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I'd like to tell you an introductory anecdote or post a GIF (soft-g) or something to ease you in to what we're about to engage in, but I don't think my chops are up to snuff, so why don't we just dive in?

There's a neat thing we provide in our stat reports on this website. It's called Team Defensive Efficiency and it has two key stats: defensive efficiency (DE), a very basic measure attributable to Bill James that simply says what percentage of balls in play a defense converts into outs, and Park Adjusted Defensive Efficiency (PADE), a metric designed almost a decade ago (gosh I'm old) by James Click, who these days graces the Rays' front office roster, serving as their Director of Baseball Research and Development. PADE, as the name implies, adjusts for each team's park's effect on their defensive performance and spits out a number that represents a percentage above or below average at turning balls in play into outs.1

You could click over to the stat report, but I'm afraid if you do that, you'll never come back here, so I'll reproduce an excerpt. Here's a table of baseball teams showing their defensive efficiencies and their PADEs, as grabbed on Wednesday night (i.e. the stats are updated through Tuesday's games), sorted by DE :

 TEAM DE PADE OAK 0.723 2.24 TBA 0.723 2.59 ANA 0.721 2 SEA 0.721 2.19 SDN 0.72 3.01 WAS 0.72 2.11 PIT 0.718 2.19 LAN 0.715 1.8 TEX 0.712 -0.07 BAL 0.712 0.92 CHN 0.712 1.08 TOR 0.711 -0.21 ATL 0.711 0.47 SFN 0.711 0.85 CHA 0.71 0.48 NYN 0.708 0.42 CIN 0.708 0.46 BOS 0.705 -1.94 NYA 0.702 -1.11 MIN 0.702 -1.18 PHI 0.701 -0.53 ARI 0.701 -0.71 CLE 0.7 -1.02 MIA 0.699 -0.76 SLN 0.698 -0.24 KCA 0.693 -2.35 HOU 0.692 -1.79 DET 0.692 -2.55 MIL 0.684 -3.4 COL 0.679 -4.25

If you haven't looked at these stats before, I think the most interesting and important part is to get a sense of scale, an idea of the spread between good and bad. Let's look at a subset (for no real reason): The worst American League defense by DE turns about 69 percent of balls into outs; the best is a touch above 72 percent. Similarly, the PADEs range from two and a half percent below to two and a half percent above average. Those don't seem like huge differences! But that's why I wanted to write this, because those spaces between top and bottom in overall defense2 don't look that large but will (don't skip to the end!) turn out to be larger than you might realize.

Let's start by adding the balls in play and outs each team has recorded to the above table:3

 TEAM DE PADE BIP Outs OAK 0.723 2.24 3770 2727 TBA 0.723 2.59 3469 2508 ANA 0.721 2 3661 2641 SEA 0.721 2.19 3673 2647 SDN 0.72 3.01 3688 2657 WAS 0.72 2.11 3612 2599 PIT 0.718 2.19 3699 2656 LAN 0.715 1.8 3599 2575 TEX 0.712 -0.07 3605 2568 BAL 0.712 0.92 3809 2713 CHN 0.712 1.08 3669 2611 TOR 0.711 -0.21 3657 2602 ATL 0.711 0.47 3655 2599 SFN 0.711 0.85 3728 2650 CHA 0.71 0.48 3606 2561 NYN 0.708 0.42 3665 2597 CIN 0.708 0.46 3693 2616 BOS 0.705 -1.94 3721 2625 NYA 0.702 -1.11 3562 2501 MIN 0.702 -1.18 3997 2806 PHI 0.701 -0.53 3592 2519 ARI 0.701 -0.71 3676 2576 CLE 0.7 -1.02 3848 2695 MIA 0.699 -0.76 3884 2717 SLN 0.698 -0.24 3823 2667 KCA 0.693 -2.35 3705 2566 HOU 0.692 -1.79 3796 2629 DET 0.692 -2.55 3566 2467 MIL 0.684 -3.4 3639 2489 COL 0.679 -4.25 3835 2604

I don't know if there's an easy way to visualize how many balls that is, to make it somehow concrete or to create a useful metaphor. If you can, then I'm happy for you. If you can't, that's OK—we'll get to more concrete ways to understand these numbers below.

