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Friday, November 11, 2005

Dr. StrangeGlove or: How I Learned to Stop Worrying and Love Zone Rating

There is a ton of mistrust of defensive methodologies, and how well they describe defensive play.  MGL’s UZR is recognized at many baseball sites as being good enough to cite with considerable confidence in its accuracy.  MGL does a good deal of work on it to perfect it, and he’s no dummy, so it’s a fair position of others to want to quote his data.

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

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
```

As described previously, it would be better to also look at Helton’s actual ZR Chances multiplied by the league average ZR, and then subtracting from Helton’s RS.

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.

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.

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	```

Feel free to square those if you can’t do that in your head.  The complete list of data used can be found here.

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```

I’m certain there is a better statistical way to compare these results, but I don’t know what it is.

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```

As DSG noted in his article at The Hardball Times, he has issues to resolve at first base and right field.  However, at the middle infield positions, shortstop and second base, DSG’s are significantly better than either ZR method.  It appears “Range” is capturing something that agrees better with UZR.  I have no comment on whether or not that makes it more “correct”.

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.

Chris Dial Posted: November 11, 2005 at 02:19 AM | 164 comment(s) Login to Bookmark
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