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July 6, 2005

From The Mailbag

MLVr, VORP, BABIP, WXRL, Stadiums, and the Dessert Cart

by Baseball Prospectus

MLVr by Team

I was wondering something about 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 work 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 version 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 of Overbay vs. Millar to the Red Sox? The answer is yes--you can plug in 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 what the effect on the Red Sox would be from there. Can I do that? The answer 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, and 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 = 5.597 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 so 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 plug 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 gap 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 "easy" approximation of taking the difference in MLVr is good enough to make the extra work not worthwhile. Hope this helps.

--Keith Woolner

Twins Tips

I've generally enjoyed your stadium columns, but please stick to the facts and economics and leave out the hyperbole. You undermine your case 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, but stick to the facts...like the fact that I-94, not I-90, runs through Minneapolis.



Maybe I should have been clearer about this, but the "$320 per resident" figure is in present value, not cumulative expense over 30 years. This is a handy economic shorthand for comparing apples to apples in terms of expenses over time--one we use whenever we say "I bought a new house for $400,000!" instead of "I bought a new house, and will be paying out $1 million in interest and principal, spread out over the next 30 years!"

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

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

--Neil deMause

Counterpoint: Pitching and Defense

I am replying to a 2001 article, 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 with a strong background in Mathematics, but am only recently tuning in on Sabremetrics. I also still play Baseball in an MSBL league organized by 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 to physical therapy to allow a catcher's occasional need for a high-stress throw.

I was impressed with the manner in which you responded to Voros McCracken's thoughtful hypothesis--in the spirit of peer review and with thoughtfulness of your own. And so I am writing with some questions, comments and opinions about a pitcher's 'ability to prevent hits on balls 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 'batting-average-on-balls-in-play'.

At my first glance it sounded like voodoo. And it still does 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 on the subject in the interim?

My initial instinct supports Mr. McCracken's conclusion. Once 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 done 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 all differences amongst pitchers will have been acknowledged in the myriad of 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 objective physical attributes over its trajectory from pitcher to hitting zone? Perhaps as follows:

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

B. Rotational Velocity (Also a vector having Magnitude and Direction. Its Magnitude is the 'RPM' value of 'spin' the pitcher imparts on 'breaking' balls. Its Direction points along the axis of rotation of the spin and helps determine the type of 'break.' Also affects 'movement' on 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 Direction don't change much, but I am working some other ideas.

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

Well, there are some other subjective things which might be considered:

1. 'He throws a heavy ball' (whatever that might mean within 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 objectively 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 pitches' (but this falls within A., B., and C. above)

7. 'He pitched for years in heavy air with a bright light 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 of play.



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 pitcher can consciously control or work on, but rather that there are simply some 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 a player must find some way to grow taller in order by become a successful first baseman. It is simply nothing but an innate (and possibly unchangeable) 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 pitchers are) that implicitly shows us all sources of variation between pitchers.

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

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 more.

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 to 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 the outcome of a batter-pitcher confrontation--the batter. Everything you've described (with the exception of #2 above) deal with the physics 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 making 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. Pitch 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 and react. Batters also use other visual cues to infer characteristics of the pitched ball. You'll hear comments like "he throws his fastball with the same arm motion and arm speed as his changeup." Batters will look at a pitchers arm motion to help guess what speed the pitch will be.

Batters also have differing levels of ability to hit pitches in different parts of the zone--a pitcher's ability to hit the right spots within the 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 the 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 the difference between a home run and a strikeout. It's certainly plausible that pitchers differ in their abilities to create different mental states 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 miss 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 on balls hit into play.

In testing this hypothesis by observing actual data, we find that there isn't a strong connection between strikeout rates and BABIP, but there was 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 influence 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 pitcher as a way to explain this phenomenon, are different questions than whether the phenomenon exists.


You Could Look it Up


With regard to the John Hiller 1973 season, I got to thinking and checking on the Willie Hernandez/Aurelio Lopez 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 explore, so we checked out the top 1-2 combinations since 1972 with combined WXRL >=10. The results are below. You'll note that Hernandez/Lopez ranks fourth. My own guess, John Wetteland/Mariano Rivera (1996) ranks third. The true best came practically yesterday.

YEAR TEA   WXRL P1                    WXRL1 P2                    WXRL2
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 other words, is it appropriate to say that one player with a VORP of 10 is equally valuable to two players with VORPs 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 replacement-level 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, if 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 plays 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 it 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 10 point OBP difference. VORP measures the effect of one player on an otherwise average team. If you replace two players on the team, then the 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 contributed 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* of production, even if the total value was less than another player's.

You don't really want an average team VORP, but a cumulative team VORP. If you average the VORPs of the players on the team, and if one team has 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, just looking at the team's park-adjusted offensive stats (or run totals), gives you the same answer as VORP would, at least for position players. For pitching VORP, all teams end up with roughly the same innings pitched totals, so the number of runs over/under the league average runs allowed, adjusted for park is basically the answer you'd get as with VORP.

No, that is one of the most important distinctions in VORP versus metrics like Total Baseball's Batting Runs or Linear Weights. A replacement-level 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 2002. Replacement level is significantly below average--about 80% of average for the position. If you think of it in OPS terms, roughly 70 points of OPS below the average for the position is replacement level.

VORP is a cumulative stat, not a rate stat, so the length of time question doesn't really apply. Similarly, if a player hits 100 home runs, he hit *100 home runs* whether it took him 2 seasons or 20. VORP encompasses how 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), that might be more what you are looking for. It expresses a player's rate of 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 (which is outstanding, BTW). VORPr (and VORP) can be less than zero, meaning that a player was below replacement level over that stretch of plate appearances.

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 in between those of SS and 2B, slightly closer to the SS average.

Pitchers "contribute" runs by preventing them from scoring. If 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 allowed

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


Prospectus GoTW


It looked like a bad Astros lineup on paper to start this season, but 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 Everett 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 Taveras, Jason Lane, Morgan Ensberg, and the disabled Jeff Bagwell, there were bound to be two or three replacement-level players.

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 brought 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 great 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 fastball that looks to good for the hitter to pass up, even though he knows it is 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 asked for a new ball from the umpire after just throwing a curve for a strike. 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 their 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 the 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 the feel issue too. It's funny how GotW was really meant to lock in on the minutiae of each game, but it's evolved into minutiae, plus a lot of my rantings on 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 you run the risk of wanting to stab yourself in the eye with the corn dog by your side. Deshaies and Dierker, by contrast, play like Nobel Laureates in their observation skills and peak-years Richard Pryor in their humor.

--Jonah Keri

Bottom of the Ninth

Nice article on the stadiums. I have this vague hope that the grandstanding politicians would bring the franchise owners into congress 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 either.

Let's just hope that, as you said, prospective cities remain intelligent and realize that building a stadium for a team to entice them to move is 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 the Distorting Subsidies Limitation Act of 1999, which would have forced companies that got special public subsidies to claim them as income, and pay taxes on them. It wouldn't have put an end to shakedowns of cities by sports franchises and other footloose corporations--Minge's original idea, taxing such subsidies at 100%, would have, but that was considered too radical to even present to Congress--but it would certainly cut into 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.


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