he makes, and what fielders they’re coming from. So let’s define a pivot chance as a double play opportunity (man on first, less than two outs, ground ball in play) where a player is awarded a putout after an assist from the fielder who initiated a play, and a pivot success is getting an assist. (This lets us include plays where the pivot was successful but the third player in the double play committed an error.)


Let’s break this down. The first column is who fielded the ball. (I’m excluding outfielders for clarity’s sake.) PIV refers to the number of successful pivots, CH to the number of chances, and % is PIV/CH. Successful double plays tend to be either of the 6-4-3 or 4-6-3 variety: roughly 60% of the time, those get converted. (The 4-5-3 double play also works pretty well – roughly 50% of the time the third baseman is able to handle the pivot.) First basemen rarely start double plays – if they’re out there fielding the ball, they’re probably not there to receive the throw after the out is recorded at second – and this drags down the overall pivot percentage for second basemen.

What we also see here is that second basemen start more pivoted double plays – shortstops, incidentally, lead all positions in double plays where they field the ball themselves and record the first putout themselves, removing the need for pivot man at all; there are 10,717 pivotless DPs started by shortstops, compared to 10,324 pivotless DPs turned by all other positions combined. (Second basemen are, well, second; they started 5,741.)

And now I have two topics to write about next week, because now I have the mystery of the secondary assist to solve, since second basemen actually don’t have as many as shortstops. Oh, bother.


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