Overview of the Plus/Minus System

If they had this book when I was playing, I would have been the best shortstop who every lived!
Ozzie Guillen, manager, World Champion Chicago White Sox

That was Ozzieís reaction (with the every-other-word expletive removed) when Pat Quinn and I were explaining the Plus/Minus System in the team version of The Fielding Bible to the Chicago White Sox a couple of years ago. Funny thing, that's probably not too far from the truth. We don't have the Plus/Minus System going back to that era, but we have evaluated past seasons using Bill James' new Relative Range Factor system. Turns out that Guillen has several of the best defensive shortstop seasons of all time based on Billís system. (For more on Billís new system, see page 199.)

In this article Iíll give you the lowdown on the Plus/Minus System, the backbone of this book. Hereís the question that we try to answer with the Plus/Minus System:

How many plays did this player make above or below those an average player at his position would make?

Thatís what you should think to yourself when youíre looking at all those plus and minus numbers. The average is zero. If a player makes one play more than the average, thatís +1.

Now let me give you the short version of how the Plus/Minus System has been developed. Weíll get into further details later.

Baseball Info Solutions reviews videotape of every game in Major League Baseball. Every play is entered into the computer where we record the exact direction, distance, speed and type of every batted ball. Direction and distance is done on a computer screen by simply clicking the exact location of the ball on a replica of the field shown on the screen. Speed is simply soft, medium and hard while types of batted balls are groundball, liner, fly and bunt. We will be introducing a new category in 2006 called fliner. A fliner is a ball that is hard to categorize because itís somewhere between a fly and a liner, so it becomes a fliner. But thatís next year.

The computer totals all softly hit groundballs on Vector 17, for example, and determines that these types of batted balls are converted into outs by the shortstop only 26% of the time. Therefore, if, on this occasion, the shortstop converts a slowly hit ball on Vector 17 into an out, thatís a heck of a play, and it scores at +.74. The credit for the play made, 1.00, minus the expectation that it should be made, which is 0.26. If the play isnít madeóby anybodyóitís -.26 for the shortstop.

The key is if a player makes a play on a specific type of batted ball, hit to a specific location on the field, and hit at a specific speed, he gets credit if at least one other player in MLB that season missed that exact ball sometime during the season. A player who misses a play on a specific type of batted ball, hit to a specific location on the field, and hit at a specific speed, he loses credit if a least one other player made the same play some other time.

Add up all the credits the player gets and loses based on each and every play when heís on the field and you get his plus/minus number (rounded to the nearest integer). Letís continue with the Vector 17 example.

Vector 17 is a line extending from home plate towards the hole between the normal shortstop and third base positions, but not the exact hole. Itís closer to the normal shortstop position. Shortstops fielded a softly hit groundball there 26% of the time in 2005. Medium hit balls on that vector were fielded 52% of the time, while hard hit balls were only fielded at a 10% rate. Overall there are about 260 vectors we use for the field. One more factor we add for outfielders is the distance of every batted ball.

Iíll get into more details a little later, but letís get to the more important question:

How do we figure out if the system works?

First Base:
Mark Teixeira, Doug Mientkiewicz, Darin Erstad

Second Base:
Orlando Hudson

Third Base:
Adrian Beltre, Scott Rolen, Eric Chavez

Adam Everett, Jack Wilson

Left Field:
Carl Crawford, Coco Crisp

Center Field:
Torii Hunter, Andruw Jones, Carlos Beltran

Right Field:
Ichiro Suzuki, Richard Hidalgo

These are all guys who have great defensive reputations, most with at least one Gold Glove. And they are all guys who rank in the top five players at their position in the Plus/Minus System over the last three years.

First Base:
Derrek Lee

Second Base:
Bret Boone

Third Base:
Mike Lowell

Derek Jeter

Left Field:

Center Field:

Right Field:
Bobby Abreu

These are all the guys who have great defensive reputations, all with at least one Gold Glove. They are all guys who rank poorly in the Plus/Minus System.

This was the first and most important way of evaluating the new defensive rating system weíve developed. As much as there was a lot of detailed, theoretical work that went into the system, there needed to be agreement between the best players in the Plus/Minus System and the best players based on visual and subjective impressions by those who know the game. Looking at the first list we felt there was a success. But the second list concerned us. How is it possible that these guys with great defensive reputations, and Gold Gloves, donít fare well? We needed to understand why the system would rate them poorly before we could believe in the system.

Letís go through each of the players who might be expected to rate well in the system but donít.

