I have to say, we’ve really loved watching how the Win Value stats we introduced a few weeks ago have taken off around the blogosphere. It was definitely a project we were excited about, and I’m personally quite pleased that you guys have responded to them as well as you have.

I did want to mention a couple of things, though. Yes, win values for pitchers are coming. We’re actively working on making sure we have the most accurate formula we can for calculating them, and because of things unique to pitchers, they simply aren’t as straight forward as hitter win values. There’s the starter/reliever issue, how leverage should be handled, the DH issue between leagues, and the various issues of what is within a pitcher’s ability to control and what could be considered outside influence. When we introduce the pitcher Win Values, though, we’ll definitely walk through them step by step, as we did with the hitters, and try to make them as transparent as possible.

I know that a lot of you are already calculating these win values on your own as well, using various inputs, especially in terms of projecting how teams will fare in 2009. That’s great, and definitely one of the fun things you can do with a Win Value system. This isn’t intended to dampen your enthusiasm for these metrics at all. However (and I know you could feel that word coming), I think there are a few things we should mention in regards to adding up Win Values for a roster.

First off, wins aren’t entirely linear. A player who is projected as a +2 win player won’t have the exact same impact on a 60 win roster that he would on a 95 win roster. There’s diminishing returns that start kicking in, and there are only so many at-bats and high leverage innings to go around.

And, of course, the specifics of the player’s skillset interact with his environment, so a change in environment could change his value. For instance, taking a flyball pitcher and sticking them in front of the worst outfield defense in the world is going to have an impact on the value of a +2 win pitcher. By just adding up individual player win values, we lose these contexts, and they matter.

Also, as many of you have noticed, the position adjustments don’t add up to zero. For each individual player, this isn’t a problem. However, the fact that the AL has a DH and the NL doesn’t makes it an issue when trying to compare teams across leagues. It’s not that hard to adjust for, but it shouldn’t be left out of the discussion if you start doing Win Value evaluations or projections for all 30 major league clubs.

Just a few things to keep in mind as we all bask in the awesomeness of the availability of these metrics.

Right now, as we see a slow moving free agent market causing players to adjust and take deals they wouldn’t have otherwise considered, I begin to wonder who will be left standing without a chair when the music stops. Are we going to see another situation as we did last year, where Kenny Lofton couldn’t find anyone to give him a job despite being a quality player? Probably.

But the train of thought led me to wonder – what on earth happened in regards to Lofton last year?

In ’07, Lofton hit .296/.367/.414, stole 23 bases in 30 attempts, and played above average defense in center field. He racked up 559 plate appearances and was worth 3.1 wins in his age 40 season. He showed no signs of decline, drawing more walks than strikeouts and posting a .118 ISO that was right in line with his career average. He didn’t get any slower, as evidenced by his eight bunt singles and quality baserunning.

His career wOBA was .359. In his final three seasons, it was .368, .345, and .349. From 2005 to 2007, he was worth a total of 8.2 wins, for a dollar value of about $30 million. He made less than half of that.

And then, last winter, he couldn’t find anyone to give him a job. Even if you had decided that he was going to suffer significant decline at age 41 (despite there being no evidence of erosion in his skills), at worst, you could have projected him as a +2 win player for 2008. The absolute worst case scenario would have led a team to expect him to be league average. And no one wanted to employ him?

Put this another way – Torii Hunter got $90 million last winter to be a slightly above average center fielder. His 2005 to 2007 three year win value was 8.5 wins, barely more than Lofton’s total. Yes, he’s younger, so you’d expect him to age better, but that just means that you think Hunter would be half a win or so better than Lofton in 2009. Hunter was paid $16.5 million last season while Lofton sat at home unemployed. In what world does that make any sense?

How Kenny Lofton was forcibly retired by MLB will remain one of the stranger stories of the last year. It will be interesting to see if baseball tosses any other quality players out of the talent pool this winter.

Yesterday, we saw Milton Bradley go to Chicago and Pat Burrell land in Tampa Bay. In general, Cubs fans and Rays fans are happy with their new acquisitions, and both teams are viewing their shiny new hitters as potentially the missing piece that could put them over the top.

