2008 Win Values

Dave · February 14, 2008 at 9:16 am · Filed Under Mariners 

“We have to analyze the talent we see and assign the proper value to it.” – Neil Huntington, Pittsburgh GM, in an article published yesterday.

The Pirates are the newest team to hire a GM with a strong belief in quantifying value. Not surprisingly, Huntington came out of Cleveland, an organization that has been using their intellectual advantage to win games for years. One of the basic fundamentals of the methods adopted by teams like Boston, Oakland, Cleveland, San Diego, and Arizona is the belief that all players have a quantifiable on field effect that can be summed in a win metric that allows for proper valuation. Evaluating talent is huge, but so is properly valuing performance – they go hand in hand, and doing one without the other is a wasted opportunity.

So, that’s what this post is about – valuing talent in terms of wins. I’ve taken the best approach to win analysis available and applied it to the Mariner roster, taking a projected performance for the upcoming year and converting that into a win value that factors in both run production and run prevention, with necessary adjustments for the position being played, the role the player will be used in, and the environment they call their home field. In the end, this allows us to size up the entire roster in terms of what we expect their on field contribution to be this season, how much that contribution is worth, and how much value they are adding to the franchise in 2008.

The starting spot for analysis of position players is offensive production. Every outcome of every plate appearance has an average run value that we can assign to that event, allowing us to convert an overall projected batting line into a run production number. This concept is known as linear weights, and is accepted as the best method for quantifying offensive value. If you want to read more about linear weights, here’s a three part series that covers the concept and shows how it works. There are a few different linear weight run estimators out there; I chose to use Weighted On Base Average (wOBA for short) because the math is the easiest to follow in getting from runs to wins.

Despite using On Base in the term, it’s a valuation of total hitting production. It gets its name from the fact that its scaled to look like on base percentage, so if you’re familiar with what a good/bad/average OBP is, you also know what a good/bad/average wOBA is. .300 is lousy, .340 is average, .400 is awesome. wOBA is presented in detail in The Book, written by Tom Tango, Andy Dolphin, and Mitchel Lichtman.

The formula for wOBA is wOBA = (0.72 BB + 0.75 HBP + 0.90 1B + 0.92 RBOE + 1.24 2B + 1.56 3B + 1.95 HR) / PA. Pretty simple – the multiplication is performed according to run values of each event scaled to look like OBP (in this case, the ratio of one to another is more important than the actual multiplications). Singles are worth a bit more than walks, but less than doubles, which are worth less than triples, and nothing is worth more than a home run. Nothing scary here. The only thing wOBA doesn’t account for is baserunning, so I’ve made manual adjustments for the necessary players who extract value from their legs.

So, all you have to do is have the data for those categories, and wham, you have wOBA. Once you have that, you can simply compare a player’s wOBA to the league average wOBA (AL average is .338, but I used .334 to account for Safeco) to get his offensive production above or below average. Note – this is not position adjusted – we’re just comparing hitters to hitters right now. Once you have the difference, you can divide that by 1.15 (wOBA’s relation to runs), multiply by a full season plate appearance estimate for each role (I used 700 for starters, 250 for bench players, both of which get reduced to 85% of that total later on, since we don’t project anyone to play 162 games), and then divide by 10.5 to convert from runs to wins. After you’ve done that, you’ve got an offensive win value compared to league average.

That’s step one. From there, it’s easy. You take your offensive wins and adjust for each position using what we know about the defensive spectrum. Catchers get +1.5 wins, shortstops and center fielders get +1 win, second baseman and third baseman get +0.5 wins, left fielders and right fielders get no position adjustment, first baseman get -0.5 wins, and designated hitters get -1.0 win. This positional scale adjusts for the quality of each player’s peers while also ensuring that we don’t make bad assumptions based on the league average line of any one position during a season. We can say with 100% certainty that it’s harder to play shortstop than to play second base, as almost every second baseman is a shortstop who got moved to the easier position at some point in their life, so we don’t ever want to assume that the average second baseman is better than the average shortstop. If we used league average offensive production by position as the comparing baseline, the values wouldn’t be fixed, which is why I prefer the defensive spectrum adjustments.

Okay, so now you have your position player’s offensive performance relative to league average and adjusted for position. Two steps left before we have our final win value. First, we don’t necessarily want to compare all players to league average in valuation methods. What’s a league average player worth? How easy is it to find one? These aren’t intuitive answers, so average doesn’t make for a great baseline. Instead, we want to compare the players to what we’d expect a team to be able to get from a league minimum player that could be acquired with little to no effort. For instance, yesterday the Mariners signed Greg Norton to a minor league contract. He might make the team, he might not, but guys of his quality are always available. He’s the walking definition of replacement level, so we want to compare our first baseman/designated hitter types to what they’d give us over Greg Norton type players. We know these players are worth about $400,000 (league minimum salary, basically), so it gives us a better starting spot for the final valuation.

The freely available talent guys historically perform, as a group, at a level about two wins below average over the course of the full season. Or, said another way, a team full of these league minimum guys would win about 50 games per season. It’s hard to do much worse than 50-110, even if you’re not trying to contend.

So, in addition to the position adjustments, we add a replacement level adjustment of +2 wins for each position. This means that the adjustment is now +3.5 for catchers, +3 for shortstops and center fielders, +2.5 for second baseman and third baseman, +2 for left fielders and right fielders, +1.5 for for first baseman, and +1 for first baseman. So, if you have a catcher who is a league average hitter, you’d say he’s about +3.5 wins offensively, while the exact same hitter would only be worth +1 win if he was a designated hitter. (Note – this is why moving Jeff Clement to DH/1B is not worth it until the Mariners are 100% certain he really can’t catch in the majors).

Okay, so, after all that, you’ve got your offensive win value compared to replacement level and adjusted for position. However, position players don’t just hit – they field, too. So, we have to build in a defensive performance adjustment. While the general range between the best and worst defenders at a position in any given year is about 50 runs (that is, +25 for good and -25 for bad), we want to be a lot more conservative in projecting defensive performance. So, for these purposes, I’ve set the upper and lower bounds at +15/-15, with most players falling in the -5 to +5 range. In other words, besides the exceptionally great or terrible defenders, this adjustment isn’t going to make a massive impact. Personally, since there is no defensive metric that contains all knowledge yet, I looked at UZR, PMR, RZR, Dewan’s +/- (when available), and eyeballed a realistic estimate based on inputs from all four. Then, you simply divide the runs saved/lost estimate by 10.5 to convert to wins, and add the defensive performance to the offensive performance you’ve already ascertained. And that’s your win value.

Let’s walk through it with Ichiro. I’ve got him projected for a .345 wOBA in 2008 (this is an optimistic projection, honestly, and only a slight step back from his 2007 performance), which the math then converts to +3.09 wins for a center fielder. I add in +0.5 wins for his defensive performance, and that gives us Ichiro as a +3.6 win player compared to a freely available center fielder. I’ve also added +.15 wins for his baserunning prowess, which brings him to +3.75 wins. Or, put another way, if Ichiro got hurt in spring training and was replaced by some combination of Willie Bloomquist and Jeremy Reed for 2008, we’d lower our win expectation for the team by about 3.75 wins.

How much is a win worth? Well, MLB as a whole is paying about $4.4 million per win above replacement in the free agent market, and we know a league minimum player makes about $400,000, so (Win Value * 4.4) + .4 will give you the player’s dollar value in terms of wins added for the upcoming season. Keeping with the Ichiro example, we have him as a 3.75 win player, which is worth about $16.9 million in on field performance. Ichiro just got a contract extension for $17 million per season, which included adjustments for factors beyond his baseball skills, including his marketing appeal. So I’d say the model worked pretty well here, eh?

Because Ichiro’s salary is higher than his dollar per win value, he’s listed on the chart as having a negative value of $100,000. That doesn’t mean we think Ichiro is overpaid or less valuable than Jamie Burke – it simply means that he’s a fairly compensated star, and not a major bargain. It’s rare that teams have bargains at the top of their payroll, though, so that’s not really a knock against Ichiro. However, it does mean that, if given the choice between trading Ichiro and trading Yuniesky Betancourt, I would trade Ichiro – it would be easier to replace his performance with the $17 million that became available than it would to replace Betancourt with the $1.25 million that became available if he was traded.

So, in terms of 2008 asset value (not on field value – please note the distinction), I’m comfortable saying that Yuniesky Betancourt is more valuable than Ichiro. That might sound like heresy, but considering there are only a handful of teams that can afford Ichiro’s contract and nearly every team in baseball would love to have Betancourt on their team, it reflects reality.

Okay, enough setup – let’s get to the table. Here are the position players projected wOBA, their associated win values, their dollar per win value, and the value difference between that and their actual salary. All dollar values are in millions.

