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by Team

I was wondering something
MLVr. I always see players plugged into a
lague average team whenever it is used, but can you plug Player X into
a current team (say, put Lyle Overbay in the place
of Kevin Millar in the Red
Sox order) and still have the results work? It seems like it would
no problem, but I just wanted to make sure there was no reason that
alluded me as to why it may not work.

–Marc Normandin


There are two ways of answering your question, depending on which
you’re really asking:

1) Can I use the MLV mathematical formula, but use the Red Sox team
average instead of an average team, so as to get the specific impact
Overbay vs. Millar to the Red Sox? The answer is yes–you can plug
whatever team you’d like to compare to, and churn the math to get a
result. It’s a fair amount of work, but definitely doable.

2) I don’t want to do a lot of extra math, but just want to
look at
Overbay’s MLVr and Millar’s MLVr on the BP stats page and figure out
the effect on the Red Sox would be from there. Can I do that? The
is that you can get an *approximate* answer from looking at their
difference in MLVr. e.g. As I type this, Millar has a -0.045 MLVr,
Overbay has a +0.247 MLVr. As a first approximation, the difference in
team scoring per game would be 0.247 – (-0.045) = 0.292 runs per
game. Boston is averaging 5.305 runs per game with Millar, so with
Overbay they’d be expected to score approximately 5.305 + 0.292 =
runs per game. The difference between the two is about 47.3 runs over
the course of a 162-game season.

The caveat here is that run scoring is not linear, and
MLVr is not as
accurate, the further away from an average team you get. In addition,
because they are in different leagues that play with different rules
(DH/no-DH), they are being compared to league averages compiled under
different circumstances, and with park effects from different sets of
parks against different baselines. Getting everything right is rather
tricky, and ultimately takes us back to answer 1) above. If we just
in Boston’s team AVG/OBP/SLG into the MLV formula, and use their raw
stats and current park factors, the difference between them is 0.248
runs/game, or about 40.2 runs per season. We’d actually expect the
to be higher when comparing two players on a high offense team than an
average offense team, so the fact that we’re getting lower results
indicates that the difference in leagues is causing an even greater
effect than the nonlinearity of offense. For most purposes, the
approximation of taking the difference in MLVr is good enough to make
extra work not worthwhile. Hope this helps.

–Keith Woolner


I’ve generally enjoyed your
stadium columns, but please stick to the
facts and economics and leave out the hyperbole. You undermine your
by using the $320 per resident figure…this assumes that every current
resident of Hennepin Co. will remain there for 30 years w/ no change in
population and even if we believe that (which I don’t) that amounts to
about $1 per year per resident…in current dollars. If you add
inflation, this becomes much less than $320 per resident in today’s
dollars. I’m no more a fan of public funding for stadiums than you,
stick to the facts…like the fact that I-94, not I-90, runs through



Maybe I should have been clearer about this, but the “$320 per
figure is in present value, not cumulative expense over 30
This is a handy economic shorthand for comparing apples to apples in
of expenses over time–one we use whenever we say “I bought a new
for $400,000!” instead of “I bought a new house, and will be paying out
million in interest and principal, spread out over the next 30 years!”

There are all sorts of fancy ways to calculate present
discount rates and estimated interest rates and the like (not
which is a separate issue). Fortunately, since what we’re after here is
“How much money could you raise today with these future payments?”
an easy answer: $353 million, since that is how much money (in
stadium bonds) would be raised with them. Divide by 1.1 million
residents (disregarding for the moment out-of-town visitors) and you
$320.91 per person.

As for I-90 and I-94, mea extremely culpa. I checked my
I checked
with my Minnesota-educated sister on corn dogs as the local cuisine,
for some reason I didn’t think to check a road map. They’re the same
in Chicago, is my only excuse–although I do manage not to confuse Renee Zellweger with Sandy

–Neil deMause

Pitching and Defense

I am replying to a 2001
so I am a little behind the times, only
recently having discovered Baseball Prospectus in connection with Will
Carroll’s interesting book ‘Saving The Pitcher’.