You know who can’t be happy about those deals, though? Bobby Abreu, and to a lesser extent, Adam Dunn. The ceiling has been firmly established for offense first corner outfielders (non-Manny Ramirez category), and it’s much lower than it has been in past seasons. There’s not going to be a Carlos Lee type deal out there for Dunn, and Abreu won’t be able to pull in J.D. Drew type money. They’re going to have to take dramatic pay cuts in order to find a team willing to employ them.

The teams that were expected to be in the market for power bats were Tampa Bay, Oakland, Seattle, Anaheim, the Yankees, the Cubs, Atlanta, and maybe Washington. The Rays got Burrell, the A’s got Matt Holiday and Jason Giambi, the Mariners signed Russell Branyan, the Yankees signed Mark Teixeira, and the Cubs signed Bradley. That leaves the Angels, Nationals, and maybe the Mariners as teams who could potentially still be interested in a left-handed power hitter with questionable defense.

Washington seems to make the most sense for Adam Dunn – he knows Jim Bowden from his days with the Reds, his best friend in the world is Austin Kearns, and the Nats are reportedly looking for a first baseman, since they don’t want to count on either Nick Johnson or Dmitri Young for 2009 and beyond. Dunn has experience at first base and would probably be willing to move there for a full time job and a decent contract. But considering that the rumored offer from Washington for Bradley was 3/30, it’s unlikely that they’d go higher than that for Dunn, especially in a market where he doesn’t have too many other obvious fits. Would Dunn settle for a contract in the 2/20 range? He might have to, because while he is younger than Burrell, they are comparable players, and his options are quickly dwindling.

Let’s assume Dunn does end up in Washington. That leaves Abreu trying to convince the Braves, Angels, and Mariners to start a bidding war for his services. None of them seem particularly interested, though. The Angels brought back Juan Rivera, which gives them four players to rotate through the OF/DH spots. The Mariners are bagain shopping, picking up the likes of Branyan and Chris Shelton, and kicking the tires on Jerry Hairston. Neither of them seem likely to offer up a high eight figures deal for an aging outfielder. That leaves the Braves as the best fit for Abreu – they know him from his time in Philadelphia, they’ve got a narrow window of contention, and they’ve got the payroll room to pay him. But with some intriguing outfield prospects coming, they’re not going to want to give out a long term deal. Abreu might be forced to settle for a one year contract from Atlanta if he wants anything close to $10 million for the 2009 season, which still represents a 33% paycut over his 2008 salary.

2/20 for Adam Dunn and 1/10 for Bobby Abreu? At the end of the season, those guys would have scoffed at numbers like that, but that might be the best case scenario for Dunn and Abreu now.

Since the season ended, most people have assumed that Jason Giambi was going to end up back in Oakland. They needed some power in their line-up, even after the Matt Holiday acquisition, and Giambi enjoyed his greatest success as a player during his first stint in the Bay Area. The steroids stuff from a few years ago made him something of a pariah among many teams and fans, and his near replacement level performance in 2007 didn’t help his image at all. There just weren’t many teams interested in Giambi, so the presumption was that he’d have to take pretty much whatever Billy Beane offered him.

After seeing Buster Olney’s report of the terms of the deal that seems to be pretty much what happened. Here’s how the deal would break down in terms of valuing Giambi as a player if the rumored terms are true.

$5.25 million base salary in 2009, $1.25 million buyout of 2010 option or $4 million base salary in 2010.

Based on a $4.5 million per win estimate of the going rate for free agents, that would value Giambi as a 1.45 win player for 2009. However, the low salary base (with incentives, surely) for 2010 makes the buyout pretty unlikely to be exercised unless Giambi pulls an Andruw Jones. In reality, the deal is probably more like $11 million over two years, with an out clause for the A’s if Giambi is just unbelievably awful. That values Giambi at something closer to a 1.2 win player.

Giambi’s actual win values, by year, the last three years:

2006: 3.4
2007: 0.5
2008: 2.6

That’s a weighted average of 2.1 wins per year, and he missed half of the ’07 season. His new deal values him at nearly half of his three year weighted average win value. Even factoring in age related decline and a move to DH, that’s some pretty serious discounting. There’s almost no downside to this deal for the A’s – they picked up a +1.5 to +2 win player for 75 cents on the dollar, and if he bombs, it has no long term repercussions.

