By Bill James

July 20, 2020

OK, we come now to the last categories of run prevention, which is hits prevented on balls in play. Range, DER, BABIP, In-Play Average. . . .whatever you want to do call. Error Percentage deals with a player’s ability to make the routine play; now we are dealing with the fielder’s ability to make the more-than-routine play.

This process is, if anything, more complicated than the double plays. It’s not easy to explain. Five points as a kind of outline:

1) We’ll call it "range". It means "preventing hits on balls in play which are potentially hits."

2) We will credit range for infielders based on assists, or quasi-assists for first basemen, and for outfielders based on putouts.

3) All fielders except catchers get credit for some share of the team’s success at turning balls in play into outs.

4) We will use a two-step process, as we did for errors, crediting range first to *the fielding position on the team*, and then to the* individual*.

5) All assists by infielders and all putouts by outfielders are regarded as range plays; however, assists by infielders and putouts by outfielders above or below average will count double, thus creating an upward-curving line for plays made.

6) In order to credit first basemen for their defensive range, we will have to create two new categories of information—first base estimated un-assisted putouts, and first base quasi-assists.

Putouts by infielders are not generally range plays. Putouts by infielders are normally either pop outs or force plays. Of course there are some infield putouts which are range plays—infielder shoots to his left to snare a line drive—but they are a small percentage of infield putouts.

The first thing we will do, to start to chip away at this problem, is to explain the First Base Estimated Un-Assisted Putouts, and First Base Quasi-Assists. You may wonder, as we are going through this, why we are explaining first base quasi-assists while we are figuring Runs Saved by pitchers. The reason that we have to do that is that Range/DER is figured on a TEAM basis, and then credit for what the team has accomplished is assigned to individual players, so you can’t run the data

for any one position until you explain the whole hairy process, beginning to end.

**First Base Quasi-Assists**

We’re going to mix and stir some existing statistical categories to create a couple of new ones. The new categories we can create will be called First Base Unassisted Putouts (Estimated), or FiBupe for short, and 1B Quasi-Assists. The reason we have to create these numbers is that, in the effort to give each player credit for his contributions to reducing the number of balls in play which become hits, we have to have some way to recognize the contributions of the first basemen. FiBupe and First Base Quasi-Assists are what we have, and I think they work pretty well.

I actually invented FiBupe twenty-some years ago, when I was working on Win Shares. I the time I called it First Base Unassisted Putouts, but I had some different acronym for it. What it is, is this.

First basemen have a large number of discretionary assists. A first baseman has about one play per game, on average, that he can resolve either by picking up the ball and touching the base himself (3 Unassisted) or by flipping to the pitcher covering (3-1). MOST first base assists are discretionary plays.

Because that is true, a first baseman’s assist total is not at all a reliable indicator of his range. Sometimes first basemen who have no range at all have very high assist totals; sometimes first basemen who have very good range have very low assist totals. Assists are pretty useless for evaluating a first baseman’s range—and putouts are TOTALLY useless, because the great majority of them don’t have anything to do with covering ground; they have to do with catching the throw from somebody else who has covered some ground.

There is, however, a way that you can tell, generally and imperfectly, how many plays the first baseman has initiated. If the first baseman likes to make plays himself (3-U) , then the first basemen’s putout total (on the team—not a single first baseman, but the team)--will be higher than the sum of the assists by the second basemen, third basemen and shortstops. You compare two things: the **putout **total of the first basemen on a team, and the **assist** totals of the other infielders. If he’s a 3-U guy, there will be a gap between the two of them. If he’s a 3-1 guy, there won’t be. It’s not absolutely reliable, but it’s pretty reliable.

