Anyone want to get together?  Buehler?  Buehler?

I’m here to tell you, friends and neighbors, that you, yes, you, can be a defensive runs saved calculator without the need to pray MGL is able to let you in on how your favorite player performed. MGL always obliges, but he doesn't have to have the burden.

You will have to do some of the work, so stop watching that baseball game and get your head into a spreadsheet.

Here’s what you are going to need:

1.	The player’s name and defensive innings 
played at position.

2.	The average number of innings a team 
played in a season.  Usually, it is about 1440, 
depending on extra inning games, etc.  In 2005, 
the average AL team had 1441.0.

3.	Obtain the league average ZR at position.  
This can be done by “back calculating” from every 
other player’s ZR.  It’s a bit tricky, but you can do it.  

4.	All you need now is how many chances each 
position has if they play every inning and the average 
run value per play at that position.  

And those are right..here:

Position	AvgZROps	Runs/play
1B	281	0.798
2B	507	0.754
3B	430	0.800
SS	532	0.753
LF	348	0.831
CF	462	0.842
RF	365	0.843

5.	Mix thoroughly.  Sprinkle lightly with arm 
and/or double play ratings.  You read that correctly. You 
don’t need assists or putouts or anything.  Yes, that’s 
mildly annoying because it makes you think, 
"that can’t be right”.  But trust me.  Just trust me.

6.	Example:

Position	AvgIP AvgOpps          AvgZR Run/play
1B	        1440	281	       0.871 0.798

last     team     INN       ZR
Helton Col   1230.7    .916 

Is that all the data I said you needed to gather/gave you?

Let’s start calculating!

Average Plays Made (PM) = Avg Chances (281) * Avg ZR (0.8710)
Average Plays Made (PM)  = 244.75

So far, so good.  That is the average plays made you 
are going to compare every first baseman to.

Now the run value of that:

Runs Saved at Position = PM (244.75) times Runs/play (0.798)
Runs Saved at Position = 195.31 Runs Saved at Position

It is very important to remember that represents the 
Runs Saved (RS) for playing every inning.  I refer 
this to a “cal” after Cal Ripken who played every 
inning for about a decade.

At first base then, the Avg RScal = 195.3.

For Helton we get:
RScal = Helton’s ZR * 281 AvgZRChances * 0.798 runs/play
RScal = 205.4

RScal+ = RScal above average (simple subtraction)

Helton’s RScal+ = 205.4 – 195.3 = 10.1 RScal+

Converting to Helton’s playing time, RSpt:

RScal+ * Helton’s Innings / League Avg Innings

RSpt = 10.1 * 1230.7 / 1440 = 8.6

Yes, that can be a one-line formula, but I personally 
like having “if he played every inning”.

To summarize Helton’s line:

last	team	INN	RScal	Rscal+ RSpt	RS/150
Helton,	Col	1230.7      205.4          10.1    8.6                  9.4

I don’t have Helton’s actual ZR chances. I think trying to re-estimate them is folly, as my “281” number is generated from some 56,000 innings and 11,000 chances.

Now you can set up your own spreadsheets and load the data. You can post weekly updates, or just be ready to look at defensive value before you post your MVP selections.

It is very important to understand that ZR chances are like plate appearances. If a fielder has only played enough innings to make 100 fielding plays, then it is too early to judge how good of fielder he is. It's like 100 PAs. So don't put too much weight, good or bad, on guy who haven't played much. It's very important for catchers too, because they always play partial seasons.

Oh, more info?

Okay, for outfielders’ arms, I calculate the average assists per inning from every outfielder and then multiply by the league average innings. Then I subtract that from the player’s assists with the proper playing time conversion. Those are straight runs added to a player’s RSpt (or RScal+).

I do not park adjust, pitching staff adjust, groundball/flyball adjust. I am really skeptical of that still – because I haven’t worked it out for myself. I’m stubborn that way, but I also have never seen the data broken out in that manner.