With Holliday and Giambi joining the organization, the A’s have significantly improved their offense for 2009. The question will be sorting out all the at-bats for the various 1B/DH types, but the depth makes it much more likely that Oakland has an offense that can score some runs next year. The A.L. West continues to tighten.

According to Ken Rosenthal, the Rays are close to finalizing a two year, $16 million contract with Pat Burrell. He’ll fill their hole at DH and give them a right-handed power bat to fit into the middle of their line-up and provide some offensive depth.

For Burrell, I’m pretty sure this is not what he had in mind heading into the winter. He made $14 million last season in the final year of a six year, $50 million contract, so he’s taking about a 43 percent pay cut and handing in his outfielder’s glove in order to get a full time job with a contender. The reshaping of this free agent economy is certainly going to be humbling for some players, especially outfielders with poor defensive abilities.

From Tampa’s perspective, they have to be pretty happy with how things have worked out. Always on a budget, they couldn’t break the bank for a true all-star caliber player, but needed to add another quality position player to try to stay ahead of Boston and New York. Is Burrell that player?

Over the last four years, he’s been pretty consistent offensively, posting park adjusted batting of +28, +21, +26, and +25 runs. Despite hot and cold streaks, Burrell’s generated similar offensive value in each of the last four seasons. By signing him up to DH, the Rays are removing the defensive penalty he brought to the field. It’s really the best fit for Burrell at this point in his career, and makes him fairly easy to evaluate going forward, as we won’t have to deal with the uncertainty surrounding defensive performance.

If we project Burrell as a +18 run hitter compared to league average (as Marcel does), that’s almost an exact fit for the -17.5 run position adjustment that comes with being a full time DH. Even with expected age related decline, Burrell’s going to be an average major league player. He should be worth right around two wins above a replacement level player.

Those two wins cost the Rays $8 million per year, or $4 million per win. This just continues the trend we’ve seen this off-season, as this shapes up to be the best buyer’s market in recent history. Based on his +2 win projection, we’d have expected Burrell to get something like 3 years and $30 million if this was a normal off-season, but the economy forced him to sign for a discount in order to solidify a job with a winner.

For only about $5 million more than they spent on Cliff Floyd in 2008, the Rays are able to add a power/patience bat to their line-up that should fit in well with their offense for 2009 and 2010. With the DH hole filled, it’s fair to say that the Rays have an average or better player at every single position on their roster right now. A very good team just got a little bit better.

Before moving on, I wanted to do one more post on the Win Value series we covered last week, emphasizing a few points that may have got lost in the shuffle. While we think these win value stats are a tremendous addition to the site and should be extremely useful, we also want to maintain integrity in how we talk about them and the ways they are used. So, with that said, here’s some things to keep in mind.

All catchers are assumed to be average defensively.

This is obviously not true, but in terms of quantifying catcher defense, we’re just not there yet. We have a pretty good idea that most major league catchers fall somewhere between -10 runs and +10 runs, based on their ability to block balls in the dirt, control the running game, and so forth. So, as a general guideline, if you think the catcher is awful defensively (maybe Ryan Doumit is a good example), knock one win off. If you think he’s just below average (Ramon Hernandez?), knock off half a win. If you think he’s above average (Kurt Suzuki?), add half a win. if you think he’s outstanding (Joe Mauer?), add a full win.

There are a few things not included.

The only aspect of baserunning that is currently included is SB/CS. Throwing arms and turning double plays are currently not included in the fielding evaluations. In general, no one’s going to be more than +5 or -5 in these minor areas, but for guys at the extremes, it could be half a win or so.

We’re measuring past performance, not necessarily true talent level.

Just because Jayson Werth put up a +5 win season in 2008 does not mean that we’re saying he is a +5 win player. It is pretty common for people to play above or below their actual level of abilities. Don’t get too wrapped up over a single season performance.

The leagues are not necessarily even in talent level in every year.

