THE BOOK--Playing The Percentages In Baseball

Any chance that the pool of pitchers for starters and backups are different in terms of GB/FB% (since backups tend to come into games late in the game, when short relievers are in who get more K’s)?

How about day versus night games being different in terms of putout and assist rate (since backups tend to play in day games following night games)?

And of course, some percentage of backups are defensive replacements late in a game, so while backups could be overall the same as regulars, it could be that the true replacement defender is worse than a regular but that these late-inning defensive replacements bring up the whole pool of backups.  So it depends on what you are trying to determine and what your definition of replacement defense is.

Tom, if you send me your list of backups and regulars or give me your definition, I can compare UZR.

MGL, sent you an email.  It’ll be interesting to compare.  But, from what I remember doing with UZR in the past, I expect to see the regulars and backups to have similar numbers.

I expanded it to break the players as:
- 25 players with most playing time: regulars
- next 25 players in playing time: bench
- everyone else: rest

That gives me 50 regular+bench players per position (400 total nonP nonDH, or roughly what you’ll find on your 25-man roster).

The SS starters were: 2.96
SS bench: 2.96
SS rest: 2.88

Here’s the full report:
C: 0.48, 0.50, 0.47

SS: 2.96, 2.96, 2.88
2B: 2.93, 2.92, 2.92
3B: 1.99, 1.94, 1.93
1B: 0.67, 0.65, 0.64

CF: 2.58, 2.57, 2.57
RF: 2.06, 2.07, 2.05
LF: 1.94, 1.97, 1.94

I think it’s fair to presume that the fielding talent of nonregulars is on par with the regulars.

This also includes the Hitting runs per 4.3 PA (i.e., 1 game).  Doesn’t include baserunning:

POS Role POper27 Aper27 offRunsPerG
C Starter 6.79 0.48 -0.04
C Bench 6.74 0.50 -0.13
C Rest 6.63 0.47 -0.20

SS Starter 1.56 2.96 -0.04
SS Bench 1.59 2.96 -0.13
SS Rest 1.58 2.88 -0.19

2B Starter 2.03 2.93 -0.01
2B Bench 2.06 2.92 -0.11
2B Rest 2.07 2.92 -0.17

3B Starter 0.74 1.99 0.04
3B Bench 0.72 1.94 -0.07
3B Rest 0.73 1.93 -0.13

CF Starter 2.58 0.05 0.02
CF Bench 2.57 0.05 -0.06
CF Rest 2.57 0.07 -0.13

RF Starter 2.06 0.06 0.11
RF Bench 2.07 0.07 0.01
RF Rest 2.05 0.07 -0.08

LF Starter 1.94 0.06 0.12
LF Bench 1.97 0.06 0.01
LF Rest 1.94 0.06 -0.09

1B Starter 8.80 0.67 0.14
1B Bench 8.73 0.65 0.03
1B Rest 8.74 0.64 -0.06

Numbers are fairly consistent for each position.

The averages are:

Starter 3.31, 1.15, +0.04
Bench 3.31, 1.14, -0.06
Rest, 3.29, 1.13, -0.13

If we focus on the “Rest”, fielding-wise, they are about .04 plays, or .03 runs, worse than average, while hitting-wise, they are .13 runs worse than average.  That makes them .16 runs worse than average, per game.  Multiply by 162 GP, and you get -26 runs, or roughly -2.4 wins.

IIRC, I think I said that this was exactly Willie F. Bloomquist.  In short, the “26th man” is WFB, at -2.4 wins.  THAT is the replacement level.

If you have 9 nonpitcher like this, that puts you at -2.4x9= -21.6 wins, or .367 team win percentage (assuming average pitching).  I’ve always been using .380, so maybe I should use .370 for nonpitchers.

Hmmm… DHs do put a little crimp on this.  I guess I should have done -2.4x8 plus half (because only applies to AL) whatever the DH replacement gap is, which I guess would be somewhat less than 2.4 wins.  So, it’ll probably be closer to 0.375 as the team replacement level winning percentage, if you have average pitching.

***

The average (component) win% for a starter is .490, while it’s .520 for a reliever. 