Catchers are done as an amalgam of caught stealing per inning above average, stolen bases per inning above average, errors per inning above average and passed balls per inning above average, at an average base advancement of 0.31 runs per. I have vacillated between a couple of catcher run value calculations. Someone needs to make an argument on which way I should go.

Is this method any good?

I like my method. I think defensive evaluations from a zone perspective is the best way. I think this method is robust due to the sheer volume of data input. How do I compare it to anything? I know UZR is pretty good, so I took MGL’s posted numbers in the Gold Glove articles, and David Gassko’s (DSG) from his article at The Hardball Times. Mr. Smith (Rally) provided all of us with all his numbers for players with 250 innings.

I have 56 data points from MGL. I have 100 from DSG. I used 122 from Rally. The reason I used 122 from Rally is because I used the guys that you have read with posted numbers. Besides, you’ll see there isn’t much point to more between Rally and me. We agree very tightly.

I made comparisons to each other, all based on 150 defensive games (1350 innings played) excluding outfield arms and double plays.

Correlations:

	vsMGL	vs DSG	vs Rally
Dial	0.82	0.60	0.97
Rally	0.80	0.61	
DSG	0.61	

What about absolute differences? You may have seen various discussions (see the AL Gold Glove article) regarding the Nick Swisher number. MGL has Swisher at +37, while Rally and I had him at average and DSG had him very negative (-23). Somebody, somewhere has something off.

Average Absolute Difference:

	vsMGL	vs DSG	vs Rally
Dial	 9.9	12.5	3.0
Rally	10.0	12.2	
DSG	12.2

By position:

		
	Correlations with MGL		
	Dial	Rally	DSG
2	1.00	0.98	0.98
3	0.88	0.88	-0.28
4	0.86	0.85	0.91
5	0.84	0.83	0.66
6	0.69	0.59	0.83
7	0.99	0.99	0.95
8	0.88	0.84	0.83
9	0.74	0.78	0.14

Rally’s method correlates well everywhere with some question at shortstop. I don’t know if his double play addition would increase that, but MGL’s doesn’t include double plays.

My rating does very well. The worst correlation is 0.69, with a 0.9 rating or greater at five of the eight of the positions.

I am using UZR as a baseline because it is well respected.

If I remove the four worst matches – the players each method disagreed with UZR the most - the correlations increase (duh). Removing those four moved my correlation to 0.87, Rally’s to 0.84, but most amazingly, DSG’s to 0.83. That’s a huge jump in DSG’s numbers. That’s basically saying 7% of these players are problematic when comparing a non-pbp method to a pbp method. I think that’s really good. I don’t know if that 7% can be eliminated.

I haven’t worked up all of the 2000-2003 data for which there is a bunch of UZR data available. One of you more industrious fellows can take my methodology, make your own spreadsheet and compare to UZR. Or you can wait until I get around to it. Which will happen. No, really.

Each of you is now armed with the ability to accurately estimate how many runs a defender saves at any moment. No more “but how good is his glove”? No more “will MGL post UZR”? Well, we still want that, but you can feel pretty confident using this methodology that you are right on it.

Plus, when you vote for MVP, or ROY, you can do it with 50% 52% more knowledge.

HTH.

In the spirit of open research, the data used to calculate these defensive ratings can be found here.]]> 2005-11-11T01:19:00-05:00 http://www.baseballthinkfactory.org/files/dialed_in/discussion/what_is_zone_rating/ Sabermetrics What is Zone Rating?

Basically, ZR is the percentage of balls fielded by a player in his typical defensive ‘zone’, as measured by STATS reporters.

The first part of understanding Zone Rating is understanding how the field is divided up.