For recent years, there’s a good bit of evidence that the AL has been better than the NL. It may even be slightly more accurate to use league specific replacement level adjustments, especially for the ’05-’07 time period. We’ll work on trying to quantify the differences in leagues going all the way back to ’02 so that we could potentially include the league differences later on.

The dollars to win adjustments aren’t super easy to calculate.

Reasonable people can differ on what the market value of a marginal win was in different years. I think my methods work pretty well, but they aren’t perfect. The margin for error is probably around $500,000 in each direction for recent years.

Most importantly, we’re not claiming decimal point accuracy with these win values.

If someone is listed at 4.8 wins, and someone else is listed at 4.3 wins, there could be enough mitigating factors that the lower win value player was actually more valuable. When the differences are less than one win, don’t be dogmatic about your conclusions. I generally use whole number win values anyway, and I think we’re best served saying that we’re aware of some of the things we haven’t covered yet, and that there’s some wiggle room in the numbers.

Make no mistake – I think these are the best single value metric for evaluating a player on the internet today. I’d use a player’s Win Value number to describe his total performance before I used anything else. But we’re not saying they’re perfect or that they can’t be improved upon. We’ll keep working on getting better data, figuring things out, and making them even more accurate in the future. Right now, they’re great. Hopefully, by this time next year, they’re even better.

Over the first five parts of this series, we’ve discussed all the components of what makes up a Win Value. Today, we tackle the conversion of that win value into a dollar value.

First off, a little background. Since we’ve set replacement level at around a .300 win% (or 48 wins per team), that means that there are about 1,000 marginal wins in a major league season. All 30 teams are fighting over these 1,000 wins, each trying to get more than 45 or so to get them in the playoffs.

Every dime a major league team spends above the major league minimum is theoretically spent in an effort to buy as many of those 1,000 wins as possible. A major league team’s minimum payroll is about $12 million, so MLB as a whole has a floor of $360 million in salary per season. Total payroll for MLB teams in 2008 was reported at $2.67 billion. That means that major league teams spent $2.31 billion to try to buy their share of those 1,000 marginal wins. Basic division tells us that the cost of a win in MLB salary was $2.31 million per win for 2008.

However, a huge share of those wins were created by players whose salaries were not determined by a free market system. Every player with zero to six years of service time had an artificially depressed salary due to not being able to qualify for free agency. As well, most players who signed long term contracts that bought out some of their arbitration and free agent years had salaries below market value as well – they had traded some potential cash for the security of a deal several years ago. The amount of money that teams are paying per win for their cost controlled players is far less than the $2.31 million league average.

So, the market of wins available for purchase doesn’t total 1,000. A significant batch of MLB players simply aren’t available for acquisition at any given time. The Cardinals aren’t trading Albert Pujols. The Mariners aren’t trading Felix Hernandez. The Rays aren’t trading Evan Longoria. The wins that these players generate are not for sale.

Who is available? Obviously, players who qualify for free agency in a given season are available. Also, there are players traded from one club to another, so those players are also available for the right price. But what is the right price?

In general, we can say that the market price of a win is the mean of the dollars per win handed out to free agents in any given year. If you approached CC Sabathia this winter and offered him $12.65 million because he was a 5.5 win pitcher and the league average cost per win is $2.3 million, you wouldn’t have gotten very far. If you want to compete in the market for available wins, you have to know what the going rate for a win is, and the easiest way to calculate that is to look at the free agent market. Let’s look back at 2007, for instance.

90 free agents signed major league contracts last winter, ranging from Alex’s Rodriguez $275 million deal to Josh Towers‘ $400,000 contract with the Rockies. The sum of those 90 contracts paid out $396 million in 2008. To figure out what the average cost per win of a 2007 free agent was, though, we need to know how many wins that group was worth.

