THE BOOK--Playing The Percentages In Baseball

When we compare SS to 2B, there’s a 4.3-run higher baseline at SS.  No surprise there.

But, when we compare the SS to 3B, there’s only a 2.8-run higher baseline at SS.  So, from this standpoint, the average SS is closer to the average 3B than to 2B.  A bit of a surprise.

However, the 3B to 2B comparison shows a 3.9-run higher baseline at 2B than 3B.  So, we have an inconsistency here, much more blatant than the one in the OF.

What if we looked at all players who played all 3 positions?  Nick Punto and Craig Counsell lead the way here, for a total of 2020 games with 115 infielders.  Those guys are -1.9 at 2B, -1.4 at 3B, -3.4 at SS.  In this case, we see just a 2-run gap between 2B/3B and SS.  2B and 3B come in very close to each other.

If I put the two together, I’ll focus on the 2.8 and 4.3 run gap between SS and the other two positions (average of 4 runs). 

The 2B and 3B can be interpreted in many ways, all of which to say that they are probably equals.  In one comparison point, the 3B is closer to SS than 2B (by 1.5 runs).  In a second comparison point, the 2B is way ahead of the 3B (by 3.9 runs).  And in the third comparison point, 2B is a bit ahead of 3B (by 0.5 runs).  Overall, you might think of the average 2B to be 1 run ahead of 3B.  Might as well call them even.

***

When I do the triple-position in the OF (3067 games), I get: 2.7 in LF, -8.6 in CF, and +3.9 in RF. 

***

These numbers continue to confirm my rule of thumb spectrum:
IF: SS 5 runs ahead of 2B/3B
OF: CF 10 runs ahead of LF/RF

***

Next up, 1B…

1B is a little trickier, because of the lack of opportunities.  Here’s how the 1B compares to 3B, LF, RF:

pos 1B other
5 -0.4 -5.3
7 -0.9 -5.4
9 -2.1 -10.6

Focus on LF and RF.  If we presume that the OF gets double the opportunities than at 1B, then we need to scale the 1B opps up by 2 times.  The -0.9 becomes -1.8.  And the -2.1 becomes -4.2.  In that case, the gaps are 3.6 runs in LF and 6.4 in RF.  Since we’ve established that LF = RF, then the gap between 1B and LF/RF (scaled up to the OF opps) is 5 runs.

For the 1B/3B, again doubling the 1B opps, gives us a gap of 4.5 runs.

From the standpoint of the 1B therefore, LF, RF, and 3B are all 5 runs away.  While the LF and RF numbers follows my spectrum, the 3B, in my view, needs to be farther away.

When I compare 1B to 2B and SS (much smaller samples), SS is only 10 runs ahead, while 2B is even with 1B.

So, the 1B, compared to the three IF positions, is only, on average, 5 runs worse.

I can’t buy it, and in this case, we get into major selective sampling issues.  While the three OF positions are all fairly similar in terms of skill set, and the three IF positions are somewhat similar, 1B shares very little with the other three IF positions. Furthermore, only very select players get to play 1B and the other positions.  In this case, this process is less than trustworthy.

When I compare 3B to the corner OF positions, there’s a 3-run gap (in the direction OPPOSITE of what we expect).  Compared to CF, there’s a 10-run gap (but in the direction we expect). 

With the 2B compared to the OF: there’s a 3-run gap in the direction we expect for the corner and a 9-run gap in the direction we expect against CF.

So, taking the 2B and 3B as a group, they are even against the corner OF, and 10 runs behind the CF.

For the SS (small sample size), it’s 10 runs against the corner OF in the direction we expect, and even with the CF.  This one, the SS, is exactly what my spectrum would have dictated.

***

Overall, I’m still stuck with the same spectrum I’ve always had:
+1.0 C
+0.5 SS/CF
+0.0 2B/3B
-0.5 LF/RF
-1.0 1B

I don’t see much to get me to change this spectrum.

Hi Tango,

I continue to think that this is some of the most important work on player valuation being done these days.  Bravo for continuing it, even if it didn’t result in new insights.

I wonder about the LF/RF differences.  UZR only includes information about out rate on fly balls (right?), but MGL’s post on Griffey in the sabermetric thread helped me realize how important preventing runner advancement can be to a player’s value.  Do you think that if “arm” information was added to the fielding ratings for outfielders that RF would come out as a more demanding position than LF?
-Justin

Crap, just noticed that you mentioned arms above.  Sorry.