A starting pitcher pitches 100% of the time as a starter, by definition.  If the average starter pitched two-thirds of the time as a starter (win % of .490) and one-third of the time as a reliever (win% that is 90 points higher, or .580), he’d have a win% of .520.

For a reliever, one-third of .520 and two-thirds of .430, we get: .460 as the average win% of the typical pitcher who is a reliever, if he were to pitch a typical distribution of starter/reliever innings.

I think it’s easy to see that if the average reliever is a true .460, then half the relievers would average .500, and the other half would average .420. 

That is, if I’ve got the average starter as a true .520, then the top-half of the average relievers would be .500.  It seems reasonable, right?

So, if the average bottom half of the relievers are .420, it’s reasonable to presume that the worst true win% should be a bit over .400, maybe .405?

***

A replacement team of .375 nonpitchers and .405 pitchers gives us a replacement team win% of .290.

(I have been using .380 and .410, for .300.)

Under this scenario, the replacement levels are:
.465: performance as relievers
.375: everyone else

(I’ve been using .470, .380.)

I looked at DH.  I selected all players with at least 50 games at DH, in any season, from 2000-2006.  That gives me 80 seasons.

(Note: average of 11.4 regular DH per season for a 14-team league… which is analogous to having 25 regular players at a particular position in a 30-team league.  That is 25/30x14=11.7.)

All DH from 30-49 games were considered “bench”.  That’s 82 seasons.

Anyone with less than 30 games at DH is “rest”.  Here are the numbers:

Starter: +0.14 runs per game
Bench: +0.02 runs per game
Rest: -0.03 runs per game

The gap between Starter and Rest at DH is exactly the same as the other positions.

We see here that the replacement-level DH (which of course includes guys like Manny Ramirez) is -.03x162=-5 runs, or -0.5 wins.

***

What is the fielding level of guys who DH?  Pretty much league average.  The SS who DH had 2.91 A per 27 outs.  2B were 2.96. The 3B were 1.90.  1B were 0.65.  The CF were 2.57, RF were 2.04 and LF were 1.97. 

***

So, in my previous post, when I was trying to figure out the replacement level nonpitcher team, I should now say:
-2.4 x 8
-0.5 x 1 x (14/30)
= -19.4 wins
= .380 replacement win% for nonpitchers

Hmmm… seems my .380 that I’ve been using is probably pretty good to begin with.

Tom, you realize that you’re talking to yourself, right?

A few things: Care to run a one-way ANOVA to check to see if the differences between those groups are statistically significant? 

Catcher putouts are somewhat deceiving as a defensive stat as catchers get a PO for catching the 3rd strike.  So, that’s probably more of a reflection of the pitchers whom they are catching.  Not going to make a huge difference, but you know how it goes.

Another small issue: pitcher replacement fielding level?

This may be a semantic issue, but there certainly is a group of, say, replacement-level fielding SS, which as a group fields noticeably worse than other SS, isn’t there?  We tend to call them “2B” and “3B”.

I posted the PO for catchers, not because I believe in it, but because I didn’t want to bother excluding anything.

Pitcher replacement fielding?  I’m quite sure it’ll be the same as the starter, but I guess, I shouldn’t have excluded them either.

As for the ANOVA, I’ll see what I can do.

What about the pinch hitter penalty for “the rest”.  Aren’t enough of “the rest” pinch hitters such that their offensive performance is severely depressed as compared to if they would start a game?

Maybe that gets balanced out by the fact that pinch hitters tend to face more opp side pitchers than if they were starters (not platoon starters of course).

And then there is the (not so unimportant) issue of what we using your (or anyone’s) definition of replacement for.  Is it replacement players that teams actually use or is it players that your or I can find for the major league minimum or so (say, less than 1 mil or even $500,000 per year)?  I think those are two distinctly different animals.  I am sure that I can field MUCH better than a .290 team with a payroll of $500,000 per player!  Of course you can’t go by salary as there are many good, well-above replacement players who are making the major league minimum, but you know what I mean.

PH: I’m not sure that the distribution of PA as PH would be that disproportionate between “Rest” and “Starters+Bench”.  I am taking the top 420 players in playing time for Starters+Bench.  And the “Rest” are also probably not facing Rivera, Hoffman, and Wagner.

Your general point is of course valid.  At the moment, I’m only looking at seasonal-data.  I suppose at some point I should break out my PBP database and do it better.