To calculate this, I did a three year weighted average of their win values, then multiplied that value by .95 to factor in aging and estimate what teams considered considered a player’s true talent win rate for 2008. In total, I came up with 88 wins, or $4.5 million per win. That’s what major league teams were paying for a marginal win last winter, so for 2008, that’s a players dollar per win value as listed on the site. I re-did this for all years going back to 2002, and the dollars per win for each are as follows:

2002 – $2.6m / win
2003 – $2.8m / win
2004 – $3.1m / win
2005 – $3.4m / win
2006 – $3.7m / win
2007 – $4.1m / win
2008 – $4.5m / win

Now, I know there’s some sentiment that teams don’t pay for wins linearly, because a six win player is worth more than three two win players. While I agree with this in theory, major league teams just don’t operate this way. If you just look at the dollar per win costs for the multi-year contracts handed out to hitters last year, the cost per win was $4.3 million for guys with an average win value of 4.4 wins per player. Alex Rodriguez signed for about $3.8 million per win last year. Teams just don’t pay exponentially more for higher win value players than they do for average and below players. You could argue that they should (and I would probably agree), but they don’t. The dollar per win scale is linear.

This afternoon, we’ll look at the opportunities that are presented to teams due the linear nature of dollar per win, and how the smart teams are exploiting this to their advantage.

For the last couple of days, we’ve been talking about the different components of the Win Value system. However, you may have noticed that we’ve been dealing entirely in runs. wRAA, UZR, the position adjustment, and replacement level are all expressed in terms of runs, not wins, and that’s why the sum of those numbers is categorized under Value Runs.

So, if all of our metrics deal in terms of runs, but we want to get to wins, we need to know how many runs it takes to make a win. This is actually quite a bit easier than it sounds, thanks to the pythag formula for expected win-loss records. For those not aware of pythag, you can get a good estimate of a team’s winning percentage by dividing the square of runs scored by the sum of the square of runs scored and the square of runs allowed. Or, in formula terms:

RS^2/(RS^2 + RA^2) = Pythagorean Winning Percentage. So, if a team scored 775 runs and allowed 775 runs, they’d have a .500 Pythag Win%, or 81 wins and 81 losses – even amounts of runs scored and runs allowed should lead to something like an even record. Not as scary as it sounds.

What happens if we subtract 10 runs from the runs scored column, so that we now have a 765 RS/775 RA team? Pythag spits out a .4935 win%, and .4935 * 162 = 79.95 wins. So, instead of 81 wins, you’re now expected to win just barely less than 80. By subtracting 10 runs, you lost a fraction more than one win.

Same thing happens if you add 10 runs to the runs allowed column – 775/785 RS/RA spits out .4935 as well. How about if you add 10 runs, so we have a 785/775 team? .5064 win%, or 82.03 wins. Again, 10 runs added equals one win gained.

For an even more precise look at the issue, you could use the improved PythagenPat method, which places a better exponent in the calculation, but the conclusion is going to be the same; 10 runs = 1 win.

So, when you see value expressed in runs, but you want it in wins, just divide by 10. Likewise, if you see it in wins but you want it in runs, multiply by 10. It might sound like a cheap trick, but it’s reality – 10 runs add up to a win. A +20 run player is a +2 win player.

Okay, so, in the first three parts, we’ve covered Batting, Fielding, and Position Adjustments, and hopefully you’ve been able to see how we’re arriving at the values used for each component. By combining those three parts, you get runs above or below average. However, as I mentioned at the end of the last post, we don’t really know how much average costs, but we do know how much replacement level costs, so we prefer to value players above replacement, as that gives us a fixed baseline of $400,000 in salary – the league minimum.

For a great read on replacement level, check out this article by Sean Smith. In it, he uses his CHONE projections to figure out the offensive production that a team could expect from players not projected to be good enough to make a major league roster next year. These guys have fallen into that Four-A category, where they show more ability than your average Triple-A veteran but not enough to hold down a major league job. They’re usually available every winter as minor league free agents, via the Rule 5 draft, or as cheap trade acquisitions where a team can acquire one of these players without giving up any real talent in return.

As Sean showed in his article, and has been shown elsewhere, the expected value of a replacement level player is about negative 20 runs per 600 PA. Or, to phrase it a bit differently, if you lost a league average player and replaced him with a freely available guy, you’d lose about two wins. That’s why the replacement level calculation in our Win Value formula is 20/600*PA. If you get exactly 600 PA during a season, your replacement level adjustment will be +20 runs. If you get 700 PA, your replacement level adjustment will be +23.3 runs. The more you play, the higher the replacement level adjustment, because you’re filling a larger quantity of playing time and that chunk won’t need to be filled by anyone else.