Has anyone actually tried to do this sort of analysis to confirm your approximated 1.5-2 run difference?
-j

If you look at the Fans’ Scouting Report, you can infer something like a 1 to 2 run difference.  Maybe John Walsh or Dan Fox can chime in.

***

Taking the 30 guys who played the most over the 5 year time period at each position, and you get these UZR:
pos Rper150_weighted
3 1.0
4 1.0
5 2.3
6 -0.7
7 -2.1
8 3.2
9 0.8

That’s about 14,000 games at each position.

Take the next 30 who played the most:
pos Rper150_weighted
3 -1.4
4 -0.4
5 -3.7
6 +0.6
7 +4.2
8 -0.4
9 -3.0

That’s about 5,000 games at each position.

Take the rest:
pos Rper150_weighted
3 -3.0
4 -5.6
5 -4.2
6 -9.0
7 -0.2
8 -6.5
9 -0.9

That’s also around 5,000 games.

Overall, you get the following:
Rper150_weighted n G class
+0.8 210 98455 Regulars
-0.6 210 36407 Backups
-3.6 1706 38045 Rest

Guys who are on the bench defense a bit worse than guys who are on the field.

By the way jinaz, the Reds have the worst fielding team in baseball, since 2003: -302 runs.  Junior is -127 of that.  Without Junior, you jump over DRays, Yanks, and Redsox.

The best fielding teams: Padres, Cubs.

Two questions:

1) How does this affect replacement-level fielding? SS & CF regulars are both about one win better than the Rest group.

2) How many runs are third basemen’s arms worth above second basemen’s?

First, we should resist the term “replacement-level fielding”.  That doesn’t exist.  You are probably referring to “fielding level of replacement-level players”.

SS and CF regulars are at 8 or 9 runs above the non-top60.  The average position is 4.4 runs above.

I don’t know that this means anything, without doing the matching exercise on the offensive side.

Also note that the “rest” group comprises 22% of the playing time.  Since I’m looking at the 5 years as a group, this will necessarily have guys with short careers.  Tulo for example appears in the “backups” bucket.

A better way to do it is on a year-by-year basis.  We did this a few months ago, and I sent mgl my file of players, and he came back with his own numbers.  I forget exactly what came of it.  I’ll see if I can find it.

Using the Fans’ Scouting Report, I get the gap in arms between 3B and 2B as 1.5 runs.  But note that in the case of UZR, the arm rating is already included, mostly (save for DP).  Anything that has to do with getting the ball and getting a putout on a batter or forceout is included in UZR.

***

Here’s how the 2B and 3B break down, by the Fans:

2B
speed: +2 runs
arms: +1 runs
rest: +2 runs
total: +4 runs (rounding error)

3B
speed: 0 runs
arms: +2 runs
rest: +1 runs
total: +3 runs

Another interesting case is Michael Bourn.  Phillies fans love him.  And of all MLB players, he’s the one guy whose fielding depends mostly on his speed (after him are Ichiro and Felix Pie).

UZR has limited data on him, though he’s excellent in that limited time.  However, when I regress, if I ignore his scouting report (his speed mostly), then I have to regress him toward the MLB average player.  And I end up with only a +4 UZR.

This is of course ridiculous.  We know the speed is a major component to fielding in the OF.  On top of which, Bourn has the other traits that are desirable for a great fielding OF.  His most similar fielders are a who’s who of top fielders:
http://tangotiger.net/scouting/sim2007_7828.html

Therefore, we must regress him to that similar population.

Another interesting one (for me) is Tim Raines, Jr.  He’s actually #1 in UZR (again, limited playing time).  We know he’s a fast runner.  But, the 2004 Fans’ Scouting report (hence, the value of historical scouting information), shows a player who is rather ordinary in other facets of his fielding game.  So, his regression point would be somewhat lower than Bourn’s.

The average OBP/SLG for the 3 IF positions was: .337/.422.  And for the 3 OF: .345/.442.  This is a 0.6 offensive win gap, per position, per 162 G.

My fielding spectrum gives the 3 IF positions an average of +0.17 wins, and the 3 OF positions an average of -0.17 wins.  That gap is 0.33 wins.

If you want to argue that I should add +0.1 wins to each infielder, and remove 0.1 wins to each outfielder, I won’t disagree with you.  That would mean you give adjustments of the following:
+0.6 SS
+0.4 CF
+0.1 2B/3B
-0.6 LF/RF

Personally, I don’t think it’s worth it.  I mean, a 0.1 win margin of error is acceptable where I sit.  And, it’s alot easier to remember the symmetrical 0.5/0/-0.5 than the above.