Re #4:  if you exclude catcher PO, which we probably should, then it looks like “the rest” are about -.03 plays, or -.02 runs.  To the extent that these players have a tendency to play more frequently with other backups, the PO and A might be a little redundant, but probably not a big factor.  They might also play more in losing games, costing them a few 9th inning fielding opps, but again that’s pretty marginal. 

So the average non-pitcher is +3 runs on defense, +19.5 on hitting, per 150G.  So fielding accounts for just 13% of non-pitcher value, or 7-8% of all player value.  A far cry from Win Shares’ 17%.

* *

Tango, is the .405 for pitchers based on empirical data?

Yet if you try and convert fielding win shares to runs it seems too conservative.  I don’t think average value over replacement is the right way to determine how much value goes to offense/defense.

How about this:  Take the sum of absolute value for every hitter’s batting runs over average, and do the same for fielding?

Yes, Win Shares is too conservative for great fielders—despite allocating far too much total value to fielding—because it insists on assigning postive fielding value to nearly all players.  In fact, something like 40% of players have negative fielding value, i.e. below replacement value (but they still have value because of their hitting). 

The only solution to this is to have positive and negative fielding WS.  Then you can give someone like Adam Everett his due, and still have a total share of the pie of 7-8%.  (Some catchers and MIs probably should get negative hitting WS too, but it’s easier to fudge that.)

I agree that you can’t do what Guy/13 is saying.

As I’ve said many times, if you treat everything separately, then it’s pretty easy to figure out the split: the standard deviation of hitting, fielding, pitching.  But, the SD are *not* additive (the variances are).  So, when you combine a player’s hitting and fielding, the spread is less than the sum of its parts.

IIRC, the spread in hitting is roughly 1 SD = .030 runs per PA.  So, per 4.3 PA, that’s 1 SD = .13 runs per game.  (A team of hitters will therefore be 1SD = .39 runs per game.)

For fielding, 1 SD is something like .015 to .020 outs per BIP.  Figuring around 4 balls in play and 0.8 runs per play, that gives us 1 SD = .06 runs per game.  (A team of fielders will be 1 SD = .18 runs per game.)

Remembering that the spread in runs scored and runs allowed is the same, then 1 SD of TEAM pitching = sqrt(.39^2-.18^2)= .35 runs per 9 IP.

For pitchers, it’s a little trickier because there’s a chasm in playing time between starters and relievers.  If we give each pitcher 162 IP (18 games), then 1 SD for each INDIVIDUAL pitcher is 1.05 runs per 9 IP.  That is, in order to get a team SD of 1 SD = .35, then the individual pitchers must have 1 SD = 1.05 runs per 9 IP.

***

Going back to our hitters, if 1 SD = .13 runs per 4.3 PA (one game), then per 162 GP, that’s 1 SD = 21 runs.  The fielding is 1 SD = 10 runs.  Combining the two we get: sqrt(21^2+10^2)= 23 runs.

So, 1 SD of nonpitchers is 23 runs per 700 PA

Our pitchers is 1.05 x 18 = 19 runs per 162 IP.

Under these calculations, the spread of nonpitchers and pitchers is 55/45.

The spread of offense/defense is 50/50.

The spread of hitting/pitching/fielding is 42/38/20.

Also note that since we’re happy with our calculation of -26 runs for nonpitchers as the replacement level, then the replacement level is around -1.13 SD for nonpitchers.

At that level then (-1.13 SD), the pitching replacement level would be -1.20 runs per 9 IP, which is roughly -0.11 wins per game, or .390 as the replacement level for pitchers.

All these numbers are quick/rough estimates.

***

At -1.13 SD, that means you have 13% of the players to the left of that level.  If you want to make it 10%, the SD level has to be -1.30.

In order to have the replacement level that BP is suggestiing, you’d have to set that level to -2 SD, which means 2.2% of ballplayers would set the replacement level.

Again, it gets a bit trickier, because of the playing time.  Do we have 18x30 ballplayers, 25x30, or 1800 (number who played last year)?

So, you have to be real careful in how you are proceeding and what everything implies.

The “Blink” replacement-level is Willie Bloomquist.

