In one of the profiles in the Stats section of the Bill James Online, we rank players in specific skills. Marcus (Scoot Scoot) Scutaro, for example, ranks low in power among all players—at the 20^th percentile—but in the middle of the pack among shortstops, at the 46^th percentile. Todd Helton ranks low in speed—21^st percentile among all players—but in the middle of the pack among first basemen (47^th percentile).

One of the skills assessed is fielding; Orlando Hudson ranks at the 92^nd percentile among second basemen in terms of fielding, but where does that rank among all players? There appears to be no obvious way to answer the question. Who ranks first—a shortstop who is at the 41^st percentile among shortstops, or a third baseman who is at the 99^th percentile among third basemen? How do we approach that question?

That is the purpose of this article—to propose a methodology to answer that question.

The first question we have to ask is “How many runs are ‘saved’ by the players at each position?” If we knew that shortstops save 50 runs a year and third basemen save 35 runs a year, then a third baseman who was +8 runs would rank ahead of a shortstop who was –8:

Crappy shortstop          50 – 8 = 42

Good third baseman     35 + 8 = 43

The problem is, we don’t know what the base is. We don’t know how many runs are being “saved” by each position.

Well, how many runs are being “saved” overall?

If we assume that offense and defense are the same thing, merely seen from a different perspective, then it must be true that Runs Saved equal Runs Scored, right? Therefore, if an average major league team scores 769 runs per season—which is the average over the years 2005-2007—then an average team must also SAVE 769 runs per season.

Of those runs, some are “saved” by the pitchers, and some are saved by the fielders (and some, of course, are Saved by the Bell.) How do we split them?

It is apparent for various reasons that I don’t want to get into right now that the lion’s share of these Runs Saved must be attributable to pitchers. What exactly the percentage is I don’t know and don’t believe that you know, but the Runs Saved by pitchers must be somewhere between 2/3 and 3/4 of all Runs Saved. Let us assume, for the purpose of moving toward an answer, that 72% of Runs Saved are saved by pitchers, and 28% by fielders.

If Runs Saved equal Runs Scored and 72% of Runs Saved are saved by pitchers, then that leaves 215.432 runs to be “saved” by fielders at the other eight positions. Let’s call it 216, since

a) there is a certain amount of guesswork involved here, and

b) 216 is a much easier number to work with than 215.432.

How, then, do we allocate these 216 runs to each of the eight defensive positions?

We can do that by assuming that the defensive differences are equal to the offensive differences. Let us assume that the an average major league team’s catchers create 70 runs per season—which is the actual average of all major league teams over the three seasons, 2005-2007—and that an average major league team’s first basemen create 99 runs per season (which they have.) Let us assume that the number of outs made by the first basemen is the same as the number of outs made by the catchers (which it is, basically—466 outs by the first basemen, 463 by the catchers.)

If catchers create 70 runs per season and first basemen create 99, then either

a) first basemen are better players than catchers, or

b) catchers must be “saving” 29 more runs a year than first basemen.

By simply choosing option (b), we can figure out how many runs to attribute to each fielding position, as a base. These are the Runs Created by the players at each position, 2005-2007 (thank you, Retrosheet):

Let’s leave designated hitters out of this, since we can assume that their Runs Saved are zero. If

a) those are their Runs Created,

b) Runs Created + Runs Saved must balance by position, and

c) Runs Saved must total 216,

then we can calculate how many runs are “saved” at each position:

These are almost the numbers that I will propose we use, but not quite. For purposes of making a simple explanation, I assumed that outs were the same at each position. They aren’t, of course; center fielders made an average of 493 outs over the three seasons, and catchers an average of 463. The average Runs Created/Out at all eight positions was .184 (.183923). If you multiply the outs by the runs created/out and save decimals, catchers are not 19 runs behind center fielders, but actually only 13. Our adjusted values, then, look like this:

216 runs at eight positions is 27 runs per position. If a team is saving 27 runs per position in 1,444 innings (an average major league team plays 1,443.5+ innings a year in the field), that comes to 1 run every 53.5 innings, or .01874 runs per inning.       

OK, let’s import some actual players here. I’ll list players from 2007, maybe one per team. Here’s a list:

The first thing we have to do is figure a “base” for each player. For purposes of this study I am going to use only the player’s defensive numbers at the position, ignoring any fielding contributions he may have made at some other position or with some other team. Several of the players we happened to pick switched teams; we’re only using Morgan Ensberg’s numbers with Houston and Luis Castillo’s numbers with the Mets. Chris Snyder played 891.1 innings at catcher for Arizona in 2007. We credit catchers with 42 Runs Saved per 1,444 innings, so that comes to 25.93 Runs Saved for Snyder, if he is an exactly average defensive catcher. That data for these 30 players:

This is the number of runs the player will be credited with saving if he is an average defender at the position. If he is a good fielder, we will move him up from here; if he is below-average at the position, he goes down.