Position Player wOBA WAR WAR $ Salary Value
Johjima 0.320 2.29 $10.48 $5.20 $5.28
Sexson 0.335 0.32 $1.81 $14.00 $(12.19)
Lopez 0.305 1.25 $5.90 $0.50 $5.40
Betancourt 0.305 1.62 $7.53 $1.25 $6.28
Beltre 0.335 2.67 $12.15 $12.00 $0.15
Ibanez 0.345 0.75 $3.70 $5.50 $(1.80)
Ichiro 0.345 3.75 $16.90 $17.00 $(0.10)
Wilkerson 0.325 0.76 $3.74 $3.00 $0.74
Vidro 0.325 0.41 $2.20 $6.00 $(3.80)
Reed 0.295 -0.06 $0.14 $0.40 $(0.26)
Morse 0.315 0.05 $0.62 $0.40 $0.22
Bloomquist 0.290 0.00 $0.40 $1.00 $(0.60)
Burke 0.295 0.20 $1.28 $0.40 $0.88
Norton 0.315 0.05 $0.62 $0.40 $0.22

A quick peak at those numbers before we move on to the pitchers.

Betancourt, Johjima, and Lopez, as a group, project to be just a bit below average. The M’s total cost for those three – $6.95 million. There aren’t too many other teams in baseball getting that kind of quality production for next to no money at those up the middle spots. While they’re all flawed players in their own way, they’re also three of the most valuable assets this organization has.

Hey, look, even projecting an offensive step back for Adrian Beltre, he’s still worth his contract. Hey national media – get a clue; the guy is a good player who is worth every dime he’s being paid.

Richie Sexson, even with a significant rebound projection, is still terrible, and his contract is a boat anchor. A +0.3 win player making $14 million at the easiest position on the diamond to find talent? Ouch.

Total wins above replacement for the position players? +14.1 wins. 14 wins out of 14 players who cost about $66 million in payroll? That’s… not good.

Okay, let’s move on to the pitchers. The process here is easier, so I’ll spend a lot less time explaining it. For starters, I developed a defensive-independent line (because, remember, we’re already counting defense in the position players) adjusted for Safeco, which gave me innings pitched and runs allowed. I then compared this to league average (4.60 ERA, park adjusted) and replacement level (5.52 ERA, park adjusted), divided the difference in projected runs allowed by 10.5 to convert to wins, and wham, you have your win value. For relievers, I built in a leverage factor as well, to account for the fact that every run J.J. Putz saves is more valuable than an average run saved.

Why am I using ERA when I have railed against it for so long? Because it’s easy for everyone to understand, and, because it’s already scaled to runs, we don’t need to show FIP or anything more fancy. The inputs I used to get my defensive independent ERA were more sophisticated than just looking at previous ERA and adjusting, so please don’t assume that I’m bowing to conventional pitcher analysis here. I’m just presenting it in the most palatable form I can. Okay? Good. Here’s the pitcher projections.

Pitcher ERA WAR WAR $ Salary Value
Bedard 3.32 4.43 $19.90 $7.00 $12.90
Felix 3.55 3.96 $17.80 $0.50 $17.30
Silva 4.41 2.20 $10.08 $12.00 $(1.92)
Batista 4.57 1.85 $8.56 $9.00 $(0.44)
Washburn 4.73 1.46 $6.83 $10.00 $(3.17)
Ramirez 5.40 0.14 $1.01 $2.75 $(1.74)
Putz 2.31 2.63 $11.97 $3.40 $8.57
Morrow 3.45 1.03 $4.91 $0.40 $4.51
O’Flaherty 4.32 0.25 $1.50 $0.40 $1.10
Green 4.05 0.53 $2.71 $0.40 $2.31
Rowland-Smith 4.20 0.30 $1.74 $0.40 $1.34
Baek 4.20 0.30 $1.74 $0.50 $1.24
Lowe 4.80 -0.04 $0.23 $0.40 $(0.17)

Pitching staff notes.

Bedard is really good. I’m happy to have him on the roster. Go Erik Go.

Felix is one of the biggest assets in baseball. A +4 win player making, essentially, the league minimum? I’ll take two, please.

Silva’s basically projected right at league average for a starter, with Batista a half win worse and Washburn about a win worse. For the last 60% of a rotation, it’s not bad, but man, did it come at a high price. $31 million for 5 wins? Such is the price of trying to build a rotation through free agency.

Horacio Ramirez is projected to pitch 110 innings, but he basically is a stand in for all starts made by guys not in the current rotation. That includes Baek, Feierabend, Rohrbaugh, whoever. Same thing with Mark Lowe’s 30 innings pitched at the bottom of the bullpen – he’s being used as a proxy for the reliever du jours.

J.J. Putz, still awesome. According to this, he’s the fifth most valuable player on the team and the third biggest value.

Brandon Morrow got a pretty nice projection as a setup man. I made it clear that I didn’t think he was cut out to start in 2008, but I think he’s got a good chance to become a quality 8th inning guy this year. That’s still a monumental waste of a #5 overall pick, but hey, at least he’s contributing something.

The pitching staff as a whole adds up to +19 wins above replacement. Thanks to Erik Bedard and projected improvement from Felix, the pitching staff is now the strength of this club.

Now, let’s take a big picture look at the team as a whole.

The team defensive-independent ERA comes out to 4.12. Over 1430 innings, that’s 654 earned runs allowed. Now, remember, we’re dealing with ERA, not RA, so we have to adjust for unearned runs that bump the total up, and this doesn’t account for defense either. Last year, the team allowed 60 unearned runs, and our projections have the team’s defense being worth about -15 runs, so we need to add about 75 runs to that total. That means this analysis projects the M’s to allow about 725 runs.

Offensively, if I plug my projections into a markov chain, I get about 735 runs scored. A team that scores 735 runs and allows 725 runs will post a .507 win%, or a record of 82-80 in a full season. How does this line-up with my WAR estimates?

+19 for the pitching staff and +14 for the position players = +33 for the roster. Since we’ve got replacement level set at about 50 wins, that gives the M’s something like an 83 win roster.

82 wins if you use projected RS/RA. 83 wins if you use WAR. I’d say win values work pretty well.

Tomorrow, I’ll talk about the potential opportunities for this club to beat these projections, and what we need to be rooting for if we’re going to be better than an 82-83 win club.

Comments

130 Responses to “2008 Win Values”

  1. Dave on February 14th, 2008 9:30 am

    And, just to head this off at the pass, my projections for the Mariners are – almost across the board – significantly more optimistic than the published projection systems, such as ZIPS, PECOTA, CHONE, etc…

    PECOTA has Ichiro projected for a .321 wOBA – I have him at .345. ZIPS has Vidro at a .316 wOBA – I have him at .325.

    I didn’t adjust the numbers to make them fit any agenda. I adjusted them to make the team look better.

  2. kenshin on February 14th, 2008 9:34 am

    Dave, 82 wins?1?! Why do you hate teh Mariners soooo Much

    Great article!

    I find it interesting that Wilkerson projects as an actual asset (assuming average defense). Also, do you thinks the M’s will have the patience to give Lopez the full complement of AB’s at 2nd or will they yank him for Willie Cairo at the earliest opportunity?

  3. Tek Jansen on February 14th, 2008 9:37 am

    I am in between classes, so I didn’t give the post a thorough read, but it looks like good stuff. Is there any indication that anyone in the M’s FO, Bavasi or someone else, uses assesments such as these in determining contract offers or trade proposals? My guess, from the AJ/Bedard trade, would be no, but others in this community have better insight and knowledge of how the M’s operate.

  4. Sports on a Schtick on February 14th, 2008 9:54 am

    Best (or worst) Valentine’s gift ever for M’s fans.

  5. julian on February 14th, 2008 9:54 am

    Offensively, if I plug my projections into a markov chain…

    Whoa, intense. Care to provide details?

  6. Gillis27 on February 14th, 2008 10:02 am

    I don’t know why everyone hates Wilkerson so much. I hate the fact that he’s replacing AJ as much as the next person, but we couldn’t do anything to stop that. Maybe Wilkerson is just a favorite of mine, but he just seems like a pretty good deal, and I feel like he has some upside from last season. But I’m highly optimistic and praying the first time I can afford to get the MLB package (growing up in South Dakota doesn’t give you many Seattle games) after graduating college, that the Mariners will shock me and the world.

  7. nadingo on February 14th, 2008 10:03 am

    This is awesome. Thanks for conducting such a thorough analysis and for clearly walking us through the entire process.

    My comment may not contribute substantially to the discussion, but it IS free of spelling errors.

  8. Dave on February 14th, 2008 10:12 am

    Rather than assuming that we hate someone, why don’t you spell out what you disagree with? Do you think a .325 wOBA for Wilkerson is too low? Why do you think he might do better than .325, and what are you basing this on?

    Comments with substance are far more interesting than drive by opinions.

  9. xeifrank on February 14th, 2008 10:12 am

    Nice stuff, thanks for this article. I printed it out and will read it during my lunch break.
    vr, Xei

  10. zDawg on February 14th, 2008 10:15 am

    I think we need to start calling you “The Professor”. While I am aware of the “numbers guys”, I am still trying to learn specifics of how they do it. This article was a great help.

    Someone who looks at the chart and sees Ichiro negative and Morse, for example, positive, would take the wrong assumptions if they did not read the meaning behind the numbers.

    Education is a wonderful thing!

    Thanks.

  11. robbbbbb on February 14th, 2008 10:16 am

    Good article. Thanks, Dave.