I nominate Sidney Ponson as replacement level for pitching.

I see 3 ways to think about a replacement team (non-pitchers):
1) Use a replacement-level 1Bman (or DH) as your generic repl player. Do this, and all other positions have an inherent defensive value, and you will conclude the average player provides a lot of defensive value.  When talking about fielding, this is what people often seem to assume (though ignoring that it implies most players have relatively little offensive value).

2) Use a repl level SS, which does the reverse:  most players have little/no defensive value, but hitting benchmark is set very low.  Almost no one does this, but it makes just as much (little) sense as #1.

3) Use a team of average repl players from each position.  I think this is clearly the right approach.  And such a team will be about -30 runs on fielding, -190 hitting.  Sure, you could assemble a replacement team of great fielders/lousy hitters, or the reverse, but on average you will have a team of decent fielders and lousy hitters.  So, compared to that baseline, a team of average non-pitchers will contribute 30 runs on defense and 190 runs on offense. That’s the value we care about. 

The SD approach uses BOTH 1 and 2:  it measures fielding value against a benchmark defined by the worst fielders, but hitting value against a benchmark of the worst hitters.  It assigns defensive value to a 1Bman in proportion to how much better he is than Ryan Howard, and to LFs in proportion to how much better than Manny he is.  As a result, the SD approach has no connection to replacement value. Ironically, this is the same mistake that Tango frequently and correctly criticizes when people talk about a replacement player who provides both “replacement offense” and “replacement defense”, but who is actually much worse (total) than any real repl player.

BTW, this is totally compatible with believing that Adam Everett is worth +30 runs (or whatever) in the field.  It’s just that his value is offset by lots of sub-replacement fielders.

Guy, that’s not what the SD approach is doing.  Your interpretation of what I’m doing is not what I’m thinking (though perhaps it’s not coming out clearly in what I’m writing).

I would never talk about replacement-level hitting and repl-level fielding as two separate things.

In fact, what we have is: fielding-talent and hitting-talent of replacement level PLAYERS.  That’s the model.

I said this:

Going back to our hitters, if 1 SD = .13 runs per 4.3 PA (one game), then per 162 GP, that’s 1 SD = 21 runs.  The fielding is 1 SD = 10 runs.  Combining the two we get: sqrt(21^2+10^2)= 23 runs.

At the -1 SD level, hitting is -21 runs and fielding is -10 runs.  It is *not* a total of -31 runs.  The total is -23 runs.  SD are not additive (variances are).

If one wishes, they can then take those players at the -1 SD level and find out that their -23 runs breaks down as -20 runs for hitting and -3 runs for fielding.  (For a team total of -180 runs on hitting and -27 runs on fielding for players at the -1 SD level.)

You have to be very careful in representing what it is that you want to represent.  You can’t simply do a “sum of the parts = whole”, without understanding what it is that is being added.

***

I also reject the idea that you can break down the -23 as -20 and -3, and then use that -3 as an input to figure out the fielding/pitching split.

Some things don’t add up and are not meant to add up.  Win Shares’ biggest failing is this.  James obviously realized this when he saw how unworkable the 50/50 split was.  In the “divide and conquer” approach of Win Shares, he has to do a 42/58 split in order for Win Shares to work on one level (but break on another).

It’s even possible that at the -1 SD level, the -23 runs breaks down as -23 runs for hitting and 0 runs for fielding.  Or even -25 and +2!

The hitting/fielding makeup of replacement-level nonpitchers has no bearing whatsoever on the fielding/pitching split.

The nonpitcher/pitcher splits, or the hitting/fielding/pitching splits, or the offense/defense splits are solely determined by the distribution of all the talent (however that is defined, and however the playing time component is handled).

Someone asked about pitchers, and we learn something new!

Taking the top 150 in innings and making them “starter”, the next 150 as “bench”, and then the rest, for 2000-2007, this is what we get:

POS Role POper27 Aper27 innouts
P Starter 0.56 1.22 520801
P Bench 0.52 1.14 222267
P Rest 0.53 1.13 165995

Innouts is IP*3.

So, we see that there’s a big gap in assists and putouts for “starters”, compared to the rest.  A grand total of 0.12 more plays per 9 IP. 

For a guy with 200 IP, that’s 2 extra runs.