Derrek Lee has won a Gold Glove in two of the last three years. How is it that heís fielded 13 fewer balls than could be expected of an average major league first baseman in that time? Thatís what the Plus/Minus System number of -13 for Derrek Lee means. (Technically, the meaning is slightly different, but Iíll explain that later). The American League Gold Glover this year was Mark Teixeira, whose +17 was the best in baseball. Why is it that the National League Gold Glover comes out at -13 over three years? OK, so his 2005 number is +2. That doesnít seem very good for the Gold Glove winner.

Well, this is the weakest position for the Plus/Minus System. Most defensive measures have trouble with first basemen. Putouts simply tell you how many groundouts were hit against the team, more a function of the pitchers and other infielders. First baseman assists might have some meaning, but there is no real consensus about what, and they are not reliable as an indicator of range due to the discretionary nature of the play on which the great majority of first base assists occur, the 3-1 flip. Some first basemen just prefer to step on the bag themselves. There are no range factors at first base. While we are measuring very meaningful information on first basemen in the Plus/Minus System, we are missing one huge element: the ability to handle throws, especially of the errant variety, made by the other infielders. Thatís a place where Derrek Lee really excels, perhaps. He saves many an error for his fellow infielders, and itís this ability that takes him a long way towards his Gold Glovesóor at least there is the perception that this is true.

Another defensive element that is not measured by plus/minus, but we are measuring in this book, is the handling of bunts. Over three years, Lee has the second highest score among first basemen in handling bunts. (See Fielding Bunts article on page 211.)

Is D.Lee a deserved Glove Glove winner? I donít think so. Just like Mike Lowell (see below), he excels in some areas but not all, and thatís not enough for a Gold Glove in my book. Scooping throws and handling bunts are important, but so is handling regular groundballs. While Lee is not bad at handling grounders, he is not excellent, either. Who did deserve the Gold Glove? Take a look at all my Gold Gloves That Should Have Been in the Player Comments section starting on page 143.

Bret Boone won Gold Gloves in 2003 and 2004. Orlando Hudson (finally) was the Gold Glove winner at second base in 2005. Booneís decline over those three years is dramatic as measured by our numbers. His plus/minus numbers went -9, -20 and -25 in that time, while his rank in double plays went from number four and number three in 2003 and 2004 to 21 in 2005. What seems evident here is that Booneís age (34, 35 and 36 over the three years) caught up with him a lot faster than the award did. He won his first Gold Glove in 1998 in the National League, then was overshadowed by Pokey Reese the next year. After he came over to the American League, he was stuck behind the automatic choice of Roberto Alomar until Alomar moved to the National League in 2002. Boone was then the choice for three years. Hereís a quote from former MLB outfielder Doug Glanville that I agree with wholeheartedly: ďMost Gold Glove winners are excellent defenders overall, however, they can also gain points by being offensively dominant, acrobatic, popular, or just because they are the incumbent.Ē In the last couple of years some of Booneís points may have come from being the incumbent.

Mike Lowell won his first Gold Glove in 2005 and is the best third baseman in baseball handling bunts. Heís the only guy who measures out at a grade ďAĒ on bunts over three years. Heís also the best at handling balls hit down the line with a +30 over three years. So far the Gold Glove looks solid. But letís look at the rest of his range. On balls hit more or less at him, heís -45 over three years. To his left heís -15. Both of those figures are the worst in baseball at third base. He looks fantastic making those great plays running in on bunts and throwing off balance, and he looks fantastic snaring those shots down the line, but his poor performance in the rest of the third base area drops him down well below average with a sub par -30 Basic Plus/Minus over three years. Enhanced Plus/Minus factors in the bases saved on balls hit down the line, since some of those would have been doubles. Lowell does improve to -21 on the enhanced system, but all in all heís not a deserved Gold Glover, as I see it.

Take Derek Jeter. Please. Donít miss Bill Jamesí article at the beginning of this book. It will tell you all you need to know. Derek Jeter is a great player to have on any team. A tremendous leader. A real winner. A catalyst to the offense. A great hitter for a shortstop. But far from a greatd defensive shortstop.

And finally thereís Bobby Abreu. He has a great arm. Honestly, thatís all you can say thatís positive about his defense. His other qualification for the Gold Glove is that he hits well enough to win it. Winning the Home Run Derby at the 2005 All-Star game didnít hurt either. But stardom clearly does help in the Gold Glove voting, and always has. The media as well as many of the fans were stumped by Abreuís Gold Glove in 2005. After the Gold Gloves were announced, Abreuís former outfield teammate, Doug Glanville, posted a very thoughtful essay (partially quoted above) on the Strat-OMatic web site (www.strat-o-matic.com) arguing that, while he liked and respected Abreu, there was no way on earth that the man is a Gold Glove outfielder.