Is Chris Snyder an above-average catcher or a below-average catcher? There is a lot that we don’t know about catchers’ defense, but we can’t worry about what we don’t know. What we are trying to figure out is how to rank the players based on the information that we do have.

National League catchers in 2007 allowed 1,562 stolen bases in 23,247.1 innings. Snyder allowed 52 stolen bases in 891.1 innings. An average NL catcher would have allowed 59.89 stolen bases in that number of innings. Snyder allowed 7.89 fewer steals than an average catcher. Valuing a stolen base at .20 runs, this makes Snyder 1.578 runs better than average.

NL catchers caught 510 runners stealing. Pro-rated to Snyder’s innings, we expect him to gun down 19.554 runners (18, plus Prince Fielder.) He actually threw out 29 baserunners, making him +9.446 in this area. Valuing a caught stealing at .35 runs, this makes Snyder 3.306 runs better than an average catcher.

Snyder had a fielding percentage of .999 (1 error in 780 chances)—the best fielding percentage in the major leagues at his position. The major league average fielding percentage by a catcher was .991 (309 errors in 35,689 chances.) Snyder thus made 5.75 fewer errors than an average catcher. Valuing an error by a catcher at .25 runs (assuming that most E-2, but not all, are on stolen base attempts), we can estimate the value of this at 1.4375 runs. (I am using major league data for fielding percentage but league data for stolen bases, on the theory that stolen base totals are league-specific, but fielding stats are in general not.)

Major league catchers had 335 Passed Balls in 43,425.2 innings. Pro-rated to Snyder’s innings, we would expect him to have 6.87 Passed Balls. He actually had 9 Passed Balls, so in this respect he was below average, negative 2.13. Valuing each of those at 0.20 runs, that is a negative .426.

Adding these four things together (Stolen Bases, Caught Stealing, Errors and Passed Balls), we estimate that Snyder is 5.90 runs better than an average catcher, based on what we know. Adding that to his 25.93 “base”, we credit him with saving 31.82 runs in 891.1 innings.

Now that I look at it, we have a problem here. Our arbitrary selection criteria picked four catchers, all of whom are pretty good defensive catchers. This is going to screw up our charts later on. Since “catcher” is the highest-valued defensive position anyway, it’s going to look like all catchers rank better than all players at any other position. I’d better throw in a couple of not-so-good catchers as well. . .let’s say, John Buck and Johnny Estrada.

While I’m expanding the field, let’s put Orlando Hudson in there, too, just because I brought up his name earlier. . .when I pose the question “Where does Orlando Hudson rank?”, I should suggest some sort of answer.

OK, following through that procedure for the catchers listed here, we have totals of +9.69 for Joe Mauer (who had the best catcher-throwing data in the American League), +12.56 for Kenji Johjima, +0.62 for John Buck, -0.84 for Yorvit Torrealba, and -4.21 for Johnny Estrada. So actually, Buck comes in a hair better than average, and Torrealba a little below average. You learn something every day.

Moving on to the first basemen. . .for first basemen we seem to have two things we can work with: The Fielding +/-, and the Fielding Percentage. Scott Thorman was +3 plays in 2007, according to the Fielding Bible Plus/Minus system. We’ll credit him with .400 Runs Saved for each play above average, making him +1.20 on that. His fielding percentage was .991. The major league average at first base was .994. Thorman was two plays worse-than-average (2.06), so he comes out +.94 plays, which is +.376 runs (actually +.378 if you work the decimals):

I hope you understand. . .my main focus here is not in determining how good a first baseman Scott Thorman is, or how bad a catcher Johnny Estrada is. It is necessary to the process that I am trying to outline that I have some system to say whether a player is +3 (three runs better than average) or -7 (seven runs worse than average), so I am dutifully going through the process of outlining how that might be done, with a little bit of actual data. I am well aware that there are probably better ways to do that, and that’s fine. . .It’s just that this question is standing in my pathway and I’m trying to climb over it to get to the finish line. If you have a better system to determine how many runs a fielder is above or below average, by all means use it.

Anyway, my system for third basemen is the same as for first basemen. .. .+.40 runs saved for each +/- play, and -.40 for each error above the major league norm for the position. For second basemen and shortstops, we’ll need to add something for the ability to turn the double play. The norm for second basemen turning a double play is about .515 Double Plays per opportunity, so we’ll credit the second basemen with .30 Runs Saved for each Double Play above .515 times GIDP Opportunities (Data from the Fielding Bible Plus/Minus in the Bill James Online.)