For pitchers, should sorting who belongs in what category be done by appearances and at that, with starts and relief appearances handled separately?  I bet a lot of LOOGYs wound up in “The Rest” because they pitch relatively few innings (40-50 IP), and probably fewer than the team’s sixth starter who gets 5-6 spot starts at 5 innings apiece plus some long-relief/mopup work for 60-70 IP over the season.  Who’s really the replacement?  Might not make a difference in this case.

The selection of replacement player should never be done after-the-fact.  If you want to know who a replacement-level pitcher is in 2007, it would *not* include Mark Prior or Felix Hernandez or Jeff Weaver (presuming each will pitch less than 50 IP in 2007).  You have to determine the players prior to the season starting.

I don’t care too much about LOOGY or role.  The expectedIP x expectedLI should be your guide.

Role offRunsPerG totPA
Starter 0.054 828430
Bench -0.086 355549
Rest -0.237 57820

The above represents the top 210 hitters in terms of PA (regardless of position) as “Starter” (generally about 400+ PA), the next 210 as in PA as “Bench” (about 100+ PA), and the “Rest” (excludes pitchers).

As you can see, the “Rest” hitters are pretty horrible, at -.237 runs per game (4.3 PA).  At 162 GP, that’s -38 runs.  But, we’ve got selective sampling issues.  PA don’t exist in a vacuum.  The better you hit, the more you’ll play.

What you should do is find out how the guys who are in the “Rest” category in year x did in year x+1.  So I did.

There are, by definition, 210x6=1260 “Starters” from 2000-2005.  How’d those guys do in the year after?  22 did not play in the following year, and 14 had less than 50 PA.  Of the remaining 1224, their (simple average) runs per game was +.02.

Of the 937 (of 1260) Bench players, they were -.10.

Of the 314 bench players in year x (with at least 30 PA in each year), their (simple average) runs per game was -.135.

On top of which, the bench players were around age 27 as well (as many guys under 27 as over 27).  This is unlike the starters and bench group which averaged 29.6 years.  So, we don’t have an aging issue to contend with.

I think it’s fair to call the offensive talent level of replacement-level players as -.135 x 162 = -22 runs.

Add in the likely minus couple of runs, and we end up with around -25 runs as the overall replacement level (-2.3 wins).

That’s .380 win % as the replacement level for nonpitchers.

Any way you want to slice it, we always end up in the same place.

"The spread of offense/defense is 50/50.

The spread of hitting/pitching/fielding is 42/38/20.”

I know I’m missing something here - but how is offense 50% compared to defense and hitting only 42% compared to pitching and fielding?

Going back to the off data in post #4 (and #6 for DH), and using the “Rest” data, here is the offensive-level baseline levels for replacement-level players:

Wins Pos
(1.0) C
(1.0) SS
(0.7) 2B
(0.1) 3B
0.0 CF
0.7 RF
0.6 LF
0.9 1B
1.4 DH

I typically use -1.0 for C, -0.5 for SS, CF, 0 for 2B,3B, 0.5 for LF,RF, 1.0 for 1B and 2.0 for DH.

Don’t forget that the above only looks at the offensive levels of the “rest”.  The SS and 3B replacement players are below average fielding-wise too.  The net effect is to bump up the 3B closer to 2B, and the SS to move away from the pack.

We can come up with a new spectrum that says this:
-1.0: C, SS
-0.5: 2B, 3B
0: CF
+0.5: LF, RF
+1.0: 1B
+2.0: DH

Compared with the one I normally use, we see that I’m too harsh on infielders (2B,SS,3B all get bumped by 0.5 runs in this new spectrum), and I was too nice on CF (bumped 0.5 runs the other way).

Dan/27:

It’s based on the distribution.  You have to remember that if 1 SD of hitting is 20 and 1 SD of fielding is 10, this does NOT mean that 1 SD of hitting+fielding is 30.  It means that 1 SD of hitting+fielding is 22.

Going back to reality, IIRC, 1 SD of team runs per 162 GP is around 60 runs.  This is for runs scored and allowed.  So, we can see that the spread of the runs is the same, and therefore, we can conclude that offense and defense is equal at 50/50.