There are some interesting pieces to look at, though, like picking out some pairs of teams for comparison. The A's and Royals are separated by 65 balls in play but 161 outs, for instance. Or: Look how few balls in play the horrendous Detroit defense has had to deal with. That's called matching a strength to a weakness. Maybe this Dave Dombrowski guy knows a little somethin' about somethin'.

Back in the main thread of things, when you add up all those balls in play and all those outs, you find that the league defensive efficiency is about .707. We can use this to figure out how many outs each team would have recorded on its balls in play if it had an average defense, and then see how many outs above or below average it actually did record.4 (I've rounded everything to whole numbers here because, eh, this ain't science. Any precision implied by decimal points would be false.)

 TEAM DE PADE BIP Outs AvgOuts OAA OAK 0.723 2.24 3770 2727 2665 62 TBA 0.723 2.59 3469 2508 2452 56 ANA 0.721 2 3661 2641 2588 53 SEA 0.721 2.19 3673 2647 2596 51 SDN 0.72 3.01 3688 2657 2607 50 WAS 0.72 2.11 3612 2599 2553 46 PIT 0.718 2.19 3699 2656 2615 41 LAN 0.715 1.8 3599 2575 2544 31 TEX 0.712 -0.07 3605 2568 2548 20 BAL 0.712 0.92 3809 2713 2692 21 CHN 0.712 1.08 3669 2611 2593 18 TOR 0.711 -0.21 3657 2602 2585 17 ATL 0.711 0.47 3655 2599 2583 16 SFN 0.711 0.85 3728 2650 2635 15 CHA 0.71 0.48 3606 2561 2549 12 NYN 0.708 0.42 3665 2597 2591 6 CIN 0.708 0.46 3693 2616 2610 6 BOS 0.705 -1.94 3721 2625 2630 -5 NYA 0.702 -1.11 3562 2501 2518 -17 MIN 0.702 -1.18 3997 2806 2825 -19 PHI 0.701 -0.53 3592 2519 2539 -20 ARI 0.701 -0.71 3676 2576 2598 -22 CLE 0.7 -1.02 3848 2695 2720 -25 MIA 0.699 -0.76 3884 2717 2745 -28 SLN 0.698 -0.24 3823 2667 2702 -35 KCA 0.693 -2.35 3705 2566 2619 -53 HOU 0.692 -1.79 3796 2629 2683 -54 DET 0.692 -2.55 3566 2467 2521 -54 MIL 0.684 -3.4 3639 2489 2572 -83 COL 0.679 -4.25 3835 2604 2711 -107

This is starting to get a little more concrete, right? We know what outs are. There are 27 of them in a game, and these numbers are small enough that we can compare them to the number of games the teams have played. The Nationals, for instance, have recorded an extra out about once every three games.

Colorado, which as you will note from PADE cannot blame Coors for this, has gifted the bad guys more outs than any other team by a wide margin. One hundred seven outs! That's a lot of outs. Honestly, is it any wonder that Josh Outman (8.72 ERA) isn't living up to his name? It's his defense's fault!

But those are the unadjusted numbers. How can we park-adjust them? Here's what we do. Take PADE and divide by 100 to get it from percentage format into a decimal that we can actually use in maths. Then multiply that by the AvgOuts we figured in Table 3 because what PADE tells us is how many more (or fewer) outs a team gets than the league average. Fairly straightforward, right? Here's the table:

 TEAM DE PADE BIP Outs AvgOuts OAA PADEOAA OAK 0.723 2.24 3770 2727 2665 62 60 TBA 0.723 2.59 3469 2508 2452 56 64 ANA 0.721 2 3661 2641 2588 53 52 SEA 0.721 2.19 3673 2647 2596 51 57 SDN 0.72 3.01 3688 2657 2607 50 78 WAS 0.72 2.11 3612 2599 2553 46 54 PIT 0.718 2.19 3699 2656 2615 41 57 LAN 0.715 1.8 3599 2575 2544 31 46 TEX 0.712 -0.07 3605 2568 2548 20 -2 BAL 0.712 0.92 3809 2713 2692 21 25 CHN 0.712 1.08 3669 2611 2593 18 28 TOR 0.711 -0.21 3657 2602 2585 17 -5 ATL 0.711 0.47 3655 2599 2583 16 12 SFN 0.711 0.85 3728 2650 2635 15 22 CHA 0.71 0.48 3606 2561 2549 12 12 NYN 0.708 0.42 3665 2597 2591 6 11 CIN 0.708 0.46 3693 2616 2610 6 12 BOS 0.705 -1.94 3721 2625 2630 -5 -51 NYA 0.702 -1.11 3562 2501 2518 -17 -28 MIN 0.702 -1.18 3997 2806 2825 -19 -33 PHI 0.701 -0.53 3592 2519 2539 -20 -13 ARI 0.701 -0.71 3676 2576 2598 -22 -18 CLE 0.7 -1.02 3848 2695 2720 -25 -28 MIA 0.699 -0.76 3884 2717 2745 -28 -21 SLN 0.698 -0.24 3823 2667 2702 -35 -6 KCA 0.693 -2.35 3705 2566 2619 -53 -62 HOU 0.692 -1.79 3796 2629 2683 -54 -48 DET 0.692 -2.55 3566 2467 2521 -54 -64 MIL 0.684 -3.4 3639 2489 2572 -83 -87 COL 0.679 -4.25 3835 2604 2711 -107 -115