    The one part that this analysis doesn’t include is the interaction between the defense and the pitching staff. (I could be mistaken, but that’s my impression on first reading.) A pitching staff geared to putting the ball in play will lean more heavily on the defense, thus magnifying the contribution of defenders. Put five Felixes on the mound and it doesn’t much matter how good your outfielders are. They’ll contribute less because they rarely get to touch the ball. Of course, I’m exaggerating for effect.

    That’s the kind of complimentary building activity that USSM has advocated and I’m in favor of. That said, I don’t think that kind of edge-pursuing is worth +/-2 wins over the course of the season, just as a WAG. But it’d be interesting to see how that works out.

  12. regfairfield on February 14th, 2008 10:16 am

    6 – I used to like Wilkerson but the guy has been pretty terrible three years running. He strikes out too much to hit for a high average, killing his on base percentage, and moving from Texas to Seattle won’t help his power. Even if he replicates last year’s numbers, he’s a below average right fielder, and once Seattle tanks his power numbers, he’ll look even worse.

  13. robbbbbb on February 14th, 2008 10:17 am

    Oh, one quick question: Where does Adam Jones come out in a wOBA evaluation?

  14. jlc on February 14th, 2008 10:18 am

    Great analysis, especially showing Beltre’s worth. Also, thanks for the link to the Pittsburgh paper, which lays out a reasonable numerical analysis very well. It also shows an example of where pure scouting wasn’t working. Gee, you mean there might be a reason to look for better analytical tools?

  15. zDawg on February 14th, 2008 10:21 am

    Also, with the Bedard numbers, I hope Bavasi extends him asap, and not be cheap about it. Bedard’s agent I’m sure also reads this stuff.

    A 5yr/$80m contract extension seems to be a bargain for the M’s.

    Now, about that corner OF defense issue…….

  16. Dave on February 14th, 2008 10:23 am

    You had to ask – I had Jones projected for a .335 wOBA (basically, the same caliber of hitter as Beltre and Sexson), which as a right fielder with +5 defense made him a +2.25 win player. And, to be honest, that’s a very conservative projection for his defense – he could easily be +15 as a right fielder.

    Even if you think he wasn’t going to hit well this year, and you give him a .320 wOBA (worse than Wilkerson and Vidro), his defense would still make him a +1.5 to +2.0 win player.

    By win value, Jones was the 6th best player on the team, behind only Ichiro, Beltre, Johjima, Felix, and Putz. And only Felix had more asset value.

    Yea…

  17. Slippery Elmer on February 14th, 2008 10:25 am

    That was a great article, Dave. I like how you explain your methods and the outcomes in terms a person who’s not a stats major can understand. A+

  18. IHaveALittleProject on February 14th, 2008 10:27 am

    Dave – I really like this kind of logical analysis and explanation. This outcome seems to line up a little more with my gut feel for how the team will perform than the other projections I’ve seen so far – seems like the pitching is good enough to have a lot of 3-5 run games for the opposition, with the offense being able to score that about half the time. Hopefully the days of giving up 6-9 runs by the 4th inning are ending with 2007, we all know the offense has no chance of catching up.

    I still hold out hope that they’ll find a way to jettison Sexson without paying his whole salary, move Raul to 1B (shouldn’t change his value much with the decrease for position change, but negated by removing the awful defense penalty) and putting someone like Corey Patterson in left.

    Also, regarding post #6, I don’t think he was attacking you, Dave. I think he was complimenting your quantitative proof that Wilkerson is more than justified at $3M, and being negative toward the masses who have said “Wilkerson, man that guy’s BA is so low, Adam Jones was the next Beltran, awwww.”

  19. terry on February 14th, 2008 10:29 am

    Great job Dave-thanks!

  20. JasonB on February 14th, 2008 10:32 am

    Question Dave:

    14 wins out of 14 players who cost about $66 million in payroll? That’s… not good.

    Plugging that in to your win value equation gives $67.64M. It seems to me that’s right at average cost… Am I missing something?

  21. planB on February 14th, 2008 10:33 am

    why do catchers get a bigger wins adjustment than SS/CF?

  22. rea on February 14th, 2008 10:33 am

    [Sexson]

  23. klosetfann on February 14th, 2008 10:39 am

    Hooray for mediocrity.

    Great post Dave.

  24. Shizane on February 14th, 2008 10:43 am

    “The formula for wOBA is wOBA = (0.72 BB + 0.75 HBP + 0.90 1B + 0.92 RBOE + 1.24 2B + 1.56 3B + 1.95 HR) / PA.”

    I am assuming RBOE is “reached base on error”….why is this greater than a single? is it because it was supposed to be an out and now the runner is on base?

    Great post!

  25. rlharr on February 14th, 2008 10:48 am

    Saying that Betancourt is more valuable in $/win overlooks the fact that players with a high number of wins are few and far between. While players like Jojima, Betancourt, and Lopez do, indeed, form a good base for a team, the more of them you have, the more you have to focus your win production on the few remaining open positions on your roster. To fill those positions with enough wins to be legitimate contenders you need to spend Ichiro-type money (unless you have Adam Jones…) and you need to find high win players willing to come to your team.

    So I don’t think that Ichiro is so easily replaced for that 17 million.

  26. erich39 on February 14th, 2008 10:49 am

    Dave,
    I am trying to figure out where the offensive value is normalized for home park differences. Are these numbers adjusted for Safeco? Does it even matter for this type of analysis?

    This might be accounted for in the wOBA projection data- what are you using for your offensive inputs on this part of the calculations?

  27. JMHawkins on February 14th, 2008 10:54 am

    14 wins out of 14 players who cost about $66 million in payroll? That’s… not good.

    Plugging that in to your win value equation gives $67.64M. It seems to me that’s right at average cost… Am I missing something?

    That’s league average for Free Agents. League average for all players is more like $2 – $2.5 per win, so the M’s are paying basically twice league average for wins out of their position players. The average for FA is higher because, as Dave puts it, the Free Agency rules are set up to steal money from young players and give it to older ones. For example, Felix is making $500,000 because he’s under team control, and not even arbitration elegible. Once he hits his arbitration years (next year, I think?), he’ll start making more. Then when he hits FA, he’ll really be raking in the dough.

    Offensively, if I plug my projections into a markov chain…

    Whoa, intense. Care to provide details

    By Tango’s The Book for the real explanation, but the nutshell (or nutcase) version is:

    A Markov chain (here) is a statistical model of the chain of events that lead to a run being scored. It shows what the average expected run value of a given offensive result is, so you can plug projections (for hits, doubles, HRs, etc.) into it and it will tell you the average run production you should expect from the player.

  28. naufrago on February 14th, 2008 10:54 am

    This is really a great post. Question:

    So, if you have a catcher who is a league average hitter, you’d say he’s about +3.5 wins offensively, while the exact same hitter would only be worth +1 win if he was a designated hitter. (Note – this is why moving Jeff Clement to DH/1B is not worth it until the Mariners are 100% certain he really can’t catch in the majors).

    If Clement can hit well enough above league average (or better than Sexson/Vidro), wouldn’t that cancel the disadvantage from the position move, from the point of view of improving the team this year?
    Not that it’s necessarily the right thing to do to bring him up, for the long term.

  29. Jed MC on February 14th, 2008 10:56 am

    I’m curious why you decided to use the same # of unearned runs for this the ’08 projections as ’07.

    Even though this may upset the ponies, I think Willie is making more than $0.4. That would make his value negative rather than 0.

    Thanks for making your projection system clear – great job.

  30. JMHawkins on February 14th, 2008 10:56 am

    Er, that should be “buy Tango’s The Book for the real explanation.”

    Buy it, really. It’s cheap for the amount of info.

  31. Nick on February 14th, 2008 10:57 am

    Doesn’t Willy Ballgame make $1M?

  32. BaltimoreDave on February 14th, 2008 10:57 am

    Dave – great post! Thanks!

    A couple questions:

    – Do the positional multipliers used to make the jump from replacement to league average (i.e +3.5 for catchers) take into account the scarcity of finding players freely available at that position, or simply correlate with value on the defensive spectrum?

    – Along the same lines – I assume the $4.4MM per win above replacement is an aggregate figure. What’s the spread from lowest to highest, i.e. are teams paying ~$2MM for an OF or 1B, and ~$6MM for starting pitchers?

    Thanks.

  33. BrianV on February 14th, 2008 10:59 am

    Great post!

    I think it’s silly that our biggest holes (1B, DH, LF) are also the easiest places to find suitable alternatives.

  34. ajdaddy on February 14th, 2008 11:06 am

    Why are you hating on Richie and Ichi and Yuni and the boys? :-) I swear, coming here from NY, the ‘die-hard’ M’s fans make it feel like rooting for a high school team. Then again, I guess M’s brass realizes that, therefore we’ll get the ‘scrappy’ Willie Ballgame having his number retired in about 10 years…
    Super article. Well presented, and well-written as always. Most excellent.

  35. julian on February 14th, 2008 11:07 am

    All right, so our point estimate is that the M’s win 82-83 games… is there some systematic way to work out the error in estimation to get some type of confidence interval? DMZ’s sims do this well, but I’d be interested to know if one can derive similar quantities from a more analytic approach.