I am a 71-year-old retired Defense Electronics Engineer
a strong
background in Mathematics, but am only recently tuning in on
Sabremetrics. I also still play Baseball in an MSBL league organized
age-group for adults. My early Baseball career was as a pitcher, but I
developed a rotator cuff tear several years ago and am now a catcher–I
have been very fortunate with my legs and my arm has responded enough
physical therapy to allow a catcher’s occasional need for a

I was impressed with the manner in which you responded
Voros McCracken’s thoughtful hypothesis–in the spirit of peer review
thoughtfulness of your own. And so I am writing with some questions,
comments and opinions about a pitcher’s ‘ability to prevent hits on
hit in the field of play’ as Mr. McCracken puts it or ‘abilities to
prevent balls in play from becoming hits’ as you put it, each as
reflected in a derived statistic called

At my first glance it sounded like voodoo. And it still
to a certain
extent. That may be because I am still trying to understand it and to
adjust my point of view. The POV of this statistic is definitely
‘data-mining-after-the-fact’ as opposed to
‘while-it-is-happening-in-real-time-on-the-field’. I guess there is an
implication that this ability is related to something that the pitcher
actually does or can do, but–at least in these 2 articles–no direct
attempt is made to describe what that might be. It could be that this
concept is still young and developing. Have there been other articles
the subject in the interim?

My initial instinct supports Mr. McCracken’s conclusion.
the pitcher releases the ball and it leaves his fingertip(s) on its
trajectory to the hitting zone, in some sense it’s all over. He has
his thing and is now an infielder. From this point on, he cannot affect
what happens to the ball, except as an infielder. It would seem that
differences amongst pitchers will have been acknowledged in the myriad
other pitching statistics gathered, including certainly–but not
limited to–those defined as Defense-Independent. To postulate
otherwise from mined data seems to impose the obligation to attempt to
identify what that real-time ability–somewhere from start of wind-up
to release point–might be.

Is it not true that the pitched ball has very few
attributes over its trajectory from pitcher to hitting zone? Perhaps as

A. Translational Velocity of the Center of Mass of the
(A vector
having Magnitude and Direction. The radar guns read a number related to
this Magnitude)

B. Rotational Velocity (Also a vector having Magnitude
Its Magnitude is the ‘RPM’ value of ‘spin’ the pitcher imparts on
‘breaking’ balls. Its Direction points along the axis of rotation of
spin and helps determine the type of ‘break.’ Also affects ‘movement’
a fast ball.

C. ‘Location’ as it passes thru the hitting zone.

A.’s Magnitude and Direction change during the
trajectory due
to gravity
and drag forces. The prevailing wisdom is that B.’s Magnitude and
don’t change
much, but I am working some other ideas.

What else is there–regardless of which pitcher it is–that
account for this postulated ability?

Well, there are some other subjective things which might

1. ‘He throws a heavy ball’ (whatever that might mean
A., B., and
C. above.)

2. ‘Batters are not getting a good look at his release
because of some
detail of his delivery’

3. ‘He keeps the ball low’ (although this could
be washed out
in statistics gathered on ‘ground-ball outs’)

4. ‘He is doctoring the ball’

5. ‘He is a ‘trick-ball’ pitcher

6. ‘He has great command and control of all of his
(but this
falls within A., B., and C. above)

7. ‘He pitched for years in heavy air with a bright
directly behind
him’ (park effects) 🙂

My point is–I can’t seem to suggest a source of this
ability which is
not subject to some nullification by ‘all- other-things-being-equal’
methods or other statistics.

I feel I am
probably missing something–perhaps from being too close to the field



Your questions are very insightful, and I appreciate you taking the
time to
put your thoughts
down in electrons.

I disagree with the implication as you have stated it–I don’t think
that either Voros or myself are saying that there is something a
can consciously control or work on, but rather that there are simply
observable persistent traits that can be attributed to individual
pitchers to a certain degree.

Similarly, if I do a survey of players’ heights, and discover that first
basemen are taller, on average, than shortstops, that doesn’t mean that
player must find some way to grow taller in order by become a
first baseman. It is simply nothing but an innate (and possibly
trait that may be useful to a decision maker in determining whether a
player is better suited for SS or 1B.

It is true that a pitcher can do nothing once the ball is released to
affect whether the ball is hit, or where it goes. I disagree, however,
that all other common pitching statistics necessarily encapsulate all
real-time ability. There’s nothing special about the recording of
observed PA outcomes (which is what the typical statistics for
are) that implicitly shows us all sources of variation between

I think you’ve missed several important ones. For the sake of example,
list a few. Note that not all of them are directly under the control
the pitcher, but they do affect the flight of the ball after release

D. Distance the ball travels to the plate–this may seem like a
constant, but given different height and arm length of pitchers, and
different release points, this will in fact vary, perhaps by a foot or

E. Wind Velocity

F. Ambient Humidity

G. Air Density

H. Air Temperature

I. Smoothness of the ball surface (how scuffed up is it?)

J. Variations in ball construction (there are tolerances for weight,
circumference, height of the stitches, etc.)

All of which are physical characteristics either of the ball or the
environment, that can affect the velocity, spin, or drag on the ball in
flight. And a pitcher could alter his delivery of the ball in response
combinations of these factors.

