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.


130 Responses to “2008 Win Values”

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

    *agree with 97

  2. 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.

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


    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?

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

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

  5. 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.

  6. 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.

  7. 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!)

  8. 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.

  9. 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?

  10. 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!


  11. 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.

  12. 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.

  13. 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.

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

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

    he looks faaaaaaaabulous.

  15. 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.

  16. 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.

  17. 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?

  18. 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.

  19. 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 …

  20. 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.

  21. 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.

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

    Here’s one simple Markov program:


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

  23. 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.)

  24. 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.

  25. 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.

  26. 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?

    vr, Xeifrank

  27. 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.

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

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

  29. 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?

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


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

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