  36. Sec 108 on February 14th, 2008 11:13 am

    Great post Dave! I look forward to the follow up tomorrow.

    This projection falls in line with where my gut has been at on this team. I do think that with some smart moves in season we could push this team into the high 80′s again and maybe beyond. Standing Pat will not do it though. It does however appear Bavasi seems ready to pull triggers this year if necessary to make his Bedard investment worth it.

  37. firemane on February 14th, 2008 11:22 am

    [i]Offensively, if I plug my projections into a markov chain, I get about 735 runs scored. A team that scores 735 runs and allows 725 runs will post a .507 win%, or a record of 82-80 in a full season. [/i]

    Great job.

    Question, though.

    The 2007 split: 792-813 (-21)
    The 2008 proj : 735-725 (+10)

    So, the aggregate is stating that going from Guillen to Wilkerson is going to cost the team 57 runs.

    And replacing HoRAM/Weaver (et al) with Bedard and Silva is going to net 88 runs.

    Okay – the pitching adjustment – I can buy that. While my own noodling is a bit more optimistic, that number is definitely in the ballpark.

    What I don’t quite get is how Guillen to Wilkerson ends up costing the team 57 runs. The team had ZERO players that were excessively over career performance, and two that were significantly under it, so the 2007 runs scored wouldn’t seem to me to be wildly over expectation. Ibanez is the only guy where age should be a significant issue.

    By runs created, Guillen supplied 95 in 2007.
    Wilkerson supplied 54 (in only 389 ABs).

    If you use Wilkerson’s last full season (2005 in Washington), which was below his career average AND below his 2007 RC/G average), he produced 84.

    A ten run decline from the offense based on Wilky sounds a lot more reasonable to me than 57. Heck, I might even buy 20. But, if Sexson and Lopez are supposed to bounce from 2007, I’m trying to figure out where all the decline is coming from.

    I suppose the same methodology used with the starting 2007 team might be helpful to see.

  38. Kazinski on February 14th, 2008 11:25 am

    Ok, I can understand factoring in RBOE’s in the wOBA, it seems to be a repeatable skill at least in Ichiro’s case, and probably Willie’s too (though with him it is more on pickoff attempts). But if wOBA is supposed to be a measure of offensive production then it should probably have a factor for sacrifices. Granted it shouldn’t be a huge factor, but show me a team that can consistently get a runner in from 3rd with one out, and I’ll show you a winning team.

  39. Jar on February 14th, 2008 11:30 am

    Dave, great post. Thanks for your hard work.

  40. msb on February 14th, 2008 11:35 am

    therefore we’ll get the ’scrappy’ Willie Ballgame having his number retired in about 10 years…

    fortunately, he doesn’t meet the requirements: “The Mariners plan to retire uniform numbers only very selectively and subject to substantially higher expectations than those applied to the Mariners Hall of Fame. To be eligible to have one’s number retired, the former Mariners should have either a.) been elected to the National Baseball Hall of Fame and been in a Mariners uniform for at least five years, or b.) come close to such election and have spent substantially his entire career with the Mariners. Eligibility shall not commence until after the former player has been voted on once for the National Baseball Hall of Fame, which for all practical purposes, means six years after retirement. In this regard, the Mariners will take into consideration the policy of other American League clubs in retiring uniform numbers.”

  41. timc on February 14th, 2008 11:41 am

    show me a team that can consistently get a runner in from 3rd with one out, and I’ll show you a winning team.

    Show me a team that can consistently get a runner on 3rd with one out, and I’ll show you a winning team.

    In other words, the offensive contribution for that sacrifice comes mainly from the batters who got the hits/walks/RBOE’s that put the team in position to cash in a run even with an out.

  42. Mariner Fan in CO Exile on February 14th, 2008 11:55 am

    Brilliant stuff, Dave, and it will take me part of a day with no work to unpack all the goodness. I trust the assumptions I understand, for the most part.

    You said, “However, it does mean that, if given the choice between trading Ichiro and trading Yuniesky Betancourt, I would trade Ichiro – it would be easier to replace his performance with the $17 million that became available than it would to replace Betancourt with the $1.25 million that became available if he was traded.”

    I feel as if Geoff Baker’s (who I like, by the way) next blog entry having to do with projections has found its topic.

    Seems to me you did something close to this for the team last year, though it may have been sans the projection part (and I don’t think it was this comprehensive). If I am wrong, and you projected the win total for last year based on some similar analysis, can you remind us what you came up with in W/L?

    Alternatively, if you plug last year’s roster into this system, what was the outcome?

  43. studes on February 14th, 2008 12:03 pm

    I think teams are paying more than $4.4 million per free agent win. I’d put the figure over $5 million, as explained in this article:

    http://www.hardballtimes.com/main/article/2007-net-win-shares-value/

    That’s based on last year’s production. This year could be even higher.

  44. Dave on February 14th, 2008 12:05 pm

    Plugging that in to your win value equation gives $67.64M. It seems to me that’s right at average cost… Am I missing something?

    Think of it this way – if you have to pay about $4.5 million per win to buy them on the free market, and you need 40-45 wins to be a real contender, then it would take a payroll of $160 to $180 million to compete if you paid market value to your entire roster.

    The M’s have a $115 million payroll. That means they have to pay about $2.5 to $3 million per win for the roster as a whole.

    why do catchers get a bigger wins adjustment than SS/CF?

    Catchers are more scarce.

    I am assuming RBOE is “reached base on error”….why is this greater than a single? is it because it was supposed to be an out and now the runner is on base?

    Some errors give more than one base. If an outfielder drops a ball in the gap, the runner probably ends up on second, maybe third. If an infielder airmails one into the stands, the guy gets second base by rule.

    Saying that Betancourt is more valuable in $/win overlooks the fact that players with a high number of wins are few and far between.

    I actually agree with you; MLB teams do not. Studies have shown that teams on a linear per win path, not an exponential per win path. They should pay exponentially greater salaries for the top tier of players, but they don’t. This is why A-Rod has actually been relatively underpaid for most of his career, compared to what the middle tier of veterans have been getting.

    I am trying to figure out where the offensive value is normalized for home park differences. Are these numbers adjusted for Safeco? Does it even matter for this type of analysis?

    Yea, I put a park factor into my projections for each player’s performance. I just didn’t spell it out in the post.

    If Clement can hit well enough above league average (or better than Sexson/Vidro), wouldn’t that cancel the disadvantage from the position move, from the point of view of improving the team this year?
    Not that it’s necessarily the right thing to do to bring him up, for the long term.

    Every decision has to balance long term and short term rewards. Yes, if Clement is a better hitter than Vidro, then putting him at DH would improve the team immediately. But by how much? I’d argue not much (I don’t think Clement is major league ready, even as just a hitter), and the long term detriment of having him lose development time behind the plate is not worth the minimal reward.

    Besides, a good organization doesn’t make moves based on “better DH than Vidro”. If the M’s were serious about upgrading that position, Clement’s not the answer – just go get one of the myriad of lumbering sluggers that are always available. Or, better yet, get a real left fielder, move Ibanez to DH, and solve two problems at once.

    I’m curious why you decided to use the same # of unearned runs for this the ‘08 projections as ‘07.

    60 unearned runs isn’t far off the league average per team in recent history. That’s the nice part about doing all the components separately – if you think it should be 50 instead of 60, just lop 10 runs off the total and add a win to the scorecard.

    - Do the positional multipliers used to make the jump from replacement to league average (i.e +3.5 for catchers) take into account the scarcity of finding players freely available at that position, or simply correlate with value on the defensive spectrum?

    They take both scarcity and defensive performance into account.

    - Along the same lines – I assume the $4.4MM per win above replacement is an aggregate figure. What’s the spread from lowest to highest, i.e. are teams paying ~$2MM for an OF or 1B, and ~$6MM for starting pitchers?

    It’s more like $5 million for pitchers and $3.5 million for hitters. Teams are overpaying for pitching right now because they undervalue defense, and they’re giving the money to the guy on the mound instead of the guy with the glove.

    So, the aggregate is stating that going from Guillen to Wilkerson is going to cost the team 57 runs.

    No – there’s absolutely no reason to use last year’s team performance as the basis for this year’s team performance. The players remaining on the roster from last year are still variables – treating them as fixed performances is just wrong.

    The projections have Ichiro, Ibanez, Beltre and Johjima regressing slightly. They have Vidro and Burke taking a significant step back. They have the Guillen to Wilkerson dropoff, as well as the Broussard to Norton dropoff. Yes, they give a bounce to Lopez and Sexson, but the aggregate is still a significant step back in terms of runs scored.

    Don’t use ’07 as the ’08 baseline. It’s bad analysis.

    But if wOBA is supposed to be a measure of offensive production then it should probably have a factor for sacrifices.

    wOBA’s not perfect – it doesn’t include baserunning or double plays either. However, the net effect of the things it excludes is tiny. If you want to toss +0.1 wins onto your favorite player because you think he’s great at bunting, fine – we’re not trying to nail things down to the decimal here.

  45. Dave on February 14th, 2008 12:07 pm

    I think teams are paying more than $4.4 million per free agent win.