Now, suppose we can break down the 1 SD = 60 runs allowed between pitching and fielding.  And further suppose that the pitching spread was double that of the fielding spread.  You might be tempted to think 1 SD = 40 for pitching and 1 SD = 20 for fielding.  But, that’s not the way it works.  In this illustration, 1 SD of team pitching is 54 runs and 1 SD of team fielding is 27 runs.

So, a hitting/pitching/fielding split would be 60/54/27 (or, prorated down to 43/38/19) in this particular illustration.

That’s why it’s critical to understand that you can simply hope to slice and dice things into a sum-of-parts-equal-whole to get what you want.

The standard deviations are not additive, but it is the standard deviations that determine the split levels.

#23 - I expect the more plays made by starting pitchers over bench is because relievers strike more batters out.

Tango/29:

I understand the SDs aren’t additive and based on that, your math makes sense.

It’s just counterintuitive that offense can be both 50% and 42% versus defense which is collectively pitching and fielding.

Are there interactions between pitching and fielding that make the total value look bigger when you look at each piece?

When pitching and fielding is a “collective”, then offense is 50%.  When defense is split into its parts, offense is 42%. I know it doesn’t sounds right, but it is what it is.

The interactions between pitching and fielding are random and independent.

One can also breakdown offense into hitting and baserunning too.

Rally/30: great point.  Here are the numbers, this time per 27 BIP:

POS Role POper27 Aper27 totBIP innouts
P Starter 0.55 1.18 537229 520801
P Bench 0.53 1.15 221787 222267
P Rest 0.51 1.09 171840 165995

BIP = BFP-SO-HR-BB-HBP

So, relievers are still a bit worse fielders than starters.  And the scrub pitchers are much worse.

I wonder if fielding talent of pitchers is inversely proportional to:
- how hard they throw
- how inexperienced they are

A lot of relievers have funky deliveries, maybe they aren’t in fielding position like starters.

Catching up, here.

Tango 20-22:
“The hitting/fielding makeup of replacement-level nonpitchers has no bearing whatsoever on the fielding/pitching split.” and “Some things don’t add up and are not meant to add up.”

I disagree.  The numbers can and should add up.  A team of average players has a total amount of value, vs. a replacement team, that can be measured in runs/wins.  We can then divide that pie into the three components, and they will add to 100%.  We can’t do that using SDs, as you say, but that’s a reason to abandon the SD approach, not to throw up your hands and say hitting is 50%, and it’s also 42%, and “it is what it is.”

The assumption of the SD approach is that value = variance.  But that isn’t always true, IF some of the variance falls below the replacement threshhold, as it clearly does.  Let’s say that scouts discover a lost village on the Amazon this winter where baseball is played.  Among the players are a bunch of 1Bmen who all hit like Pujols, but can’t field to save their lives.  Playing in MLB, they are +70 runs on offense, -50 runs on defense, so 20 runs above replacement on average (I know, they should DH, but these were NL scouts).  The SD method says :  there is now more hitting and fielding value in our league than before, as we now have larger SDs for both hitting and fielding.  Position players are now more valuable, relative to pitchers.

The replacement value approach says:  nonsense.  We’ve just added a few average position players to the league, so the relative value of pitchers and positions players has not changed.  What HAS changed is the share of total value derived from hitting (up) and fielding (down).

It comes down to this:  we all agree there is a substantial pool of players whose fielding ability is below that of a replacement player (not “replacement fielder").  They are playing in the majors DESPITE, not because of, their fielding talent.  They are hired for their bats; accepting their fielding is a price paid to acquire the bat.  But the SD method wants to assign positive (or at least zero) fielding value to all those players.  In fact, the more of these players there are the larger the fielding SD, and that will perversely increase the total amount of fielding “value.” To me, it’s much more accurate to say they have negative fielding value, but are still net above-replacement players because of their bats.

The SD method says :  there is now more hitting and fielding value in our league than before, as we now have larger SDs for both hitting and fielding.  Position players are now more valuable, relative to pitchers.

No, that’s not what it says.  If you are going to compare the position players to pitchers, you do not split the hitting and fielding.  You must combine them.  And in your example, the SD approach, hitting+fielding v pitching, remains exactly the same.

But the SD method wants to assign positive (or at least zero) fielding value to all those players. 