This is the actual formula, again reminding you that we are referring to TEAM totals, not totals for individual first basemen or individuals at other positions:

**Formula 26: First Base Estimate Unassisted Putouts (First)-- (FiBupe-1)**

First Base Putouts

Minus .70 times assists by the team’s pitchers (since about 70% of pitcher’s assists are 1-3),

Minus .86 times assists by the team’s second basemen (since about 86% of second base assists are 4-3),

Minus .78 times assists by the team’s third basemen and shortstops (figure it out),

PLUS .115 times Estimated Runners on First Base against the team. (If the team has many runners on first base, that causes outs to be recorded at other bases. Plays aren’t 4-3; they’re 4-6, and they aren’t 5-3, they’re 5-4. It is VERY clear, in analyzing fielding stats, that an increase in runners on first base leads directly to an increase in putouts recorded by the second baseman and third baseman.)

Minus .0575 times Balls in Play Against the defense. (I think the function of the .0575 times balls in play is that it drives the totals down closer to where they should be. I think the estimates otherwise come in a little bit high, so we take away a few plays to make them come in closer to where we believe they should be.)

Fibupe-1 = 1BPO - .7 Ast(p) - .86 Ast(2b) - .78 Ast(3b+ss) + .115 ERO1B - .0575 BIP

**Formula 27: Second Estimate, First Base Un-Assisted Putouts (FiBupe – 2)**

All of that above is ONE estimate of the FiBupe (first base unassisted putouts , estimated.) There is a second estimate, which is simply 10% of the balls in play against the team. Dead simple.

FiBupe – 2 = (BIP vs. Team) * .100

**Formula 28: First Base Estimate Unassisted Putouts (Combined) **

Then we combine these two estimates, two times the first (complicated) estimate, plus the second (simple) estimate, divided by three.

FiBupe = (2 * FiBupe-1 + FiBupe-2) / 3

The purpose of FiBupe-2 is to stabilize the data. The other way, you occasionally get numbers that seem unrealistically high, sometimes are obviously unrealistically low. The addition of the second estimate moves them all toward the center, moves the high-end estimates down and the low-end estimates up, thus keeping them all within the bounds of reason.

**Formula 29: First Base Quasi-Assists (1BQA) **

So those are estimates of the UN-assisted putouts by each first baseman. These are plays that would be "assist" plays, if the first baseman wasn’t so close to first base that he didn’t need to make an assist. To that, we add the ACTUAL assists, the assists actually recorded by the team’s first basemen.

1BQA = FiBupe + PO(1b)

The combined number, which I call first base quasi-assists, will be used to stand in in the analysis that follows for the first baseman’s range. The highest totals of the last hundred years were by the St. Louis Cardinals of 2008 and 2009 (first baseman: Albert Pujols) and by the Chicago Cubs of 1990 and 1991 (first baseman: Mark Grace.)

It is my belief that good first basemen will have high totals of Quasi-Assists, and poor first basemen will have lower numbers. That belief, however, is 20 years old, and is based on research that I did 20 years ago, when it was not possible to do the kinds of research that we do now. (The organized data sets did not exist, and personal computers couldn’t deal with that much data. Or a third that much.) As we apportion Runs Saved to Individual First Basemen in the studies which will be coming, we’ll have to watch the numbers for the first basemen and see whether they pass the smell test, whether we believe and can credibly argue for the validity of our conclusions.

**What is a "Range" Play?**

Infield assists (counting first base quasi-assists as actual assists), ignoring for the moment assists by pitchers, are distributed 20% to first basemen, 30% to second basemen, 30% to shortstops, and 20% to third basemen—20, 30, 30, 20. The actual numbers have stayed astonishing close to those percentages for 120 years. If we divide the 2,550 teams in this study into five groups based on the timeline, the percentage for third basemen has never gone lower than 19.7% or higher than 20.7% for any of the five groups, and is 20.01% overall. The percentage for second basemen has never gone lower than 29% or higher than 29.9%, and is 29.5% overall. The percentage for shortstops ranges over time from 29.5% to 31.3%, and is 30.6% overall, and the percentage for first basemen has ranged from 19.2% to 21.2%, and is 19.8% overall.

So. . 20, 30, 30, 20; those numbers work astonishingly well over time. If we were to include assists by pitchers in the data, different story. Pitchers now make less than half as many assists per game as they did 120 years ago, the numbers declining steadily from 361 assists per team/season in the earliest period of our data to 174 per team/season in the most recent seasons.