    My calculation is $4.4 million per win + $400,000, actually. So, a one win player is worth $4.8 million in this estimate. Based on the numbers I’ve run, this is really close to reality.

  46. BaltimoreDave on February 14th, 2008 12:14 pm

    Studes,

    That’s great stuff. Do you – and Dave C. – see those figures climbing even higher as more teams lock up their young talent through their arbitration and early FA years? To me, that trend will point to fewer players hitting free agency in their peak years, leading to even more over-valuing and higher marginal cost – particularly for starting pitchers and up-the-middle players.

  47. Tek Jansen on February 14th, 2008 12:21 pm

    Dave, should I read from your answer in #44 that you do expect Norton to make the team?

    DMZ should update his post on the the quality, lack thereof, of M’s bench. Yeesh.

  48. Dave on February 14th, 2008 12:24 pm

    Don’t get too caught up in the names of the end of roster guys. Norton, Ramirez, and Lowe could all be subbed out for any number of different names and the projections wouldn’t be significantly different.

    But, to answer the question, I wouldn’t be surprised if Norton makes the team. The team wants to carry a LH pinch-hitter to fill the role Broussard played last year, and they don’t really have any other internal options. I think two of Norton/Cairo/Reed make the team, in addition to Burke/Bloomquist/Morse, and that’s your bench.

  49. bakomariner on February 14th, 2008 12:32 pm

    Dave, re-44, I assume you have Norton making the team out of Spring Training then?

  50. joker on February 14th, 2008 12:32 pm

    “I actually agree with you; MLB teams do not. Studies have shown that teams on a linear per win path, not an exponential per win path. They should pay exponentially greater salaries for the top tier of players, but they don’t. This is why A-Rod has actually been relatively underpaid for most of his career, compared to what the middle tier of veterans have been getting.”

    I’d think regarding the linearity of the payout of scrubs vs. stars would also have to do with the increasing *risk* involved with giving out massive contracts. A-Rod’s hindsight production might be underpaid on the scale, but the potential damage from him blowing out a labrum and never being the same is also exponentially worse than if a Beltre did. In the non-Yankee/Sox division, a 27 million dollar payroll anchor pretty much ends your chances. Period. Sexson bombs? It’s not **as** bad. Does the exponential risk and exponential reward balance out to linear payouts? I dunno, but that has to be a factor.

  51. bakomariner on February 14th, 2008 12:35 pm

    48- I’d be fine with the bench of Norton, Reed, Burke, Willie Boom-Boom and Morse…although Jimerson is a good defender/pinch runner too…maybe Jimerson instead of Reed…they need a right-handed outfielder to spell the three lefties out there…

  52. Desmond on February 14th, 2008 12:44 pm

    Great read, thanks.

  53. lailaihei on February 14th, 2008 12:46 pm

    I appreciate the post, Dave.
    If players were paid exponentially based on wins, what would that formula be like?

  54. Russ on February 14th, 2008 12:59 pm

    Wow…my head asploded.

    Thanks for this Dave. Nice work and great analysis.

  55. Dave on February 14th, 2008 1:01 pm

    An exponential win payout system would go something like this:

    +1 win: $3 million per year
    +2 wins: $7 million per year
    +3 wins: $13 million per year
    +4 wins: $19 million per year
    +5 wins: $26 million per year
    +6 wins: $33 million per year

    Of course, as you’ve probably noticed from the fact that Bedard and Felix are both in the +4 to +4.5 win range, only inner circle hall of famers in their primes get +6 win projections. This is the A-Rod/Pujols category.

  56. derubino on February 14th, 2008 1:13 pm

    Great post. I just had my first frustrating experience with trying to explain to someone why data shows a HBP or single to be more beneficial to an offense than a walk. “He reached first base. It’s all equal.” Gah.

  57. gwangung on February 14th, 2008 1:15 pm

    “He reached first base. It’s all equal.” Gah.

    I hit you in the thigh. I hit you in the groin. It’s all equal.

  58. planB on February 14th, 2008 1:16 pm

    An exponential win payout system would go something like this:

    how is +3 +6 +6 +7 +7 exponential?

  59. Kazinski on February 14th, 2008 1:17 pm

    Timic,
    Show me a team that can consistently get a runner on 3rd with one out, and I’ll show you a winning team.

    Yes, but those teams are few and far between. Which of course means that when a team does get a runner on third with one or fewer outs it is extremely important to be able to get them in. There have been a lot of players over the years, especially in the NL that have made a career off of coming off the bench and launching a lazy fly ball into the OF to score the run from third. It is a talent that managers value enough to spend a roster spot on and it doesn’t seem to be rewarded at all in the wOBA. SF bunts are often the only positive offensive contributions from pitchers in the NL, and it should be accounted for.

    I’d like to see the percentage of a teams runs are scored via getting a runner on second with nobody out, ground out to right side/SF bunt, sacrifice fly, I’ll bet it’s significant. We are all Earl Weaver’s in the fact that we think the 3 run home run is the ideal offensive weapon, but there is nothing wrong with racking up runs from small ball when the opportunity presents.

  60. gwangung on February 14th, 2008 1:19 pm

    I’d like to see the percentage of a teams runs are scored via getting a runner on second with nobody out, ground out to right side/SF bunt, sacrifice fly, I’ll bet it’s significant. We are all Earl Weaver’s in the fact that we think the 3 run home run is the ideal offensive weapon, but there is nothing wrong with racking up runs from small ball when the opportunity presents.

    Uh-oh….I smell several references coming up…

  61. Dave on February 14th, 2008 1:20 pm

    how is +3 +6 +6 +7 +7 exponential?

    Well, the actual numbers I presented are +3, +4, +6, +6, +7, and +7. You can quibble with the term exponential if you want to, since obviously +4 isn’t twice as large as +3, but the point is the same. I’d favor a nonlinear payment method if I was running a club – MLB teams, however, do not. History shows that they do indeed pay on a linear scale.

  62. bat guano on February 14th, 2008 1:20 pm

    Once again, great post Dave. I think I understood it all, except that, try as I might, I fail to see where you worked in the extra wins that the team as a whole is bound to get based upon the fact that Raul is such a great guy, Vidro is a “professional hitter”, J-Rod is a battler, etc., not to mention the veteran grit that new additions Miguel Cairo and Brad Wilkerson bring to the table. Can we assume that tomorrow’s post will address this apparent shortcoming in your analysis?

  63. lailaihei on February 14th, 2008 1:23 pm

    I played around with some formulas in excel and decided that this was pretty close…
    +1 win: $2.6 million per year
    +2 wins: $7 million per year
    +3 wins: $12.3 million per year
    +4 wins: $18.4 million per year
    +5 wins: $25.1 million per year
    +6 wins: $32.4 million per year
    The formula is (W*2)^1.4

  64. mfan on February 14th, 2008 1:27 pm

    Exponential value in relation to contributed wins is a very interesting topic, I think. What is the theoretical reasoning behind that? In one way, it seems as if a run is a run and a win is a win. On the other hand, if you had an entire team of .1 win players, you run out of spots before you’ve accumulated enough wins to do anything. Is the exponential value due to a lower opportunity cost for premium players? That is, you put one A-Rod in and you’ve still got 8 spots left in the lineup to take advantage of, whereas if you put in nine players that total A-Rod’s win production, you don’t have any more fertile soil in which to grow your wins.

  65. CCW on February 14th, 2008 1:30 pm

    I find it interesting that a rigorous analysis like this produces exactly the result that most of us would intuitively expect. Below average offense, below average defense, pretty good starting pitching, pretty good relief pitching, mix and bake for 162 games, and you end up with just about a .500 team.

    The other thing that is missing from the M’s that you would find in many other teams that project to .500 is any upside. The only significant breakout potential this team has is in Felix and Lopez. Meanwhile, there are at least 5 players who very well might fall off a cliff this year – Vidro, Ibanez, Wilkerson, Kenji, Sexson. Also, an injury to any of Betancourt, Ichiro, Beltre, Bedard, Kenji or Felix would crush them.

  66. Jeff Nye on February 14th, 2008 1:34 pm

    mfan, it’s about scarcity.

    Higher win value players should get exponentially more because there just are so few of them.

    If, say, A-Rod is a 10 win player, you can’t replace his production with nine one win players, because you only have nine lineup spots to work with.

    Does that help?

  67. Dave on February 14th, 2008 1:37 pm

    Actually, mfan’s right as well. Every roster spot comes with an opportunity cost, so filling them up with lower tier players means that you can’t fill them with higher tier players. So, along with scarcity, lower tier players are inherently slightly less valuable than their absolute win value due to the opportunity cost.

    It’s both, really.

  68. everett on February 14th, 2008 1:39 pm

    Posts like this are the reason I absolutely love this site. Keep up the great work.

  69. Jeff Nye on February 14th, 2008 1:39 pm

    Yeah, that’s what I was trying to get at with my 10 win/9 lineup spot example, but I didn’t really do a good job of getting the point across.

    I should just stick to talking about ponies.