1B are: .357/.463, which compared to the 6 IF/OF positions of .341/.432 puts them at +1.0 wins ahead of them.  This is exactly what I’ve got my fielding spectrum at.  So again, the spectrum works.

C: .318/.394 is 1.3 wins behind the IF/OF.

Since catcher is such a unique position, I could definitely be tempted to change the spectrum for them.  When I look at Patriot’s historical data for catchers:
http://walksaber.blogspot.com/2007/12/hitting-by-position-2007.html
They have runs per game at 86% of the league average.  This puts them at 12 runs below league average, consistent with what happened in 2007.

I think we all see catcher as a slightly below average position (off+def).  That is, if you have to cut corners (salary, whatever), you do so at 2B and C.  Giving C a +1.0 win boost for their position (rather than +1.2) accomplishes this.

So, I’m happy with the spectrum:
+1.0 C
+0.5 SS/CF
+0.0 2B/3B
-0.5 LF/RF
-1.0 1B
-1.5 DH

(I realize that it doesn’t add up to 0 wins, but c’est la vie.)

Note: DH should be -2.0 wins, since a bad fielding 1B (-1 win) coupled with the 1B adjustment (-1.0 wins) gives you -2.0 wins.  However, because of the DH penalty on offense (harder to hit while DH than to do so as 1B), I scale that up to -1.5.

Actually, I didn’t consider basestealing and baserunning.  That probably puts the catchers at -1.5 hitting wins.

I just ran hitting by position for 2000-2007.  Excluding pitchers, PH, and DH, I get:

c +13
1b -15
2b +7
ss +11
3b 0
lf -10
cf +3
rf -9

I can understand treating 2b and 3b as equals on the spectrum - second basemen as a group are not better fielders, are worse hitters, and MLB confirms it by making them the lowest paid position.

The gap between rf/lf and center looks like a match, same with 1B vs corner OF.

I’m not sure we should be making 2b-3b-ss = OF though.  Pretty much every move between the spots involves an infielder who couldn’t handle an infield spot going to the outfield, from Sheffield and Tartabull to BJ Upton and maybe Rickie Weeks and Ryan Braun sometime soon.

On a lesser level teams will take a backup infielder (Freel, Figgins, Burke) and have him learn the OF, but you rarely see an OF come up and learn to play backup infield.

This spectrum would keep the right balance within infield and outfield groups, but put infielders on an even par with outfielders:

c +13
1b -13
2b, 3b +3
ss +8
lf -8
cf +2
rf -8

Tango, did you control for age?  Aren’t there more moves from CF to the corners, SS to another position, etc., as a player ages?  Wouldn’t that make the gap look wider than it is.

Also, it is REAL important to regress a fielder’s UZR to something other than zero based on not only his age but his speed rating.  Remember my article on speed and UZR?  At most positions there was a huge correlation between speed and UZR, especially in the OF (not so much at third and SS I think, and more than you would expect at 1B).  A player with top-notch speed is probably +4 or more on the average, so a player like Bourne needs to be regressed to a number a lot higher than zero.

And maybe you just use speed and not age.  I have not looked at whether there is an independent relationship between age and UZR and speed and UZR, or whether age is just a proxy for speed.

Note: The 3 IF and 3 OF I have as a 0.33 win gap, not as equals.

In your first chart, you have an 11 run gap between the IF/OF.  In your second chart, you have a 9 run gap.  So, it’s a good job of trying to smooth things out.

The whole thing really hinges on 2B/3B relative to CF.  You’ve got them virtually equal.  And in my view, I can’t see how that can be.

I agree with your position about the IF goes to OF, as I’ve shown in the past.  The movements rarely go from OF to IF.  (Almost any OF who go to the IF, outside of Melvin Mora, were IF in the minors.)

I’ll have to look over studes’ work on how much players are being paid at each position, relative to their value.

Once we get the relative value of CF to 2B/3B set, everything else is relative to those positions, and we agree on those relative positions.

I’m definitely conflicted on the CF/2B issue, since all lefthanders must go into the CF pool.  But, any lumbering oaf won’t be in the CF pool, but can exist in the 2B/3B pool.  Really tough call.

***

Btw, in the late 40s, the average CF = average 1B in offense.  Just thought I’d throw that out every now and then, for those who want to argue that the average at each position must be, overall, 0.

There are two things I’m overdue on.  One is the Community Forecasts, along with the other 10 pro forecasters that I have.