The TEAM has a certain number of hits prevented by range, right? It’s a team thing. The 1944 Cincinnati Reds had 547 Hits Prevented, the highest number of any team except some Federal League teams, and the 1930 Philadelphia Phillies had only 109, the lowest number ever. When we assign credit for range plays, the individual totals for the 1944 Cincinnati Reds will have to add up to 547, and the individual totals for the 1930 Phillies will have to add up to 109. Those parameters are the cage within which these animals are free to roam.

The reason that it has to be done that way is that every team records 27 putouts per game, minor deviations from that number. The number of assists varies a little bit; bad teams have a few more assists than good teams do, but that’s a relatively small difference, as well. The best defensive team records no more putouts than the worst defensive team; actually a few less (per inning.) You cannot use the number of fielding plays that the players make as evidence of the defensive quality of the TEAM, because that number is always essentially the same. What you have to do instead is (1) assess the defensive quality of the team by other methods, and (2) assess the impact of each player’s defensive contribution relative to the team. Hence, the two-step process.

Thus, when we look at "range" in this stage of the analysis, what we are looking at is the range of the players at one position, relative to the range of players at other positions on the team, compared to historic norms. Make sense? The historic norms for infielders are 20-30-30-20.

I’m going to need a real-life team here to illustrate the process. . . let’s choose the 1986 Mets. On the 1986 Mets, the four infield positions recorded these numbers of assists:

First Base (mostly Keith Hernandez) 315

Second Base (Wally Backman) 463

Shortstop (Rafael Santana) 525

Third Base (Ray Knight)   287

Which makes these percentages:

First Base (mostly Keith Hernandez) 315 19.8%

Second Base (Wally Backman) 463 29.1%

Shortstop (Rafael Santana) 525 33.0%

Third Base (Ray Knight)   287 18.1%

Normal percentages, basically, except that Santana is picking up a few plays from Ray Knight. All of those plays count as contributions toward the position’s Range number. However, we will double-count plays made above or below what we are calling the position norms—20-30-30-20. That means "bonus plays" for each infield position, as follows:

First Base (mostly Keith Hernandez) 315 -3

Second Base (Wally Backman) 463 -14

Shortstop (Rafael Santana)   525 +48

Third Base (Ray Knight) 287 -31

Which makes these new totals:

First Base 315 - 3 = 312

Second Base 463 -14 = 449

Shortstop 525 + 48 = 573

Third Base 287 - 31 = 256

Disappointed that Hernandez doesn’t show up well, but I believe that over the course of his career, he looks great. (I just spot-checked the Mets’ data in the surrounding years, 1985 and 1987. Mets first basemen are credited with 389 plays made in 1985 and 346 in 1987, so the 1986 data is just a little bit atypical for some reason.) I’ll spell out more careful formulas in a minute; for now, I’m trying to explain the system in a way that makes intuitive sense. What we will have to do in the outfield is different, for several reasons. Many differences:

1) There are almost always more outs recorded in the infield than in the outfield. With the 1986 Mets, for example, the four infield positions recorded 1,590 Assists or Quasi-Assists; the outfielders recorded only 1,067 putouts, which is an above-average number. Even dividing by four in the infield and three in the outfield, the numbers are larger in the infield.

2) Balls in play converted into outs by infielders would generally be singles, were the play not made. Balls in play in the outfield, if not caught, would very often be doubles or triples.

3) Outfielders switch positions much more freely than infielders do. A player does not normally play shortstop one day, first base the next—or second base one day, third base the next, although that does happen. But outfielders play left field one day, right field the next so often that, historically, the three outfield positions have not even been distinguished one from another in the official stats. Records which do distinguish have now been created for most of baseball history.

It is my opinion that speed in the outfield is the greatest variable in changing balls in play into outs, the largest component of DER. I don’t know that I could *prove* that, and you are free to disagree with me and construct your own accounting system, but my point is that a system which gave 60% of the credit for hit prevention to the infielders and 40% to the outfielders would not be accurate. Also a position-by-position accounting of the left fielders, the right fielders and the center fieldermen would be difficult to use. The different natures of the positions force infielders and outfielders to be treated somewhat differently.