  70. mfan on February 14th, 2008 1:55 pm

    Bottled farts are pretty scarce, too. That doesn’t mean people pay high prices for them. They would have to have more value than, say, bottled water, to fetch the higher price. What I’m interested in is why VALUE increases exponentially (or some other non-linear way) with performance. Also, if this is true, why isn’t the premium paid? Fewer bidders, perhaps?

  71. Robobobot on February 14th, 2008 2:08 pm

    I cant imagine if we had someone like mark teixeira playing first base. We are so close to being a legitimate team. Then I remember we are rooting for Seattle and there is no hope for championships in this city. No the Seattle Storm doesnt count.

  72. Robobobot on February 14th, 2008 2:10 pm

    And this is my favorite article by the way. Thanks.

  73. AK4Sea on February 14th, 2008 2:12 pm

    Note to self –
    Dave is smarter than you.

    I’m going to keep reading this until it makes sense, and then I’m going to read it once more for good measure.

  74. todda70 on February 14th, 2008 2:20 pm

    This is why I come to this site daily, for articles like this. Thank you Dave. This needs a buy the author a beer button to make it complete.

  75. RaoulDuke37 on February 14th, 2008 2:20 pm

    Good God Dave. Thanks for the stat ride!

  76. planB on February 14th, 2008 2:23 pm

    I didn’t mean to quibble; just didn’t understand that by “exponential” you meant “non-linear”… thanks!

  77. Jeff Nye on February 14th, 2008 2:34 pm

    Not that I really want to go down this particular road, but bottled farts, if they truly are scarce (not an expert on this sort of thing) are scarce only because nobody wants them, so it’s not worth the time and effort to create them.

    If there was a demand, they’d be pretty easy to produce; there is, however, a demand for high win per dollar baseball players, so they’re scarce because they can’t be produced as easily as bottled farts.

    Make sense?

  78. Dayve on February 14th, 2008 2:36 pm

    This site gets nerdier and nerdier each time I visit.

    Keep up the great work!

  79. hans on February 14th, 2008 2:40 pm

    Dave, this is fascinating.

    I would be interested to see this same type of forecast and value assessment done while carrying uncertainties through the calculations. Obviously there is a fair amount of uncertainty in the projections, and the uncertainty is not the same from one player to another. I assume there is also some uncertiainty in correlating wOBA to runs, and runs to wins. It would be interesting to capture this uncertainty and see how it affects the results. One method of doing this might be taking a logic tree approach and assigning weights to various outcomes of branches in the tree based on their judged probability of occurence. The result, a probabilistic distribution of anticipated player value, would be immensely valuable to a franchise or agent.

    Is this what Cleveland is doing already?

  80. hans on February 14th, 2008 2:45 pm

    Darn spelling errors! occurrence

    My proofing skills are lacking today:
    I assume there is also some uncertainty in correlating wOBA to runs, and runs to wins, etc.

  81. JMHawkins on February 14th, 2008 2:48 pm

    A question about RBOE. It’s included here with player projections, indicating it’s a skill. Is it really? Maybe Ichiro’s speed causes hurried throws, but it seems more like random luck for the player and should just be factored into the overall Runs Scored calc the way unearned runs were for pitchers. Not sure it makes any great difference to the calculations here, but we don’t want to call someone underpaid just cause they hit the ball to Chone Figgins a lot…

    Have there been any attempts to detrmine if reaching on an error is indeed a skill?

  82. msb on February 14th, 2008 2:50 pm

    I should just stick to talking about ponies.

    ponies!

  83. anchorjim on February 14th, 2008 3:07 pm

    Dave,

    Great post. One thing that’s been bothering me, though, is the idea that a win is worth $4.4 million over the minimum salary. It seems to me if the market is $3.5 million for a win from a position player and $5.0 million for a win from a pitcher, then for a smart shopper the real market value is $3.5 million for a win. Why go out and buy $4.4 million or $5.0 million wins when you can get $3.5 million wins?

    With that big a market disparity, it seems that it is insane to spend any money in the free agent market on pitchers, with the exception of short-term fliers on players you are hoping to rebound from injury or bad years (like the Colon move USSM was advocating.)

  84. studes on February 14th, 2008 3:24 pm

    Just for fun on the details:

    My calculation is $4.4 million per win + $400,000, actually. So, a one win player is worth $4.8 million in this estimate. Based on the numbers I’ve run, this is really close to reality.

    Actually, mine is too ($380,000 actually). We’re pretty far apart. Have you published your analysis anywhere?

    Studies have shown that teams on a linear per win path, not an exponential per win path.

    Actually, that’s not true. Nate Silver found an exponential relationship, and I believe one exists once you get past the interpretation of long-term contracts.

  85. HamNasty on February 14th, 2008 3:33 pm

    Great post Dave, added to the goodness that is my day so far. Also great analysis on the opportunity cost of each position, maximizing that gives you a winning team. Finding 9 cheap guys that are +1.5 wins isn’t going to get it done.

    One question about the difference between a walk, HBP, and single. Why are they weighted differently? I will agree with whatever reason is given because of the source of it, I would just like to know the reasoning.

  86. planB on February 14th, 2008 3:39 pm

    One question about the difference between a walk, HBP, and single. Why are they weighted differently?
    HBP and singles potentially do more damage than BB. You might have no runners on base, in which case a single and a walk produce the same result. If you have a runner on second and the batter singles, you will have runners on first and third or even score a run; thus a single is potentially better than a walk.

    HBP vs BB is a little different, and I don’t think I can accurately repeat the crucial factor. I think it has something to do with one being totally random and the other being slightly less or more likely in higher-leverage situations.

  87. planB on February 14th, 2008 3:40 pm

    above should read “you will have runners on first and third or even score a run, as opposed to having runners on first and second”

  88. HamNasty on February 14th, 2008 3:42 pm

    85- Thanks and makes sense.

  89. planB on February 14th, 2008 3:44 pm

    also I feel like I’m dissing walks and should clarify, a single is only slightly better than a walk, whereas a walk is waaaayyyyyy better than an out

  90. TomC on February 14th, 2008 3:47 pm

    So, If I understand it correctly, a 50 win team can be bought for about $16 million in payroll (40 man roster x $400K per). Assuming a median pennant contender will have 93 wins, then a team will have to spend $205.2 million on payroll [$16M + (43 * 4.4M)] if they want to do it through free agency or veterans.

    This is payroll territory only the Yankees and Red Sox can approach. Logically, therefore, a consistent pennant team either has to be freakishly lucky or has to have some contribution from their farm system.

    Assuming a $120M payroll, the Mariners have a $104 million pool to pay players over the league minimum. At $4.4 Million per additional win that equates to 23.6 wins above baseline 50. That is 74 wins rounded up.

    To routinely compete at that payroll level, the Mariners will therefore need to either make canny and below market free agent/veteran signings (a skill not heretofore demonstrated) or get something around 19 wins above average from their young guys. That is only slightly less than the boost they will get from the veterans/free agents. The problem is the franchise (i.e. Bavasi and McLaren) does not seem to understand this. They will squander the opportunities for the young guys to develop and trade away the most promising ones for that ever illusory free agent/veteran who will get them to the Promised Land.

  91. mfan on February 14th, 2008 3:49 pm

    77 – I understand that supply side factors will have an influence on the eventual price. However, I’m not interested in the price. I’m interested in the value to teams. Scarcity has nothing to do with demand and value.

  92. planB on February 14th, 2008 3:59 pm

    “Scarcity has nothing to do with demand and value.”

    Hmmm, I don’t know if I can really refute that, but my initial reaction is that can’t be true. It seems as though the three are interrelated… farts are common, and there is no demand, so they are not valuable (yes, bottled farts specifically are scarce, but that seems like a poor analogy, given that bottling them would be easy enough given demand)… if a profession is in demand, professionals of that kind are valued… and if they are scarce (due to difficulty or other reasons), they are even more valuable…

    I don’t know, no specific point really, but can you elaborate? It seems like scarcity not only has something to do with demand and value, it is a primary factor.

  93. Klatz on February 14th, 2008 4:08 pm

    What is the financial payoff on average for making the playoffs? The front office obviously thinks that the 2007 team was better than your analyses have them; they paid dearly for Bedard in the hopes of winning the division.

    Suppose a team was near the threshold for making the playoffs or losing a playoff spot, how much should a team be willing to spend to insure a playoff spot?

  94. xeifrank on February 14th, 2008 4:13 pm

    Ok, I took the time to run the numbers on your Ichiro example to make sure I understand this process correctly. I am coming out with a slightly different number. Could you please show me where I went wrong. :)

    1) wOBA = .345
    => (.345 – .338) = .007

    2) (.007 / 1.15) = 0.006086957

    3) Step 2 * 700 = 4.261

    4) (4.261 / 10.5) = 0.4058

    5) Add positional adjustment (based on spectrum)
    => (0.4058 + 1) = 1.4058

    5) Add positional adjustment (convert from LG Ave to Replacement level)
    => (1.4058 + 2.0) = 3.4058

    6) Add defensive performance
    => (3.4058 + 0.5) = 3.9058

    7) Add in baserunning prowess
    => (3.9058 + .15) = 4.0558

    I get a slightly higher number. Any ideas as to where I went wrong? Thanks!