The other, which is overdue by years, is linking my Fans fielders to the Retro or Lahman player IDs.  Once I do this part, then I will have an exact profile of players that move from position to position, including the speed and arm portions of their skillsets.  This will go a super long way in telling us how representative, or not, the guys who play multiple positions are.  For example, if we find that only the slow CF move to the corner positions, then we know we can’t trust those figures to apply to fast CF.  Same applies for the 2B/3B moves, etc.

I haven’t decided which of these two projects I should do next.

By the way jinaz, the Reds have the worst fielding team in baseball, since 2003: -302 runs.  Junior is -127 of that.  Without Junior, you jump over DRays, Yanks, and Redsox.

LOL.  er… ::sob::

Go Reds!
-j

I agree, 3B/2B vs CF is where the question lies.

For me the selective sampling is enough to explain it.  I think if we forced Torii Hunter, Andruw Jones, Coco Crisp, and Mike Cameron to spend a season as infielders we’d see them lose a lot of runs relative to position.

If infielders who move to center are losing runs, its more about mismatched skill sets instead of lessor fielding ability.

If outfielders really were a better group of players, collectively, than infielders, teams should move some of their outfielders to the infield until the gap closed. 

Or more specifically, they should stop moving their infielders to the outfield.  Billy Hall, Gary Sheffield, Mike Cuddyer, Soriano, Carlos Lee, Mark Teahen - Back to the infield with you!

From 1956 to 1969 I have, per 650 PA:
Outfielders: +28
3b, 2b, ss: -30

From 1970-1984:
OF: +22
IF: -29

And now:
OF: +16
IF: -18

So perhaps MLB has been moving in the optimal direction.  Maybe you’re right and we aren’t quite there yet, just closer than 30 years ago.

There probably has been some convergence, as MLB discovered you didn’t have to sacrifice as much on offense as they thought to get quality IF defense (Ripken, Trammell, etc.).  And as Tango has noted, the elimination of turf probably reduced the value (variance) of defense relative to offense.  But some of what you’re seeing is just the generic decline of variance we expect to see over 50 years, as quality of play improves (the “Stephen J Gould” effect).

Personally, I don’t think we’ll ever see OF and IF converge, and they may be about as close as they’ll ever get.  The boundary is determined by the inherent correlation, if any, btwn fielding skill and hitting skill.  If we break down fielding skills, and think about their likely correlation with offensive ability, I’d guess something like:
Foot speed:  Strong
Arm:  Weak
Lateral range (IF):  weak (some correl with speed)
Glovework: None

If this is right, we’d expect OF to always be somewhat better hitters than IF as a group.  And if there is some correlation btwn throwing ability and hitting, that would help explain both why 3B tend to be better hitters than 2B, and why RFs are as good offensively as LFs (or even a bit better in some periods) even though they are somewhat better fielders.

Well, that’s some fantastic data right there.

I’ve got my three OF as -5 runs as fielders and the three IF as +5 runs as fielders, total, per team.  So, you are right, I am saying that the average OF overall is better than the average IF.  Using your “now” numbers, that puts the three OF as +11 runs and the three IF as -13 runs, for off+def.

If someone wants to try this, maybe someone can tell us the total salary being paid to, say, the 150 infielders (2b,ss,3b) and 150 outfielders with the most playing time in 2007.

In order to support my position, I’d have the OF as +330 runs and the IF as -390 runs (+33 wins and -39 wins), for these 300 players.  That would mean that, as a group, the OF would be paid about 150MM more than the IF).  If that’s not the case, I’ll relent.

Just caught up for the in between years.  Here’s the offensive gap between OF and IF, by time period:

56-69: +58
70-84: +51
85-92: +35
93-98: +37
00-07: +34

The time periods represent nothing more than the way I imported my retrosheet databases.

Here’s one interpretation: That as MLB teams moved from a suboptimal position, with too many good outfielders crowded out of positions while crappy hitting infielders held jobs.  The Dodgers are the best example of a team using this to their advantage:  Both Davey Lopes and Bill Russell were minor league outfielders I believe.  Then they reached the optimal level in the late 80’s, and its remained ever since.

But its foolish to assume that the times we live in are an equilibrium and will not change.  So maybe the hitting gap will shrink in the future if teams believe the fielding gap is not that large.  Two outfielders who probably would be more useful as infielders are Mike Cuddyer and Billy Hall, because they weren’t bad defenders. 

Soriano should probably be in the outfield, as his defense was really bad at 2nd and very good in left.  If we look at a LF as -5 and 2B as 0 in position adjustments, its a no-brainer.  But leftfielders are outhitting second basemen by 17 runs per year, so that makes it a tougher decision.

