Are season sample sizes too small to be meaningful, especially for a unified theory?

A few years ago someone mentioned to me that a sample size less than 1,500 was not meaningful.  I've been thinking about that, especially for fielding stats, the third rail in a unified theory for one stat that allows comparison of all players, regardless of position and era.

War on WAR.  Friday, March 8, 2013

I’m a smart guy.  I understand baseball and really enjoy the numbers, even those on the uniforms.  I like playing with the numbers.  However, my math skills are largely confined to arithmetic.  I am not a statistician or operations research person.  Those are the really smart guys who have come up with the new stuff in recent years.  So declaring war on them or their concepts is useless for me.  I need to confine my concerns to common sense things.

There are two things about WAR for non-pitchers that should be examined:
1. WAR is a total, not an average
2. defensive WAR, more properly called fielding WAR, is suspect.  The more the really smart guys delve into fielding stats in general the more they see a need to develop more methods of measurement...

Then there’s Defensive Wins Above Replacement (dWAR).

Brian Kenny on his MLB network Clubhouse Confidential TV program once described multiple defensive metrics that come to opposing conclusions about Yankee center fielder (CF) Curtis Granderson.

Here’s an historical puzzle for me – Willie Mays dWAR, Plate Appearances (PA) and home park:
1954 2.1 641 NY Polo Grounds
1955 0.7 670 NY Polo Grounds
1956 1.3 651 NY Polo Grounds
1957 0.6 669 NY Polo Grounds
1958 1.7 685 SF Seals Stadium
1959 0.4 649 SF Seals Stadium

During his physical prime the pattern for Mays is up, down, up, down, up, down.  Why?  PA suggest that he was not injured in these seasons.

Starting in 1960 Candlestick Park was Willie’s home park.

1960-1966 (age 35) dWAR for Willie Mays is between 1.3 (1963) and 2.0 (1962).

Did the fielding of Willie Mays improve with age?  How likely is that?  Stuff like this make me suspicious of fielding stats.
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Now I'm wondering if the Willie Mays puzzle isn't just small sample size.  Here are his chances (put outs (PO) + assists (A) + errors (E)) for center field:

1954 465
1955 428
1956 434
1957 438
1958 453
1959 362

For his career Mays was never in double digits for errors in a season.  His assists 1954-1959: 13, 22, 14, 14, 15, 6.  In 1959 Mays was down in games and innings.  PO were well over 400 each of those years except 1959: 351.

Fast forward to 2014, batting data top ten sorted by plate appearances (PA).

Rk	Player	PA	Year	Age	Tm	Lg	G	AB	R	H	2B	3B	HR	RBI	BB	IBB	SO	HBP	SH	SF	GDP	SB	CS	BA	OBP	SLG	OPS	Pos
1	Ian Kinsler	726	2014	32	DET	AL	161	684	100	188	40	4	17	92	29	1	79	5	3	5	20	15	4	.275	.307	.420	.727	*4/H
2	Nick Markakis	710	2014	30	BAL	AL	155	642	81	177	27	1	14	50	62	4	84	4	0	2	10	4	2	.276	.342	.386	.729	*9/D3
3	Matt Carpenter	709	2014	28	STL	NL	158	595	99	162	33	2	8	59	95	2	111	8	2	9	3	5	3	.272	.375	.375	.750	*5/H9D
4	Freddie Freeman	708	2014	24	ATL	NL	162	607	93	175	43	4	18	78	90	4	145	8	0	3	18	3	4	.288	.386	.461	.847	*3
5	Hunter Pence	708	2014	31	SFG	NL	162	650	106	180	29	10	20	74	52	3	130	3	0	3	13	13	6	.277	.332	.445	.777	*9/H8
6	Jose Altuve	707	2014	24	HOU	AL	158	660	85	225	47	3	7	59	36	7	53	5	1	5	20	56	9	.341	.377	.453	.830	*4/HD
7	Brian Dozier	707	2014	27	MIN	AL	156	598	112	145	33	1	23	71	89	1	129	9	3	8	8	21	7	.242	.345	.416	.762	*4
8	Mike Trout	705	2014	22	LAA	AL	157	602	115	173	39	9	36	111	83	6	184	10	0	10	6	16	2	.287	.377	.561	.939	*8/D
9	Evan Longoria	700	2014	28	TBR	AL	162	624	83	158	26	1	22	91	57	11	133	9	1	9	15	5	0	.253	.320	.404	.724	*5/D
10	Josh Donaldson	695	2014	28	OAK	AL	158	608	93	155	31	2	29	98	76	5	130	7	0	4	16	8	0	.255	.342	.456	.798	*5/DH

Josh Donaldson June 25, 2013
by NewJack984
via Wikimedia Commons

American Conference MVP Mike Trout was number 8 with 705 PA.  Let's see how many chances Trout had in center field: 390.  So Trout had 81% more PA than fielding chances.  In center Trout has some time to adjust to the mind numbing boredom of waiting for something to happen.  It's completely different than his facing a pitcher who could snuff out his life with any pitch.  At the plate Trout is ready.

At the opposite end of the readiness spectrum would be the third baseman who is closer to the batter than any fielder in fair territory other than the pitcher who is not expected to actually handle many, if any, chances.  Plus, unlike the first baseman, the player at third must also make a long accurate throw.  Let's look at Josh Donaldson (number 10 in PA), late of the Oakland As after being traded to Toronto for some unimaginable reason.  Donaldson must ward off the boredom of these tedious games and spring into action more quickly than any of his teammates.

Josh Donaldson had 482 chances at third base in 2014 for which he was awarded 2.7 dWAR.

Another third baseman: Evan Longoria (number 9 in PA): 396 chances, dWAR -.1.

Somewhere someone thinks that makes sense.  If a batter had 400 PA how seriously would we view his batting stats?

Catcher Russell Martin recently got a fat five year contract partly because he is good at deceiving umpires: pitch framing.  Just how many pitches did Martin frame successfully and how would we actually know?

Russell Martin ($82 million) and other catchers who don't play much.  Wednesday, November 19, 2014

Unfortunately for Toronto, they were so busy looking at Martin's ability to deceive umpires into thinking balls are strikes (pitch framing) that they did not notice that Martin had only 460 plate appearances (PA), embarrassingly short of the meager 502 PA needed to qualify for leading in an average stat like batting average.
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A plate appearance is an intense event, usually involving multiple pitches, and allowing for much preparation and plenty of time to ponder between pitches.  Fielding, especially at third base, is a random occurrence, which suddenly happens, usually with long gaps between events.  It may require the player to come alive and perform with split second timing.  There's no real prep time other than getting set for each of about 150 pitches, most of which will not result in the ball being hit anywhere near the player at third.

So, what the heck?  We're pretending to measure fielding down to the nth degree and then massaging it with some alchemy so that its sparse numbers can sprout into something that is comparable to what results from a plate appearance or, even more bizarre, from a batter faced by a pitcher.

Unified theory, indeed.