    Q: If .338 is the AL league average, what is the NL league average for wOBA?

    vr, Xeifrank

  95. mfan on February 14th, 2008 4:27 pm

    92 – You’re confusing value and price. Value and scarcity come into play to determine price. It’s like saying “I’d be willing to pay $.03 for a bottled fart.” The bottled fart has a value to me of $.03. I would then look at the price of the bottled fart and make a determination of whether I’d like to make the purchase. In this case, if price <= $.03, I’d buy it. If not, I wouldn’t. What I’m interested in is how a player’s value changes, all else constant, as their ability to create runs increases and to what degree that relationship is non-linear or exponential. Their prices are a different issue.

    The determination of price then, through the market, takes into account how all the teams value that type of player (or fart, if you prefer) and how many of that type of player there are (that type of player’s scarcity). So, scarcity, in most cases, will influence price, but really has nothing to do with the value teams place on a player like that.

  96. mfan on February 14th, 2008 4:30 pm

    Also, you’re right, bottled farts was a poor choice for the analogy as they really aren’t scarce. They could be produced easily enough I presume.

  97. DoesntCompute on February 14th, 2008 4:47 pm

    mfan, I think you are splitting hairs trying to seperate value and price. Price is the measure, the unit, of how valueable a player is. Each team wants to win the most games they can. A player’s value to a team is determined by how much they help the team win and how hard it is to find other players that can contribute at the same level.

  98. jlc on February 14th, 2008 4:47 pm

    93 (Klatz) – Nate Silver in Baseball Between the Numbers comes up with figures for marginal wins. In one model, he has “an additional regular-season win is worth about $650,000 and a playoff appearance $25 million.”

    Of course, that’s a crude summary of the intricacies he goes into, but it’s a place to start.

  99. MKT on February 14th, 2008 4:57 pm

    44. Yea, I put a park factor into my projections for each player’s performance. I just didn’t spell it out in the post.

    That’s my only complaint with the article. There was all that careful work, carefully spelled out, but I looked in vain for a correction for park effects.

    Turns out you did take park effects into account — that’s good. I can’t fathom leaving it out of the explanation though, given that you explained everything else step by step.

  100. planB on February 14th, 2008 4:57 pm

    Yeah, thanks for the elaboration, but I agree with 98. The whole point of this exercise is attempting to assign a price that more closely resembles (ideally, exactly resembles) actual value. Isn’t it?

  101. planB on February 14th, 2008 4:58 pm

    *agree with 97

  102. The Ghost of Spike Owen on February 14th, 2008 6:46 pm

    What this post really brings home to me is that my resentment at being forced to watch another season with Richie at first has not been misplaced. He really is that bad and that overpaid.

  103. Teej on February 14th, 2008 8:27 pm

    Dave,

    Even though it’s 2008-specific, this would be a very nice addition to the “suggested reading” tab. I can’t tell you how many times I’ve wondered how you’re getting your linear weights numbers. This is a good, highly broken-down summary. Nice work.

    I do have one question:

    If I’m not mistaken, you’re giving players a value relative to replacement level, but within that, you’re using a fielding adjustment that’s relative to league average. Is there any “apples and oranges” problem inherent in that? Is the difference so small within that minor adjustment that it doesn’t really matter?

  104. klosetfann on February 14th, 2008 8:47 pm

    This is totally off-topic, but [deleted, totally off-topic]

  105. thefin190 on February 14th, 2008 9:18 pm

    hmm, I would love to see what these OT people actually write. I am always curious because by the time I get there, either Dave or Derek has deleted it. It always gives me a chuckle to because for some reason people do it despite being deleted everytime.

    Anyways, just wanted to say great post Dave. I feel much smarter just by reading it. And also, this proves that Dave isn’t a pessimist, but simply just telling the facts. The fact that he bumped up values of the players should say something. But also, making a post the next day about how to avoid the mediorce records also shows he has hope in the team.

  106. Dave on February 14th, 2008 9:21 pm

    I am coming out with a slightly different number. Could you please show me where I went wrong.

    There were a couple of adjustments that I made that weren’t spelled out completely in the post. I used a lower league average wOBA (.334) to account for the effects of Safeco Field, then multiplied the offensive win totals by .85 to account for the fact that we don’t project anyone to get 700 PA.

  107. Wilder83 on February 14th, 2008 9:28 pm

    Dave, you really outdid yourself this time. You get an A for effort alone.

    I want to see the exact same analysis for the other 29 teams on my desk by tomorrow morning so we can run everyone’s numbers together in the afternoon.

    Good night and good luck!

    (Seriously, amazing analysis. Someone buy this man some tickets!)

  108. Steve T on February 14th, 2008 9:32 pm

    95, etc.: I think you’re ignoring the real issue, which is, how much would BILL BAVASI pay for these bottled farts? Because he’s shown time and again that he’ll pay more.

  109. Adam S on February 14th, 2008 9:48 pm

    Terrific post. It’s why I read this site. Thanks.

    Since I expect this will make the features list or recommended reading, I figure you’ll want to fix a typo — “+1.5 for for first baseman, and +1 for first baseman. ” Obviously you meant +1 for designated hitters.

    Since you already have formulas and projections around, can we hope for a most overpaid, best bargains in baseball post soon?

  110. Wilder83 on February 14th, 2008 9:52 pm

    Dave, one thing I want to disagree with you about:

    Second base is a more difficult position than shortstop. Most second basemen are converted from shortstop, but that is because they lack the tools (e.g. speed, range, arm) to play shortstop. However, second basemen inherently put themselves in awkward throwing positions that shortstops rarely ever experience. If I were to change any of your numbers, I would at least put second base equal to shortstop on the defensive spectrum.

    The point is certainly debatable and I don’t know how much of a difference the change in numbers would make. One thing is for certain, though, either Betancourt’s value would decrease or Lopez’s value would increase.

    I don’t think my suggestion would change the overall outcome, but I thought I would throw my opinion out there concerning shortstop vs. second base defense.

    Now get back to work, Dave. Your other 29 reports better be on my desk by 9 A.M. in the morning!

    ;)

  111. gwangung on February 14th, 2008 9:53 pm

    I also think this post should be bookmarked as a case study on analyzing a team’s value. The logic, the math and so forth really can be applied across seasons.

  112. Dave on February 14th, 2008 10:18 pm

    Shorstop is a harder position to play than second base, just as third base is harder than first base, and center field is harder than a corner outfield spot. This is undeniably true.

    Think of it this way – the pool of players who could play second base include every second baseman, every shortstop, and a half dozen third baseman. The pool of players who could play shortstop is every shortstop, maybe half a dozen second baseman, and one or two third baseman.

    As such, shortstop gets the larger positional adjustment, because the pool of players is demonstrably smaller. The smaller the pool of players you get to pick from, the less offensive performance you should expect to get from that position.

  113. Sidi on February 14th, 2008 11:05 pm

    Second base is a more difficult position than shortstop. Most second basemen are converted from shortstop, but that is because they lack the tools (e.g. speed, range, arm) to play shortstop. However, second basemen inherently put themselves in awkward throwing positions that shortstops rarely ever experience. If I were to change any of your numbers, I would at least put second base equal to shortstop on the defensive spectrum.

    That conflicts with everything said by traditional analysts and the statheads. There’s a reason shortstop was considered an offensive black hole until the last 20 years at best(and really, A-Rod was the one to shatter that idea).

    But, by and large, converting someone from SS to 2B is much easier than 2B to SS. And SS is probably the second or third most difficult position to move a random player to. First is pitching (although I’d love to see David Eckstein pitch…for the team we’re facing). Second and third have to be SS and catcher, and I’m not sure which would be more difficult to force someone into.

  114. msb on February 14th, 2008 11:05 pm

    may I just say? Felix’ numbers may just go up.

    he looks faaaaaaaabulous.

  115. JMHawkins on February 15th, 2008 12:40 am

    mfan, I think you are splitting hairs trying to seperate value and price. Price is the measure, the unit, of how valueable a player is. Each team wants to win the most games they can. A player’s value to a team is determined by how much they help the team win and how hard it is to find other players that can contribute at the same level.

    I think the separation comes from the cost of player being both the dollars paid in salary and the roster spot consumed. In some sense, the roster spot is even more important than the salary, since in theory, the owners could open up the checkbook to add more dollars, but they absolutely can’t buy more roster spots.

    Hmm, I tried looking at this from the roster spots as currency view. Here’s a table:

    Average Team wins 81 games (ie. is .500)
    RL team wins 50 games
    Playoff team wins 93 games
    Average team is 31 WAR
    Playoff team is 43 WAR
    There are 25 Roster spots
    Average team gets 1.24 WAR per roster spot
    Playoff team gets 1.72 WAR per roster spot
    Playoff team gets 0.48 more WAR per roster spot than avg team

    Round things a bit and we can say the average roster spot in the league produces 1.25 WAR, and playoff teams average +0.5 WAR above that.

    So that sets 1.75 WAR as a benchmark. Any roster spot (ont he 25 man roster) below that is dragging you away from the playoffs and needs to be made up for by someone above that. Every RL player on the roster requires a +3.5 WAR player (or the equivalent) to make up for him. Put another way, for every Willlie Bloomquist on the roster, we need a Felix if we’re going to be a playoff team. If we don’t have a Felix, a Betre and a Johjima together will do.