I’m sure that if we look at salaries teams are paying based on Tango’s model.  When Soriano, Hunter, Lee, Wells, and Ichiro average around 100 million on their recent contracts, and Carlos Guillen gets 4 years, 48 million, it doesn’t appear that teams are giving much of a positional bonus.  Doesn’t mean its right though.

Those time periods are very close to what I use.

I use 57-68, 69-81, 82-92, 93-present.

Around 1982 or so is when the starter/reliever dynamic made a sudden change.  Might be 1983.

In 1993 or 1994 is when the runs per game exploded.

The low point in scoring was 1968, and expansion was 69.

Just doing it real quick, and not focusing on just the top 150… just a straight adding up. 

From 2001-2006, 2.1 billion$ was spent on 2B, SS, 3B.  2.87 billion$ was spent on the outfield.

That difference is 770 million$ over 6 years, or an average of 130 million$.

In post 22 I said:
“That would mean that, as a group, the OF would be paid about 150MM more than the IF).  If that’s not the case, I’ll relent. “

Looks like I can’t relent!

To the extent that MLB teams are properly paying their IF and OF, it looks like my spectrum works.  To the extent that we want to create a model of converting wins to dollars, my spectrum works.

To the extent that we want to know how much *should* teams be paying their IF and OF, it’s possible that we need more work.

22:

This is only using the Primary Position query and Salaries table from the new Lahman database, and top 30 players at each position:

Pos---Salary---PA
2b---$74.7MM----16,695
3b---$155.1MM---15,656
ss---$135.8MM---17,858
lf---$172.6MM---15,478
cf---$144.2MM---16,797
rf---$127.3MM---16,340

IF---$365.6MM---50,209
OF---$444.1MM---48,615

Great job, thanks!

Per 2100 PA, that’s a 3.9MM difference. 

With a 2.25MM per win converter, that’s a 1.7 win difference.

Using my spectrum, I have a 24 run difference between IF and OF (2.4 wins).

In order to get it down to 1.7 wins, I need to chop off 0.1 wins for each OF position, and add 0.1 wins for each IF position.

That’s what I had said in post 12, when I said the “margin of error” was 0.1 wins.

If we apply this, we get the CF at +0.4 wins and the 2B/3B at +0.1 wins.  The rest move relative to these positions.

The salaries matched your theory perfectly, so I’ll have to relent.

But I’d like to see some consistency out of teams though.  If they are smart enough to recognize outfielders are better players, then they should be moving some outfielders to replace crappy infielders if there’s any evidence at all they can handle it.

Case in point: Mike Cuddyer.  At 3B he’s -3 UZR runs per 162.  At second he’s -15, in right field he’s -9.  So if your alternatives are Alexi Casilla and Nick Punto, Cuddyer absolutely should be going back to the infield.

From a scouting perspective, one of the main differences between OFs and IFs is the way they’re trained to throw the ball at a young age.  Outfielders learn to use a significant windup and long release, while infielders are much more about getting the ball out of their hand as quickly as possible. 

It is not particularly hard to change from being a quick thrower (IF) to a long thrower (OF).  It is significantly harder to go the other way.  It’s not impossible, but it requires a hell of a lot more work to turn a kid who has been playing CF his whole life into a SS than vice versa, simply because of the nature of throwing the ball and current training techniques. 

This could account for some of the differences.  If we accept that there is a population of players that are being groomed as outfielders as teenagers, it is unlikely that many of those players will ever end up as major league infielders.  However, since a significant portion of talented high school infielders will end up in the outfield, it does strike me as somewhat logical that this shift would lead to OFs being generally more talented than IFs once we get to the ML level.

Very interesting thought about the throwing/windup.  This would explain the ease of IF and OF moving to 1B: both groups need to learn how to throw 10-30 feet.

Dave, how much do you think the GB aspect affects things?  Since 3B and 1B are so similar in terms of catching groundballs, how much of a learning curve does a corner OF have over a 3B.

(Excepted: Gary Sheffield. It was a truly pathetic sight to see him at 1B in the playoffs.  He had no heart in it.  What was Torre thinking?  Putting any of his other OF there would have been better.  I’d rather put Ichiro at 1B than put Sheffield there.)

Does anyone know of any work done on historical positional adjustments?

Sky, here you go: http://www.hardballtimes.com/main/article/historical-hitting-by-position/

It’d also be possible to repeat Tango’s procedure using Rally’s retrosheet-years database, divided into decades perhaps.  Not a small undertaking, but it’d be very interesting to see how actual defensive numbers change over time.
-j