Further details

The short version of the Plus/Minus System explained above summarizes it well, but each and every position has at least one special adjustment to improve accuracy. Letís go through each position:

First Base Ė There is a big difference between how a first baseman positions himself, depending on whether heís holding the runner or not. To approximate this, we break down all plays involving first basemen into two categories, Holding Required and Holding Not Required. Holding Required is any situation where thereís a man on first with second base open. We may refine this in the future, but we found that since the outcomes are very different with runners being held this adjustment made an important difference in improving the accuracy of the first base plus/minus numbers.

A second adjustment for first basemen was mentioned earlier. Thatís Enhanced Plus/Minus. Basic Plus/Minus counts the number of plays above or below what could be expected by an average first baseman. Enhanced Plus/Minus takes the ďvalueĒ of those made plays and hits into account. Hereís the question that we try to answer with Enhanced Plus/Minus: How many bases does the player save for his team above those saved by the average first baseman?

For example, Eric Chavez has a Basic Plus/Minus of +10 and Enhanced Plus/Minus of +15. Simply said, that means, Eric Chavez made 10 plays more than expected in 2005, saving his team 15 bases. It can work the other way too. Joe Crede made 11 plays more than expected, but it only saved his team two bases. What likely happened here was that Crede played off the line a lot last year. He saved a lot of singles on balls hit into the shortstop hole, but he missed some doubles on balls to his right that other third basemen get to.

Second Base and Shortstop Ė The key adjustment for these two positions is made on hit-and-run plays. We consider any play where the runner on first is breaking towards second a hit-and-run play. It may have been intended as a straight steal, but if the batter hits the ball, it becomes a hit-and-run in practice, at least from the standpoint of the defense. On these plays, either the second baseman or the shortstop is breaking towards second to cover a possible throw and the dynamics of the defense change completely. For the Plus/Minus System, we use Hit-and-Run as another variable.

We donít use the Enhanced Plus/Minus adjustment for middle infielders, since almost all of the plays they donít make become singles, rather than extra base hits.

Third Base Ė At third base we make the same Enhanced Plus/Minus adjustment as first base, but not the Holding Required adjustment.

Outfield Ė A key addition that we made to the system last year was to move from three types of balls hit into the air to six different kinds. Prior to doing the Plus/Minus System for the 2004 season, we had three types of balls hit to the outfield: soft, medium and hard. Initially, we didnít think that a distinction between line drives and flyballs was necessary. If itís hard hit, itís hard hit. However, after doing extensive video analysis for Johnny Damon to see why his plus/minus number was so low in 2004, we discovered that the distinction was necessary. Itís pretty obvious, now that we know it. A hard hit flyball simply stays in the air longer than a hard hit liner, giving the fielder more time to make the play. So now we have six types of balls hit to the outfield, with soft, medium and hard hit flyballs and soft, medium and hard hit liners. Next year we move to nine categories as we add in ďfliners.Ē

For outfielders, we also use the Enhanced version of the system, since balls not fielded by outfielders frequently wind up as extra-base hits.

Estimating runs and wins

One thing we want to do in the future is translate these plus/minus numbers and all the other defensive metrics we have in this book into one number. That might be a number similar to Runs Created, but for defense not offense. Maybe itís called Runs Prevented. But between you and me, you can use the rule of thumb that Bill James used in his article on Derek Jeter and Adam Everett.

That is, use a number a little less than half of the plus/minus number as an estimate of runs prevented. Since the value of a single is a little less than half a run, you can use a ďlittle less than halfĒ of the plus/minus figure to estimate runs prevented. Adam Everettís plus/minus figure of +33 could be estimated as preventing about 15 runs. Then using another rule of thumb that estimates the value of a win at 10 runs, Everettís defense generates an extra 1Ĺ wins for the Astros in 2005. Since the Enhanced Plus/Minus System also factors in the value of extra bases, and each extra base is worth somewhat less than a single, you might use an even lower value (.20 for each plus/minus, perhaps?) for the difference between the Enhanced value and the Basic value. Since defense is not an exact science, however, I would suggest that using half and rounding down for both Basic and Enhanced Plus/Minus is close enough as an estimate. After all, itís not horseshoes or hand grenades.

Doing a Runs Prevented calculation will be much more complicated than this estimate as we try to factor in our bunt rating, double play rating, outfielder throwing arms, errant-throw handling, Defensive Misplays (see page 239), etc. In fact, keep in mind that this estimating technique to translate plus/minus to runs or wins is relative to average. For example, Adrian Beltreís +71 over three years at third base doesnít exactly compare to Adam Everettís +76 at shortstop. Both of these numbers are relative to the average player at their positions. But much more skill is required of the average shortstop than the average third baseman.