    It’s too late for me to think through this any more tonight, but I think the key to figuring out the correct non-linear value of wins lies in 1.75 WAR per roster spot.

  116. milendriel on February 15th, 2008 1:50 am

    I think it’s worth pointing out that playing time isn’t equally distributed between the roster spots. You can only have so many players on the field at a time. So the average WAR per roster spot for a playoff team will vary between starting position players and the bench (also between bullpen guys). You’d have to have someone like Beltre on the bench to get 1.75 WAR from that bench spot. Dave has the entire bench’s contribution (5 people) as 0.24 WAR, so I’m guessing a really good 5-man bench probably wouldn’t contribute more than 2-2.5 WAR.

    Slight digression–obviously the M’s bench is pretty sad, but in terms of impact on the standings, there’s probably more than .25 wins to be had if the bench is leveraged correctly (for instance, pinch-running Bloomquist when a stolen base is needed, using Reed as a defensive replacement). So I’m not sure a straight-up WAR valuation for the bench is the way to go, since roles are important. Having 5 Mike Piazza’s on your bench would be nice when you need to pinch-hit, but you’re not going to be able to cover for a poor baserunner or fielder in a high leverage situation.

  117. milendriel on February 15th, 2008 2:12 am

    Also, a question. I summed the “Value” column for the roster and got $42.25. Can this number be interpreted in any way? Does it mean that building an 82-83 win team exclusively through free agency would cost $42.25 more than the M’s are spending?

  118. popsey55 on February 15th, 2008 3:55 am

    Great Article! I agree with almost all of it.

    I got a question for you though. Do you believe that a player’s worth is based completely on his production vs Salary?

    On the field Betancourt may be more valuable than Ichiro; but what about marketing, ticket revenue, merchandise revenue, fan loyalty, media/broadcasting, etc. ???

    Trading a player like Betancourt would not disrupt any of the above mentioned team revenues, but trading the franchise player would cause a snowball effect of decreased revenues, especially if the team didn’t win right away. Clearly swapping franchise players for young stars with tiny salaries generates the greatest value, and I would be just fine with that, but a lot of fans see that as being disloyal to the players.

    I’m actually pulling an all nighter (5:40 am currently here) so forgive me if my post doesnt make sense at all or I forgot something. Again I’m just wondering what you guys think about assigning impossible to calculate intangible values (like the effect on team revenues) to players.

    Clearly Steinbrenner has a HUGE advantage being in the New York market, but the man is not just shelling out money to any super star he finds interesting. The man knows how to add value to the team, on the field, and in his wallet.

  119. msb on February 15th, 2008 8:21 am

    hmm. off the top of my head —Kevin Brown, Randy Johnson, Carl Pavano, Jaret Wright, Raul Mondesi, Jason Giambi, Roger Clemens for half a season …

  120. JMHawkins on February 15th, 2008 10:17 am

    I think it’s worth pointing out that playing time isn’t equally distributed between the roster spots. You can only have so many players on the field at a time. So the average WAR per roster spot for a playoff team will vary between starting position players and the bench (also between bullpen guys). You’d have to have someone like Beltre on the bench to get 1.75 WAR from that bench spot. Dave has the entire bench’s contribution (5 people) as 0.24 WAR, so I’m guessing a really good 5-man bench probably wouldn’t contribute more than 2-2.5 WAR.

    Yep, I was thinking about last night too. If you somehow convinced a +4 WAR guy to play Roberto Petagine for you and pinch hit three times a week, he wouldn’t be a +4 WAR any more. Which rhymes too much if you say it out loud.

    So maybe you divide the roster up into 14 starters (9 lineup spots plus a 5 man rotation), and 11 reserves (the bench plus the bullpen). I’m going to make a wild guess here and say an average bench+bullpen could be worth 5.5 WAR (Dave has ours at just about this, but we have a weak bench, decent middle relief, and JJ Putz, so maybe that works out to average) or 0.5 WAR per reserve spot. That would leave 38 WAR for the 14 starters, or 2.71 per spot.

    Then you have different economies for starters vs reserves. Call 0.5 the PLWARr (Playoff-Level WAR, reserves) and 2.71 the PLWARs (ditto, starters). Now back to the “Betancourt is a bargain, Ichiro is expensive” issue. For every Betancourt (1.65 WAR, or -1.06 PLWARs) you need an Ichiro (3.75, or +1.04 PLWARs) to be a playoff team. Wow.

    That also gives us a way to compare Ichiro and Beltre. Both are essentially washes on the $ per WAR scale, while Ichiro is +1 PLWARs and Beltre is essentially at PLWARs. So the real value of Ichiro is that he allows us to take advantage of the $6.28M bargain that is Betancourt.

    Or, put another way, you need an Ichiro plus a Felix to make up for a Vidro. Assuming everyone else is a Beltre. Yikes, it just highlights that it ain’t easy to win in this league.

  121. joser on February 15th, 2008 11:14 am

    This discussion of value in terms of roster spots, as an additional dimension to value in $, is really interesting (in fact, it might be interesting to actually graph the teams along those two dimensions). It’s probably worth noting that some spots are more fungible than others — your right fielder and left fielder can be interchangable, but one spot on your bench has to be your backup catcher, and so on. So that’s going to modify the calculation as well (in addition to the whole defensive spectrum adjustment — even if your shortstop is enough of an athlete to play in the outfield, you’re not going to put him there except in an emergency especially if he’s never played that spot since little league). This actually reveals more value in utility players like Bloomquist, who can open up a bench spot for someone else, and relievers who can go long vs LOOGies.

  122. tangotiger on February 15th, 2008 11:15 am

    Here’s one simple Markov program:

    http://www.tangotiger.net/markov.html

    John Beamer had a more extensive one in The 2008 Hardball Times Annual.

  123. tangotiger on February 15th, 2008 11:19 am

    I also want to say how incredibly refreshing the rather large number of readers of this site are.

    Not only do you come armed with baseball passion, you are also very willing to see things in a different light. In many boards, you get a group of people that are simply disbelieving in looking at things in any other way. That so many readers are like this is pretty cool.

    (I didn’t mean to be sappy, nor do I wish to derail this thread. Please read, and go on.)

  124. joser on February 15th, 2008 11:56 am

    Well, Dave and DMZ and the mods act as kind of a Maxwell’s Demon for rationality and open-mindedness, closing the gate against the insensible and obdurate and forcing them to go elsewhere. This migration they may be increasing the entropy of those other forums, making them worse, but they certainly make this one better.

  125. Edgar For Pres on February 15th, 2008 12:06 pm

    First off I really liked how you did this and it made using WAR very clear.

    Where do you get the number that 10.5 runs = 1 win? I’m sure this is an approximation and I’ve seen it around before (this site and others). It seems like it could vary a little depending on the RA value of the team and the scoring environment. If anybody has a link to the “original” research showing this I’d appreciate it.

    I would love it if there was some spreadsheet that could automatically do all this. Maybe when we do our annual projections I’ll throw something together unless somebody does it first which would be amazing.

  126. xeifrank on February 15th, 2008 1:52 pm

    Couple more questions. You use 5.52 as the replacement level ERA for the American League, what is the replacement level ERA for the National League?

    You also mentioned that you threw in a leverage adjustment for Putz. Would you care to explain at what point in the calculation you did this and what that adjustment was? And then do you have a smaller leverage index adjustment for the setup man or anybody else in the bullpen and if so, what is it?
    Thanks!

    vr, Xeifrank

  127. mfan on February 15th, 2008 2:17 pm

    100 – PlanB

    I think we’re just talking different languages about the same concept. The price is what you have to pay, the value is what you’d be willing to pay. We don’t assign prices, we assign values and then make purchasing decisions based on our valuation and the price (which is determined in the “market”). I have no qualms about assigning a dollar-based value to players, but if some crazy owner is willing to pay a brazillion dollars for WFB, there is nothing we can do about that. His price is a brazillion dollars regardless of what we want to “assign”. Again, I think you’re confusing price and value… What I think “our goal” is is to properly assign value so that we can look at prices and determine the type of player that looks to be a bargain, based on their value and price. Think of value as the price we’d get in a utopic world where prices actually reflected value. Then, look at the current prices and see where you can find large differences in value and price. That’s where you start to build good, economically sound teams.

  128. MickieB on February 15th, 2008 4:01 pm

    Wilder83- Very very funny. I agree, let’s all chip in and donate tickets.

  129. Tuomas on February 16th, 2008 3:13 pm

    Was A-Rod really the player who killed the idea that shortstop is supposed to be an offensive black hole? I thought it was Ripken and Yount. Ripken put up a 128 OPS+ in ’88. Yount, in his last season at short in 1984, put up a 126. Tony Fernandez had a good run in the mid-80s for Toronto. A-Rod is the best offensive shortstop since Banks and one of the best hitters ever, but did he really revolutionize the position?

  130. eponymous coward on February 16th, 2008 7:46 pm

    129-

    Arky Vaughn, Joe Cronin and Honus Wagner all say “Hi” as well.

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