So what we do is, at this stage of the analysis we put all three outfielders together, and we increase their putouts by 14%. So we have seven defensive players fighting to share the credit for preventing hits, like this:

First Base (mostly Keith Hernandez) 315 -3

Second Base (Wally Backman) 463 -14

Shortstop (Rafael Santana) 525 +48

Third Base (Ray Knight) 287 -31

Outfield (Wilson, Dykstra and Strawberry) 1067 +150

Which makes these new totals:

Second Base 463 -14 = 449

Shortstop 525 + 48 = 573

Third Base 287 -31 = 256

Outfield 1067 + 150 = 1217

And then we add the assists by pitchers:

Pitchers 231 = 231

First Base 315 - 3 = 312

Second Base 463 -14 = 449

Shortstop 525 + 48 = 573

Third Base 287 -31 = 256

Outfield 1067 + 150 = 1217

Total   3,038

So the eight fielders who are in fair territory, on the 1986 Mets, will get credit for 3,038 plays made.

A zero-competence defense would allow hits on 36% of balls in play (.360). The 1986 Mets beat that by 398 hits; that is, they allowed 398 hits fewer than they would have allowed with a zero-competence defense. So 3,038 plays made conspire to prevent 398 hits, or .131 hits prevented by each play. This number varies widely from team to team. 90% of this value will be attributed to the team’s eight fielding positions, excluding catchers. The other 10% will be attributed to the team’s pitchers, and allocated based on the Ball-in-Play batting average against that pitcher (BABIP).

I have left two threads dangling here: Why are outfielders’ putouts expanded by 14%, rather than some other number, and why are pitchers assists not modified by the comparison to the norm?

There are four reasons we don’t adjust the pitcher’s assists to any central point:

1) Frankly, it would be an accounting nightmare to try to credit each pitcher with "good range" points.

2) There is no "norm" or "central point" for pitchers assists which holds over time. Unlike the other infield positions, the frequency of pitcher assists has changed greatly over time.

3) While of course some pitchers are quicker than others, all pitchers’ range is severely limited by their distance from the batter. They just don’t have __time __to react and cover ground, the way that other fielders do. The amount of ground a fielder covers is proportional to his distance from home plate. Second Basemen and Shortstops cover more ground than first basemen and third basemen, in part, because they are further from home plate. Outfielders cover more ground than infielders because they are further from home plate, thus have more time to cover the space. Pitchers are just too close to the plate to have a lot "range" plays, rather than "reaction" plays.

4) Pitchers and catchers are also the only players on the field who HAVE to stand in a designated place on the field. The other fielders can move in and out and left and right to increase their chances to make a play. The pitchers can’t.

As to why outfielders’ putouts are inflated by 14% at this juncture. . . .that is the number that makes an average outfielder as valuable, in hit prevention, as an average infielder. On the Mets (see chart above), the four infielders (not including the pitchers) are credited with 1,590 plays made, or 398 each, on average. The three outfielders are credited with 1,217 plays made, or 406 each. On an average team, they’re about equal. Tomorrow, I will write out the formulas that spell all of this out.

(The data from the 15 sample teams that we are following could not be any more supportive for the credibility of the First Base Range numbers. The 1960 Pittsburgh Pirates (first baseman: Dick Stuart) have BY FAR the lowest first base range number, 220. The 1992 Blue Jays (first baseman: John Olerud) have the highest, 423, with the 1984 Tigers close behind at 412. The 1984 Tigers’ regular first baseman was Dave Bergman, a light-hitting first baseman who had a 17-year major league career, mostly as a defensive substitute.)