I do think you
underestimate the number of variable physical factors in play.

I think you are overlooking the other primary factor in determining
outcome of a batter-pitcher confrontation–the batter. Everything
you’ve described (with the exception of #2 above) deal with the
of the ball in flight–what trajectory it takes, the spin, etc. But
the batter is trying to integrate all of those factors as well in
his decision of how and when to swing. And the batter is not
making that decision solely on observing the pitched ball.

To use the baseball phrase, pitchers can disrupt a hitter’s
timing. Batters anticipate what pitch will be thrown, and where.
selection and sequencing can make it harder or easier to hit the same
ball thrown in a different situation. Some pitchers do hide the ball
better, or alter their arm angles unpredictably, giving the batters a
fraction of a second less time in which to visually pick up the ball
react. Batters also use other visual cues to infer characteristics of
the pitched ball. You’ll hear comments like “he throws his fastball
the same arm motion and arm speed as his changeup.” Batters will look
a pitchers arm motion to help guess what speed the pitch will be.

Batters also have differing levels of ability to hit pitches in
parts of the zone–a pitcher’s ability to hit the right spots within
strike zone to different batters could also affect his overall success,
even if that is not reflected in his ball/strike ratio.

The “mental” side of the game, a battle between deception and
anticipation, can easily alter a batter’s ability to place the bat in
right place at the right time, and with the right bat speed. The same
physical pitch, delivered when the batter is anticipating a fastball
down-and-away instead of a curve that paints the black inside, can be
difference between a home run and a strikeout. It’s certainly
that pitchers differ in their abilities to create different mental
in batters.

And in any event, we do not need to identify the cause for the
effect to
observe that an effect exists. It is plausible, for example, to
hypothesize that:

1. Pitchers may have an ability to make batters swing and miss.

2. Pitchers with this ability may record more strikeouts

3. Pitchers with this ability also have more “near-successes” (balls
almost missed, but instead just hit weakly) than pitchers who don’t
many bats.

4. Pitchers who have a higher ratio of weakly hit balls
out of
all balls hits will have a lower batting average on those balls.

Thus, pitchers with high strikeout rates should have lower averages
balls hit into play.

In testing this hypothesis by observing actual data, we find that
isn’t a strong connection between strikeout rates and BABIP, but there
a plausible reason to suspect it might be true. It could not be ruled
out a priori, or assuming all else was equal.

In the end, the observation that pitchers have at best modest
over whether balls in play become hits is based on the evidence, across
single year, multi-year, and full-career statistics. Whether
this is a result of conscious action, or innate characteristics of a
as a way to explain this phenomenon, are different questions than
the phenomenon exists.


Could Look it Up


With regard to the John Hiller 1973 season, I got to
thinking and
checking on the Willie Hernandez/Aurelio
combo from 1984 and was
astonished to find that Senor Smoke nearly matched Willie in many
respects. Where does this duo stand in terms of a 1-2 punch?



Thanks for the question. It seemed like an interesting point to
so we checked out the top 1-2 combinations since 1972 with combined
>=10. The results are below. You’ll note that Hernandez/Lopez ranks
fourth. My own guess, John Wetteland/Mariano
(1996) ranks third. The true best
came practically yesterday.