Hey, you want to really pile on a team that doesn't need you in its ear? Check out Boston. They've posted a respectable DE this year, just a tad below league average, but that park, per the PADE methodology, means that the Red Sox should have been recording a whole lot more outs, so their PADE-based outs "above" average winds up worse than all but four teams in baseball.

But even if we use the devices of "one out every N games" as we did above with Washington, we're still operating in the realm of outs and balls in play, which aren't natural numbers that we're used to dealing with. They're a little foreign. Do you, off the top of your head, know what the run value of an out is? I'm sure a couple of you will raise your hands (stop showing off), but I'm equally sure that most of you will need to go look it up, just like I do. Maybe I'm projecting. Either way, though, the question is how to translate these "extra outs" numbers into runs. And here's where it gets complicated and where we have to start getting into estimation, where we leave the realm of actual facts and enter fantasy lands that we hope approximate reality.

The problem is that we don't know which balls were caught by Matt Joyce from Tampa but were not caught by Carlos Gonzalez in Colorado. Which teams are turning gappers (likely doubles and occasional triples) into outs? Which teams are letting infield bleeders (likely singles) through? Which team is really bad at the Bermuda Triangle play where two outfielders and one middle infielder all converge and nobody catches the ball while the runner hustles his way into second for the cheapest "double" you'll ever see?

We don't know. There's data out there that claims to know things of this sort, and if there's an official Baseball Prospectus position on that data, I haven't heard it, but you can count me as one of those convinced by Colin Wyers's work in the area showing that the biases in at least some of that data are too significant to ignore. So I don't want to use that data. I want to figure out what we can know from the objective numbers we have on the defensive efficiency stat report and that we can figure for decades and decades into the past if we want.

So what we have to do is make some estimates. The two ways to convert Outs Above Average into runs that immediately come to (my) mind are like so:

1. Pretend that every ball that was caught would have been a single (and conversely that every ball that wasn't caught was a single);

2. Pretend that the additional outs or hits are made in the same proportion as they are made league-wide.

Figuring a value for the Outs Above Average the first way is easy. In 2010,5 the linear weights value of a single (for the offense) was 0.4595 and the value of an out was -0.1645. Thus the value of turning what would be a single into an out is 0.624 runs saved for the defense. (And the value of turning an out into a single is obviously -0.624.) Let's add those values to our table:

 TEAM DE PADE BIP Outs AvgOuts OAA PADEOAA OAA-RAA PADEOAA-RAA OAK 0.723 2.24 3770 2727 2665 62 60 39 37 TBA 0.723 2.59 3469 2508 2452 56 64 35 40 ANA 0.721 2 3661 2641 2588 53 52 33 32 SEA 0.721 2.19 3673 2647 2596 51 57 32 35 SDN 0.72 3.01 3688 2657 2607 50 78 31 49 WAS 0.72 2.11 3612 2599 2553 46 54 29 34 PIT 0.718 2.19 3699 2656 2615 41 57 26 36 LAN 0.715 1.8 3599 2575 2544 31 46 19 29 TEX 0.712 -0.07 3605 2568 2548 20 -2 12 -1 BAL 0.712 0.92 3809 2713 2692 21 25 13 15 CHN 0.712 1.08 3669 2611 2593 18 28 11 17 TOR 0.711 -0.21 3657 2602 2585 17 -5 11 -3 ATL 0.711 0.47 3655 2599 2583 16 12 10 8 SFN 0.711 0.85 3728 2650 2635 15 22 9 14 CHA 0.71 0.48 3606 2561 2549 12 12 8 8 NYN 0.708 0.42 3665 2597 2591 6 11 4 7 CIN 0.708 0.46 3693 2616 2610 6 12 4 7 BOS 0.705 -1.94 3721 2625 2630 -5 -51 -3 -32 NYA 0.702 -1.11 3562 2501 2518 -17 -28 -10 -17 MIN 0.702 -1.18 3997 2806 2825 -19 -33 -12 -21 PHI 0.701 -0.53 3592 2519 2539 -20 -13 -12 -8 ARI 0.701 -0.71 3676 2576 2598 -22 -18 -14 -12 CLE 0.7 -1.02 3848 2695 2720 -25 -28 -16 -17 MIA 0.699 -0.76 3884 2717 2745 -28 -21 -18 -13 SLN 0.698 -0.24 3823 2667 2702 -35 -6 -22 -4 KCA 0.693 -2.35 3705 2566 2619 -53 -62 -33 -38 HOU 0.692 -1.79 3796 2629 2683 -54 -48 -34 -30 DET 0.692 -2.55 3566 2467 2521 -54 -64 -33 -40 MIL 0.684 -3.4 3639 2489 2572 -83 -87 -52 -55 COL 0.679 -4.25 3835 2604 2711 -107 -115 -67 -72

These acronyms are getting absurd, I realize, but hopefully it's pretty clear what everything means. Is it? Maybe it's not. "PADEOAA-RAA" is "Park Adjusted Defensive Efficiency–based Outs Above Average hyphen Runs Above Average." Got it? That's the runs total for the outs figure that's based on PADE. The column to the left of that is the runs total for the outs figure that's based on raw defensive efficiency. So we've got runs! Finally! We know what runs are.

The Padres, then, if you like PADE and you assume that every ball they caught that other teams missed would have only been a single, have been 49 runs above average on defense this year. In their run environment, that's over five wins easily. Sadly, this is the Padres we're talking about, so we're looking at the difference between 64 wins (17 1/2 games out of first) and their current 69 wins (12 1/2 games out). Defense turned them from pitiful into an also-ran!

On the other end of the spectrum are the Rockies, who currently have a run differential of -101. All else being equal, were their defense average instead of pitiful, they could be … well, they could be the Padres, who have a -37 differential.

Enough N.L. West talk. Ready for the final addition? Here we go.

In 2010, the breakdown of singles, doubles, and triples6 on hits in play went like this: about 75.4 percent were singles, 22.4 percent were doubles, and 2.3 percent were triples. (Rounding is why there's an extra 0.1 percent.) Multiplying each of these percentages by the linear weights values of each event (0.4595 again for singles, 0.7595 for doubles, 1.0295 for triples) results in a "hits in play" linear weights value of 0.5396. Going back to the same outs value of -0.1645 means that a potential hit turned into an out by this accounting saves 0.7041 runs for the defense. Does that make sense?

Final table!