It does no such thing.

***

You seem to be falling into the trap that I’m urging all to avoid.

You can’t start with the three components separate (say, 43/38/19), and then try to say it doesn’t add up to 50/50.

You have to choose first: are we talking about three independent components, or two.  Once you’ve established that, you can’t go from one to the other.

The SD approach works, as evidenced by this entire thread.  I always end up with a nonpitcher replacement level of around .380, regardless of the approach I take.

Here are the total UZR per 150 games for the “regulars” that Tango sent me from 2000 to 2006:

3 1.32
4 0.44
5 1.40
6 1.13
7 .96
8 1.95
9 1.13

That works out to +1.2 runs per 150 GP, which, works out to +.01 outs per game for the regulars, compared to all players (including themselves).

The data from post#4, PO+A for the same 7 positions, is:
4.06 Starter
4.05 Bench
4.04 Rest

So, UZR and range factor pretty much match.

***

If someone is looking for a shortcut, then the fielding talent level of replacement level players is league average.  The hitting talent level of replacement level players is -2 wins per 600 PA or 140 GP.

There is no such thing as “replacement level fielding” and “replacement level hitting”.  The correct terms to use are in the preceding paragraph.

Similarly for pitchers, one should use the terms:

“relief performance for replacement level pitchers”

“starting performance for replacement level pitchers”

If, as an illustration, Joel Pineiro or Joe Mays is a replacement level pitcher, you would create a stat line for the standard replacement level pitcher, both as a starter and as a reliever.

This ensures that you have ONE baseline (the replacement level pitcher), but for a particular context (start/relief role).  This is exactly the same as constructing a stat line for the replacement level pitcher at Coors and in the Astrodome.  Different stat lines for different contexts, but all based on the same SINGLE baseline (the replacement level pitcher).

http://baseballprospectus.com/chat/chat.php?chatId=346

I really like Clay.  His stubborness though:

DanBudreika ((Haymarket,VA)): How many wins should a REPLACMENT level team be expected to produce?

Clay Davenport: A totally replacement team - bad hitting, fielding, and pitching - would win maybe 25 games in a 162-game season.

Most defintions of replacement level assume that you’re only replacing one thing at a time (i.e., average defense, replacement-level hitting). The WARP definition of replacement level is lower than that, but if the world can survive multiple definitions of zero degrees (Celsius, Fahrenheit, Kelvin, Reaumur, Rankine) then I think it can survice an alternative replacement level.
...
The level of fielding that gets you moved to another position is replacement level fielding. It should be close to what the worst regular or semi-regular in the league has.

Fielders who hit at replacement level are generally pretty good, because they have to be offering the team something to earn a spot on the roster - teams get to select the players they’ll keep, they aren’t drawn at random. And it is probably true that there are more players in the minor leagues who can field at an acceptable major league level than hit - it isn’t as unique a skill, more people can do it.
...

I like the theoretical setup that treating hitting, pitching, and fielding as seperate entities allows. But I do hear plenty about the level being “too low”.

If you are going to talk about reality, there is no such thing as treating hitting and fielding as separate entities.  Clay in the middle of his talk that I quoted shows a realization for this, but doesn’t follow through.

For some reason or other, this really bugs me every time it’s brought up.  Furthermore, it’s compounded by Nate’s MORP, which is based on WARP.  MORP (salary value) has to have an exponential function to make WARP and salary match.  However, if WARP were more properly calculated, MORP would be linear.  It’s the classic two-wrongs-make-a-right, but leaves all with the impression that salary and value are exponentially related.  If WARP had a .300 repl level, WARP and salary would be linearly related.

IIRC, the spread in hitting is roughly 1 SD = .030 runs per PA.  So, per 4.3 PA, that’s 1 SD = .13 runs per game.  (A team of hitters will therefore be 1SD = .39 runs per game.)

Tango I’m sure you’ve probably been over this before but how do you get the team of hitters SD (.39 rpg) from the individual SD?

You just seemed to have multiplied by 3, and ditto for fielders and pitchers?

John,

The team variance is just the sum of individual variance. So if you have 9 players and an individual SD of .13, Var = .13^2 and team Var = .13^2*9. The team SD is the square root of team Var, or .39.

Thanks David. I should have known that!