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## COMMENTS (7 Comments, most recent shown first)

CharlesSaegerAlso, you might want to lower the FiBupe. It includes air outs, which isn't included for the other infielders. I get that it will no longer go 20-30-30-20 in distribution, but first basemen make many fewer plays than third basemen once you include the popups/line drives for the third basemen as well. Two reasons:

* There are more right-handed batters than left-handed batters, and right-handed batters pull ground balls towards third base/shortstop, and

* Since first basemen play towards the bag with a runner on first, the second baseman makes more plays on balls in the hole (I'm defining this as a batted ball direction angle between 16° and 33°). On the other side, the shortstop is more willing to let the third baseman get to these balls since he's often closer. My Statcast queries show third basemen getting 83% of the outs in this range against LHB and 39% against RHB, while first basemen get to 22% of these against LHB and 59% against RHB.

10:40 AM Jul 21stbjamesrjm1026

I assume in Formula 29 it is supposed to be AS(1b) not PO(1b) based on the description of the formula above it.

You are correct. Thank you for catching that.

10:35 AM Jul 21stCharlesSaeger(And if someone comes up with better 1b putout formulas, please let everyone know. They're nasty to estimate.)

7:59 PM Jul 20thCharlesSaeger"Minus .0575 times Balls in Play Against the defense." Your recollection of why you added this has to be right. When I played with the formula back when the Win Shares book came out almost 20 years ago, I saw this as counterbalancing the adjustment for runners. Basically, if there's no runner on first, the assist will always go to first. Since your formula already assumes an average number of runners on first when you made the assumptions like 86% of 2b assists go to 4-3 and 70% of p assists go 1-3, you need a counterbalance when adjusting for number of runners and stuff.

7:58 PM Jul 20thchuckBill, in one of the recent articles I asked if pop flys and/or infield flys will be treated differently than other fielder outs in what you're doing here, and you responded with the question: “How would you do that with 1921 data, for example?”

You do say in the piece here today that these outs generally do not demonstrate range, nor do the putouts for infielders on force plays. For the latter, the player making the assist is getting the lion’s share of the credit. You may be coming back to the percentage split of credit for the popups in one of your next articles, but I thought I’d report what I saw from a little digging.

I looked through all the World Series game logs from 1903 (am currently up to 1939) and noted the number of pop fly outs to the pitcher, catcher or infielders, or balls to outfielders described as pop flys. What I found was that these (mostly) infield pop outs had a pretty narrow range of occurrence in terms of PO per 9 innings. That is, it didn’t fluctuate as much as strikeout rate did.

1903-1910 combined:

262 pop outs in 730.2 innings = 3.2 per 9 innings. (K/9 was 4.9)

1911-1919:

360 pop outs in 959.1 innings = 3.4 per 9 innings. (K/9 was 4.4)

1920-1927:

321 pop outs in 908.1 innings = 3.2 per 9 innings. (K/9 was 4.3)

I thought maybe this rate is just the rate we would see for GOOD pitching staffs, as this is only World Series play. I’ve been going through game logs for the 1921 White Sox, who had subpar DER as well as strikeout rate, to compare. So far, through almost 2 months of the season, the rates are:

3.0 per 9 for White Sox pitchers

3.0 per 9 for opponent pitching.

I would guess that the majority of pitchers in this earlier era would be getting pop outs at around that same rate (3 to 3.3 per 9 innings), and that there would be a few outliers- the Luis Tiants, Jim Palmers or Catfish Hunters of the time, who 1 to 2 more than that. I understand that without all the data, one couldn’t say how much pitcher credit should be assigned on an individual basis. But perhaps there’s enough data to show that pitchers in this time were getting these outs 3 to 3.3 times per 9 innings. While that’s not a ton, it’s sizable compared to the K/9 of the time.

Starting around 1928, PO/9 finally rises out of that 3.3 area (at least in the World Series), but I'm only up through 1939.

6:38 PM Jul 20thrjm1026I assume in Formula 29 it is supposed to be AS(1b) not PO(1b) based on the description of the formula above it.

1:15 PM Jul 20th3for3I always had the view from watching games that Santana had terrible range. Surprised he showed up well here, but this is far and away his best season BBr saved as well (+9), so this isn't some strange systemic flaw.

9:51 AM Jul 20th