 TEAM DE PADE BIP Outs AvgOuts OAA PADEOAA OAA-RAA PADEOAA-RAA OAA-RAA-2 PADEOAA-RAA-2 OAK 0.723 2.24 3770 2727 2665 62 60 39 37 44 42 TBA 0.723 2.59 3469 2508 2452 56 64 35 40 39 45 ANA 0.721 2 3661 2641 2588 53 52 33 32 38 36 SEA 0.721 2.19 3673 2647 2596 51 57 32 35 36 40 SDN 0.72 3.01 3688 2657 2607 50 78 31 49 35 55 WAS 0.72 2.11 3612 2599 2553 46 54 29 34 32 38 PIT 0.718 2.19 3699 2656 2615 41 57 26 36 29 40 LAN 0.715 1.8 3599 2575 2544 31 46 19 29 22 32 TEX 0.712 -0.07 3605 2568 2548 20 -2 12 -1 14 -1 BAL 0.712 0.92 3809 2713 2692 21 25 13 15 15 17 CHN 0.712 1.08 3669 2611 2593 18 28 11 17 12 20 TOR 0.711 -0.21 3657 2602 2585 17 -5 11 -3 12 -4 ATL 0.711 0.47 3655 2599 2583 16 12 10 8 11 9 SFN 0.711 0.85 3728 2650 2635 15 22 9 14 11 16 CHA 0.71 0.48 3606 2561 2549 12 12 8 8 9 9 NYN 0.708 0.42 3665 2597 2591 6 11 4 7 5 8 CIN 0.708 0.46 3693 2616 2610 6 12 4 7 4 8 BOS 0.705 -1.94 3721 2625 2630 -5 -51 -3 -32 -4 -36 NYA 0.702 -1.11 3562 2501 2518 -17 -28 -10 -17 -12 -20 MIN 0.702 -1.18 3997 2806 2825 -19 -33 -12 -21 -13 -23 PHI 0.701 -0.53 3592 2519 2539 -20 -13 -12 -8 -14 -9 ARI 0.701 -0.71 3676 2576 2598 -22 -18 -14 -12 -16 -13 CLE 0.7 -1.02 3848 2695 2720 -25 -28 -16 -17 -17 -20 MIA 0.699 -0.76 3884 2717 2745 -28 -21 -18 -13 -20 -15 SLN 0.698 -0.24 3823 2667 2702 -35 -6 -22 -4 -25 -5 KCA 0.693 -2.35 3705 2566 2619 -53 -62 -33 -38 -37 -43 HOU 0.692 -1.79 3796 2629 2683 -54 -48 -34 -30 -38 -34 DET 0.692 -2.55 3566 2467 2521 -54 -64 -33 -40 -38 -45 MIL 0.684 -3.4 3639 2489 2572 -83 -87 -52 -55 -59 -62 COL 0.679 -4.25 3835 2604 2711 -107 -115 -67 -72 -75 -81

This method, of course, pushes the teams at either end even farther out to the extremes. The A's, for instance, add five runs by this method and clock in at 40 runs above average. The team's pitching staff has gotten a lot of love (not undeservedly! They're fifth in baseball in Fair Run Average) and the offense has received some notice in the second half (fifth in baseball in runs since the All-Star break—no, seriously, go look), but boy howdy, a four- to five-win defense is an awfully nice thing to have, isn't it?

And how about the American League Central? Here are the Tigers: 75-67. Here are the White Sox: 76-66. And here's the gap between the two teams on defense, rounded to a nice round number: 50 runs. I don't know what kind of runs-to-wins conversion you prefer in your baseball analysis, but the ones I favor have 50 runs being worth way more than one win.

Noting, by the way, that the Tigers have received just a .261/.292/.408 line from their designated hitters this season, it's certainly fair to ask whether Brandon Inge's plus defense at third and .218/.275/.383 batting line might have served Motor City better than its collection of DHs and Miguel Cabrera's dastardly defense at the hot corner. (To be fair, Cabrera's FRAA stands at just -2 for the season. On the other hand, Inge's is +3 in less than 3/5 of the playing time, and, again, the gap between Detroit and Chicago is one game.)

So! We've come to the conclusion and my utter lack of narrative structure in this piece is about to be exposed. I don't have a conclusion. I'll have to steal a trick from Tommy Bennett and ask you all a question instead:

Do you like defense? Is defense fun?

1. If you're interested in how PADE came to be, the easiest thing to do is probably a date-sorted search for "PADE" in our archives. If you scroll to the bottom, you'll see a group of articles by Click, the first couple of which have the (sorry, Russell) gory mathematical details. â†©

2. Here's as good a place as any to mention this: I might use shorthand throughout this article about "overall defense" or similar terms, but it's important to acknowledge here that defensive efficiency (and necessarily PADE, since it's based on DE) measures the simple act of turning balls in play into outs. It doesn't measure throwing runners out from the outfield or turning double plays or deterring the running game or picking players off or whatever else defenses do. The point here isn't that those aspects of defense don't matter—it's that they're pretty hard to measure with a simple number the way we can with defensive efficiency.

I would suspect that each of those elements pales in comparison to the importance of turning potential hits into outs, by the way, but there's a reason I'm putting this in a footnote. It's an aside. You shouldn't take it seriously. I'm just talking here.

Anyway, I'm also ignoring the pitchers' effect on all of this. A pitching staff that gives up more hard-hit balls than others would tend to have a lower defensive efficiency than its defense "deserves." â†©

3. Balls in play are here determined by taking plate appearances and subtracting walks, strikeouts, hit by pitch, and homers. Sacrifice bunts, despite being a thing that are given away freely, are not removed from the equation. They count as balls in play.