Orlando Hudson in 2007 was +20 plays made, meaning that he made 20 more plays than one would expect an average second baseman to make. That makes him +8.00 runs. His fielding percentage was .985 against a major league for second basemen of .984, so he’s almost average there, +0.28 plays. He had 166 Double Play Opportunities and turned 89 Double Plays, whereas an average second baseman would have turned 85.5, so he’s 3.5 Double Plays above average.

I give a little less weight to a Double Play because there are more people involved in it, so that it gives a less clear or less certain indication of the player’s individual performance. Anyway, adding those together, Hudson is +9.17 Runs Saved, above his base, which is 26.22. We thus credit him with saving 35.39 runs.

The norm for Double Plays per opportunity at shortstop is higher than at second base, probably because there are more 5-4-3 double play attempts than 3-6-3. Anyway, the norm for shortstops is about .615; otherwise the process is the same.

John McDonald, Toronto’s magic-fingered shortstop, fielded .982 against a major league norm of .972; that made him 4.465 plays better than average. According to The Fielding Bible he was +26 plays. He turned 63 double plays in 110 double play opportunities, a below-average figure; he’s 4.65 plays below average. Adding these together, McDonald is about 10.79 Runs better than an average shortstop:

            (4.465 * .4) + (26 * .4) – (4.65 * .30) = 10.79

Adding that to his “position base”, which was 19.93 runs, we credit McDonald with saving 30.72 runs in 799.1 innings.

Some people will object that Fielding Percentages (errors) and the Fielding Bible’s +/- measure the same plays, thus that our calculation is redundant. It is true that it can be redundant, sometimes.

But I think the better arguments are on the other side of the issue:

1) “Errors” were not a great idea and are not a good way to evaluate a fielder by themselves, but they are a very specific observation. A player who is charged with an error has, in almost all cases, made a clearly observable mistake. A fielder who is “+” a play may simply be benefiting from team positioning decisions, or he may be benefiting from some poorly-understood wrinkle in the +/- range evaluation system. It’s not really the same thing.

2) An event which is observed twice, by different evaluation systems, is more concrete than an event which is observed by one system but missed by another. Assuming that this is a redundant measure—which it is sometimes—that’s OK, because an event which can be observed by both systems is more tangible and more certain than an event which appears in only one.

3) In many cases or perhaps most cases, errors actually are not plays that would show up in the fielder’s plus/minus range. Certainly many of them would not—overthrows allowing advancement, errors made in receiving throws from another fielder, etc.

For outfielders, we have the two elements we had for first and third basemen--+.40 for a “plus” play in the Fielding Bible, -.40 for an error (or +.40 for an error not made.) Also, for outfielders, we have “throwing” data. . .what do we do with that?

A left fielder “allows advancement” on about 40% of advancement opportunities. We’ll credit him with .15 runs saved for each base not advanced below. 400, and charge him with .15 for bases advanced beyond .400. Center Fielders and Right Fielders the same, except that the norm is about .55. (Runners don’t go first-to-third on balls hit to left.)

OK, I figured the “Individual Plus/Minus Run Elements” for each of the 33 fielders now in our study. This is the data, added to the chart above:

            So Kenji Johjima and NL MVP Jimmy Rollins are listed now as the players who saved the most runs.

            These numbers, however, are raw totals, rather than per-inning averages. In order to compare players on a level playing field, we have to convert these into per-inning averages. For cosmetic reasons I’ll list them per 1000 innings.

            By this analysis, the highest-rated defensive player among these 33, in the year 2007, would be Joe Mauer of the Twins. Mauer, playing a critical defensive position with outstanding defensive numbers, is credited with 32.31 Runs Saved in 777.2 innings, which is 41.5 Runs Saved per 1000 innings:

             So we have reached our goal line. These are the numbers by which we can give a reasonable answer to the question: Where does Orlando Hudson’s defense rank him, among all major league players? He ranks at about the 85^th profile, if this group of players is representative of all major league players.

            I’m a little surprised that the number isn’t higher. If Hudson ranks at the 92^nd percentile among second basemen, and second base is a relatively high-value defensive position, one might guess intuitively that he would rank higher than the 92^nd percentile among all players. But having gone through this exercise, I see why this cannot be true. Second basemen in general cannot rank ahead of catchers and shortstops. If Hudson ranked ahead of all other second basemen, but below the catchers and shortstops, that would put him at about the 75^th percentile—ahead of the first basemen, third basemen, the outfielders and all of the other second basemen, thus ahead of six positions, but behind two. Because the numbers spread out, he does rank ahead of a good many of the shortstops and some of the catchers, and he ranks higher than the 75^th percentile—but not back up to the 92^nd.