The field is divided into 22 equal ‘slices’.  Each slice runs from home plate to the outfield fence.  The first slice running along the left field line is Zone ‘C’.  (Zones A, B, Y and Z are in foul territory).  The last zone is Zone ‘X’. Like any ‘pie’ slice, or wedge, gets wider as you approach the outfield wall.  Zone C is about 7 feet wide at the third base bag, and about 20 feet wide at 300 feet from home plate.
The next 21 zones (D - X) divide the field equally until you get to the right field line.  The dividing line between zones M and N runs right over second base, splitting the field in half.

STATS ZR zone grid

With this division of the field understood, ZR becomes much easier to visualize.

For infielders, only ground balls are considered for zone rating.  Line drives, pop-ups and fly balls are not included.  This serves to, oh so slightly, under-rate the defensive value of all infielders, but presently this information is not readily available.  First basemen are responsible for all bunts that travel more than 40 feet and land in his area of responsibility.

Zones of Responsibility

While each ball is recorded for location, distance and speed, not every ball is a defensive player’s responsibility. That is, only balls that could reasonably be fielded from a typical defensive position are considered to be in a player’s zone.

Infield

First Base: The first baseman is responsible for covering zones V through X, the three zones closest to the right field line. This includes all grounders hit within approximately 25 feet of the right field line, and anything right up the line as well.

Second Base: The second baseman is responsible for zones O through T. The left boundary of Zone N is second base, so the right boundary (about 8 feet from second) is where the second baseman’s zone starts, and runs up to Zone U. Notice that Zone U is not in anyone’s zone. It is ‘the hole’ on the right side and not an infielder’s ‘responsibility’.

Third: The third baseman is responsible for covering zones C through F, the four zones closest to the left field line. This includes all grounders hit within approximately 35 feet of the right field line, and anything right up the line as well.

Shortstop: The shortstop is responsible for zones H through L. The right boundary of Zone M is second base, so the left boundary (about 8 feet from second) is where the shortstop’s zone starts, and runs up to Zone G. Notice that Zone G is not in anyone’s zone. It is ‘the hole’ on the left side and not an infielder’s ‘responsibility’.

Outfield

Outfielders are assigned two zones: one for line drives and one for fly balls. Since line drives aren’t in the air as long, they have smaller zones.

For a ball to be assigned to an outfielder, it must travel a certain distance. Corner outfielders are responsible for all line drives in their zones that travel between 280 and 340 feet. They are also responsible for all fly balls and popups that travel over 200 feet. The center fielder is responsible for all line drives between 300 and 370 feet and all fly balls and popups over 200 feet.

The left fielder is responsible for Zones F through H on line drives and C through I on fly balls and popups. Zone J between the centerfielder and left fielder is unassigned.

The center fielder is responsible for Zones L through O on line drives and K through P on fly balls and popups.

The right fielder is responsible for Zones S through U on line drives and Zones R through X on fly balls and popups.  Zone Q between the centerfielder and right fielder is unassigned.

On line drives, the zones J and Q are unassigned between the outfielders, while on fly balls, those zones are covered.

Using these zones, STATS determines how many balls are hit into each fielder’s area of responsibility. An infielder’s zone rating is equal to the number of outs made divided by the number of balls hit into the player’s zone. ‘Outs Made’ equals every ball fielded within the zone that is turned into an out, plus all balls fielded outside the zone turned into an out.  When a player fields a ball outside his zone and turns it into an out, it is counted as both an out and a ‘ball in zone’ for the purposes of calculating his zone rating.  This is a flaw in ZR, as balls outside the zone should be counted only as an out.  Otherwise it takes away a “range” aspect of the rating.

An outfielder’s zone rating is equal to balls hit into his zone which do not result in hits, divided by the number of balls hit into his zone. The player is credited with both an ‘out’ and a ‘ball in zone’ for balls caught outside his zone, just like the infielders.

This explains exactly how the zones are defined.  The reason these zones were selected is because these are the zones where balls are turned into outs at a greater than 50% rate.  The greater zone is not so much arbitrary, as drawn from a reasonable expectation that a fielder should make the play, since his peers do.