Outs are determined by taking balls in play, subtracting hits, and adding back in homers (because homers are hits, too, so when you subtract hits from balls in play, you're subtracting homers, even though they're not balls in play; you have to add them back in to fix that). â†©

4. There's another effect I'm intentionally ignoring here, which is that teams with good defenses wind up with fewer opportunities to turn balls in play into outs than teams with bad defenses. Every time an out is not made, a new batter gets to come take his turn and that new batter has some chance of putting another ball into play. Seeing that this effect exists is straightforward. Figuring out the size of it … well, let's just call it beyond the scope of this article. â†©

5. This was the most recent year I could easily get the data for. Luckily, 2010 featured 4.38 runs per game league-wide, while 2012 has so far been at 4.34, so the differences between the two environments are relatively insubstantial. I'm not using the linear weights from 2002, after all. â†©

6. I'm ignoring homers even though some potential homers are also potential outs. Mike Trout proves this seemingly every night. The number is far, far too small, though, for me to want to skew things with their inclusion. â†©

This is a free article. If you enjoyed it, consider subscribing to Baseball Prospectus. Subscriptions support ongoing public baseball research and analysis in an increasingly proprietary environment.

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eddiewinslow
9/13
A very enjoyable read. Probably would have been a bit better with an introductory GIF (hard-g), though.
doctawojo
9/13

Yes, that's a pun, but it's also true. He helped me with PADE.
lesmash
9/13
Nicely done, Jason. I, for one, needed the step-by-step explanations, so thanks for that. If there's something I am going to take away from this article, it is that many baseball teams continue to ignore defense - or at least they undervalue it - and they do so to their own detriment.

On a separate note, I wonder how long it will be until we see a team adopt a completely unusual defensive approach. I know some teams (the Rays!) love to play shifts, but I'm thinking about a team that plays 5 infielders against certain hitters and 4 outfielders against others. And they do so every night, depending on the match-ups and scouting reports. I would think, if nothing else, it might drive opposing hitters a little crazy . . . and that's a plus right there.
mhmosher
9/13
Holy mackerel.
jjgreen33
9/13
This is the best BP piece in a very long time. Terrific, illuminating work.
doctawojo
9/13
Thanks!
hotstatrat
9/13
I think the Cabrera move to third was a success. It was Delmon Young's lack of willingness to DH and resulting horrible output from that spot that was a failure. Injuries to Broesch and Dirks didn't help either, nor did Ryan Raburn's horrible season. Proof will be that Detroit continues with it after Victor Martinez returns.
doctawojo
9/13
I'm a little unclear on the Delmon Young part of this -- he's DH'd almost 100 times this year.
jfranco77
9/14
Outstanding article.

FWIW, FanGraphs has the Rockies hitters (adding up everyone over 100 PA) at -40.3 fielding runs. Only Todd Helton and DJ Lemahieu are positive fielders, and Fowler, Pacheco, Rutledge, and Chris Nelson are all about -8 or worse.

Objectively, I can see why they'd be bad. Rutledge really isn't a shortstop. Pacheco isn't really a 3B, and I'm not sure he's really a 1B either. I wouldn't have expected CarGo to be below average, or Fowler to show up at -10.7. Cuddyer is -1 run which is fine.
nickkappel
9/14
Can we use Team Defensive Efficiency to explain why bad pitchers (on a team w/high TDE) who pitch to contact have good numbers, and vice versa?
eliyahu
9/14
I've already +1'ed above, but that's not enough. This was an excellent article. One of the most memorable I've read here.
asekoonce
9/14
I enjoyed this article, but I think that one needs to be careful in measurements like this one. In particular, I wonder about the PADE figures. As Colin Wyers (I think) has reminded us, the error bars are very important in these statistical calculations. I am a bit suspicious of the methodology that creates PADE; the errors there could be substantial.

On the other hand, I thank you very much for putting those DE and PADE numbers into a context that makes sense. I had often wondered if those small differences in DE really amounted to significant differences in terms of runs and wins; thank you for doing the calculation for me!
doctawojo
9/14
I agree 100% that knowing about the error/uncertainty around the figures is important, and it's something I should have mentioned in the article. Thank you for raising that.

I don't actually have a substantive response at the moment, though. Maybe it's something I can follow up on later.

Your second paragraph is what I was hoping people would take from this -- not so much "hey Detroit has lost 50 runs!" as "how much difference is it actually making on the field when a team is 1% above average at catching balls?" Whether a team actually IS 1% above average is the harder part.