—- — —— ——————– —— ——————– ——
2004 NYA 13.90 Mariano Rivera 7.45 Tom Gordon 6.45
2003 LAN 13.37 Eric Gagne 9.25 Guillermo Mota 4.12
1996 NYA 13.02 Mariano Rivera 6.88 John Wetteland 6.14
1984 DET 11.89 Willie Hernandez 9.15 Aurelio Lopez 2.74
1997 BAL 11.84 Randy Myers 7.35 Armando Benitez 4.50
1998 SDN 11.51 Trevor Hoffman 8.32 Dan Miceli 3.19
2000 CHA 11.37 Keith Foulke 8.22 Bobby Howry 3.15
2002 ATL 11.34 John Smoltz 7.11 Mike Remlinger 4.23
1996 SDN 11.05 Trevor Hoffman 7.72 Tim Worrell 3.33
1977 PIT 11.03 Rich Gossage 8.12 Kent Tekulve 2.91
1986 TOR 10.97 Mark Eichhorn 6.24 Tom Henke 4.73
2004 LAN 10.93 Eric Gagne 8.00 Guillermo Mota 2.93
2004 MIN 10.90 Joe Nathan 7.71 Juan Rincon 3.19
2003 HOU 10.78 Billy Wagner 6.55 Octavio Dotel 4.23
1993 LAN 10.72 Pedro Martinez 5.59 Jim Gott 5.13
1995 CLE 10.71 Jose Mesa 7.20 Julian Tavarez 3.50
1990 OAK 10.48 Dennis Eckersley 6.83 Rick Honeycutt 3.65
2000 BOS 10.29 Derek Lowe 7.30 Rich Garces 2.99
2001 NYA 10.24 Mariano Rivera 5.81 Ramiro Mendoza 4.43
1975 CHA 10.22 Rich Gossage 7.63 Dave Hamilton 2.59
1980 KCA 10.19 Dan Quisenberry 8.18 Marty Pattin 2.01
1973 DET 10.16 John Hiller 9.64 Lerrin LaGrow 0.52
1996 CAL 10.12 Troy Percival 8.38 Chuck McElroy 1.74
2002 LAN 10.12 Eric Gagne 8.25 Paul Quantrill 1.87

–Steven Goldman


1. Are VORPs additive? In
words, is it appropriate to say that
one player with a VORP of 10 is equally valuable to two players with
of 5 each?

2. Can you only compare players of the same position, or is it
appropriate to say that (for example) a catcher with a VORP of 10 is
more valuable than a pitcher with a VORP of 9?

3. Is it possible to calculate an average VORP per team that can be
compared to other teams’ average VORPs?

4. In the definition of VORP, what is meant by ‘a
player’? Is this some sort of ‘average’ player? For
example, if your VORP is 10, does that mean you contribute 10 more
runs beyond what the AVERAGE player at your position contributes?

5. What is the time-frame for the contribution of runs? For example,
your VORP is 10, does that mean you contribute 10 more
runs per SEASON, or some other length of time?

6. How do they determine a player’s ‘position’ when that player
MULTIPLE positions?

7. How and why does VORP apply to pitchers if the definition of VORP
includes ‘runs contributed’?


Hi Mark,

Strictly speaking, VORP is not additive, because the model of offense
uses is nonlinear. I’ve explained this elsewhere in more detail, but
basically going from a .380 to .390 OBP generates more marginal runs
than going from a .300 to a .310 OBP does–even though it’s the same
point OBP difference. VORP measures the effect of one player on an
otherwise average team. If you replace two players on the team, then
effect is compounded.

That being said, it’s darn close, and much more
convenient to
add VORPs
together, and you will see this commonly done.

One of the strengths of VORP is that is can be used to
compare players at
different positions, or to compare position players to pitchers. So in
that way you could say that a VORP of 10 is more valuable than a VORP
of 9–although since VORP is measured in runs, a one run difference is not
very large. Also, it depends on exactly what you mean by “valuable”–what having the larger VORP literally means is that the player
more runs above replacement level in the playing time he had than the
other player did in the playing time the other player had. If their
playing times were not equivalent, one could have a much higher *rate*
production, even if the total value was less than another player’s.

You don’t really want an average team VORP, but a
team VORP.
If you average the VORPs of the players on the team, and if one team
15 position players, and another uses 23, the latter will have a lower
average VORP, just because it’s divided across more players. However,
since all teams in a league field the same set of position players,
looking at the team’s park-adjusted offensive stats (or run totals),
gives you the same answer as VORP would, at least for position
For pitching VORP, all teams end up with roughly the same innings
totals, so the number of runs over/under the league average runs
adjusted for park is basically the answer you’d get as with VORP.

No, that is one of the most important distinctions in
versus metrics
like Total Baseball’s Batting Runs or Linear Weights. A
player is one who is “easily available” to any team–a AAA journeyman
or end of the bench player. There’s a research article I wrote
explaining replacement level in gory detail in Baseball Prospectus
Replacement level is significantly below average–about 80% of
for the position. If you think of it in OPS terms, roughly 70 points
OPS below the average for the position is replacement level.

VORP is a cumulative stat, not a rate stat, so the length
time question
doesn’t really apply. Similarly, if a player hits 100 home runs, he
*100 home runs* whether it took him 2 seasons or 20. VORP encompasses
much playing time the player in question got, and is a number of runs
contributed over replacement level *given that amount of playing
time.* There is a rate stat version of VORP–“VORPr” (VORP-rate),
might be more what you are looking for. It expresses a player’s rate
production in runs per game above replacement level. e.g. a player
with a
.500 VORPr contributes half-a-run above replacement level per game
is outstanding, BTW). VORPr (and VORP) can be less than zero, meaning
that a player was below replacement level over that stretch of plate

I weight the positions the player actually appears at in
determining his
own unique “positional average”–a player with 60% of his PA as a
shortstop, and 40% as a second baseman will have a positional average
between those of SS and 2B, slightly closer to the SS average.

Pitchers “contribute” runs by preventing them from
replacement level is a 6.00 RA, and our star pitcher has a 3.50 RA over
180 innings:

RepLvl pitcher: 180 IP * 6.00 RA / 9 = 120 runs

Star pitcher: 180 IP * 3.50 RA / 9 = 70 runs allowed


Compared to RepLvl, Star pitcher prevented 50 runs from scoring

Thus, his VORP is 50.0




It looked like a bad Astros lineup on paper to start this season,
not as bad as it has been. Three losses in games that went into extra
innings scoreless is just hard to take. Two wins on the road. Wasting
good outings by the starters. The negatives have been numerous. For
all of the criticism of Phil Garner‘s selection of Adam
for the
leadoff position on Opening Day (myself included), I have to admit that
the alternatives were not terribly attractive. The bottom line is that
with Brad Ausmus, Everett, Willy
Jason Lane, Morgan Ensberg, and the
disabled Jeff
, there were bound to be two or three replacement-level

But thanks for mentioning Jim Deshaies‘ work on the Astros
broadcasts. I
think the Astros are blessed with two great color commentators on their
TV broadcasts as J.D. works the road games and Larry Dierker was
back to work the home games (perhaps the team’s best off-season move).
Both offer more insight than most former players. And JD has some
cliches that I haven’t heard anyone else use. My favorite is the
‘dessert cart fastball.’ In case you don’t know, that’s a high
that looks to good for the hitter to pass up, even though he knows it
bad for him.

J.D. can add plenty of levity to the broadcast, and I am afraid that
this year we will need it.

Dierker points out little nuances that I miss, even though I have
watched lots of ball games in my 34 years. The other day he correctly
predicted that a pitcher was going to throw a fastball, because he
for a new ball from the umpire after just throwing a curve for a
Dierker said that feel on a curveball is very important and if a
pitcher has just thrown one for a strike, he will want to keep the ball
if he plans to throw another.

The Astros are bad, maybe VERY bad. But these two guys still make
games worth watching.



Seems to me, Scott, that you can use “dessert cart __” for just about
anything. Dessert cart marriage, dessert cart drinking binge, etc. So
fact that it’s at once funny, apt, and applicable to virtually any
situation means I’m officially stealing it for myself.

That’s great stuff about Dierker’s predicting a fastball based on
issue too. It’s funny how GotW was really meant to lock in on the
of each game, but it’s evolved into minutiae, plus a lot of my rantings
the game’s broadcasters. Think about how rare it is for someone to
studiously watch a full nine innings of a game, without flipping the
channel–you really do need the announcers to be at least decent, or
run the risk of wanting to stab yourself in the eye with the corn dog
your side. Deshaies and Dierker, by contrast, play like Nobel Laureates
their observation skills and peak-years Richard Pryor in their humor.

–Jonah Keri

of the Ninth

Nice article on the stadiums. I have
vague hope that the
grandstanding politicians would bring the franchise owners into
and talk to them about how they have consistently fleeced cities across
the country to build stadiums and then they turn around and sell the
team for 3-5x their purchase price. But that is just a dream and it
will not happen.

Perhaps there could be a law someday saying that governments cannot
authorize paying for sports stadiums–but doubt that would happen

Let’s just hope that, as you said, prospective cities remain
and realize that building a stadium for a team to entice them to move
a money-losing proposition.



Actually, such a law was proposed in Congress several years ago: David
Minge, a Congressman from Minnesota (what are the odds?), introduced
Distorting Subsidies Limitation Act of 1999, which would have forced
companies that got special public subsidies to claim them as income,
pay taxes on them. It wouldn’t have put an end to shakedowns of cities
sports franchises and other footloose corporations–Minge’s original
idea, taxing such subsidies at 100%, would have, but that was
too radical to even present to Congress–but it would certainly cut
the incentive to demand public money.

Minge’s out of Congress now, but that shouldn’t stop you from
calling up
your own representative and asking if they’d support reintroducing his
bill. It’s a longshot, but, hey, many stones to build an arch.


Thank you for reading

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