The replacement level calculation serves to do two things in our calculations – adjust the scale so that the baseline value is $400,000 at zero wins, and rewards players who stay on the field. For instance, Chipper Jones was outstanding in ’08, posting a .446 wOBA and a +4.9 UZR. However, he only racked up 534 PA, so the Braves had to give approximately 66 PA to people who weren’t Chipper Jones. Therefore, Chipper’s replacement level adjustment is just 17.8 runs – we presume that the folks who filled in for him were about 2.2 runs below average in those 66 PA, and that comes out of Chipper’s replacement level adjustment. Players who stay healthy and can take the field everyday have value above and beyond their rate statistics, and scaling the replacement level adjustment to plate appearances rewards them for that extra value.

If you’re having a tough time visualizing what a replacement level player looks like, there’s probably not a better example in baseball than Willie Bloomquist. Over the last three years, he’s racked up 644 PA – just barely more than one season’s worth – and accumulated the following totals:

-16 batting, -3.8 fielding, +0.9 position adjustment = -18.9 runs below average. He’s not a very good hitter, but he can play a bunch of positions, run the bases okay, and doesn’t cost much. He is, essentially, the poster boy for replacement players. By adding in the replacement level adjustment, we’re simply adjusting from saying that Chase Utley is +58 runs above average to +78 runs above Willie Bloomquist. And, since we know that players of Bloomquist’s quality are available for $400,000, we can then value Utley’s performance based off that baseline.

So, that’s wRAA+UZR+Position+Replacement. It comes out as Value Runs, and tells you how many runs above a replacement level player each position player was. Tomorrow, we’ll talk about the runs to wins conversion and the wins to dollars conversion.

Continuing on with our series explaining win values, today, we get back to positional adjustments. We spent a lot of time talking about them the last few weeks, so if you haven’t read those articles, I’d suggest catching up first. A basic summary of the need for position adjustments follows below, for those who want a short version.

Since we started off with wRAA (which is offensive runs above or below league average) and UZR (which is defensive runs above or below league average at a specific position), we need to calibrate the scale to make up for the fact that some positions are significantly harder to play than others. It is much harder to find a +5 SS than it is to find a +5 2B, and we need to represent that in the Win Value system. That’s what the position adjustments are there for.

Traditionally, offensive position adjustments have been popular, which aligns the positions by adjusting on the basis of the difference in offensive runs. However, due to the variability in offensive performance from year to year, that can lead to miscalculations, such as believing that an NL 2B and an NL SS were equal in 2008 because they had the same batting line. Clearly, shortstops are better defenders than second baseman, and we have to reflect this in their value.

That’s why we prefer a defensive position adjustment. The position adjustment scale we use is as follows:

Catcher: +12.5 runs (all are per 162 defensive games)
First Base: -12.5 runs
Second Base: +2.5 runs
Third Base: +2.5 runs
Shortstop: +7.5 runs
Left Field: -7.5 runs
Center Field: +2.5 runs
Right Field: -7.5 runs
Designated Hitter: -17.5 runs

To read more about how these were arrived at, check out these threads at The Book blog.

The position adjustments are then scaled to match the games played at each position for a particular player. This way, players that spend time at multiple positions get a hybrid adjustment based on their playing time at the respective spots.

Once you add the wRAA, UZR, and position adjustment together, you have the sum of a player’s value above or below league average. If we used Chase Utley as an example, he gets 37.1 wRAA, 19.2 UZR, and 2.3 Position Adjustment for a total of +58.6 runs. In 2008, Chase Utley was 58.6 runs better than a league average player. If you want to start handing out credit for the World Series title in Philly, give him the most, because that’s outstanding.

However, now we have value above or below average, but what is average worth? Clearly, it’s worth more than zero, as teams pay significant cash for league average players every winter, and a team full of league average players would win 81 games and generate positive revenue for their franchise. But, in terms of dollar values, we don’t have a fixed baseline for what a league average player is paid.

However, you know what we do have a fixed baseline for? The league minimum player. MLB has set $400,000 as the least any player can get paid, so we know that a player who is completely replaceable is worth $400,000. That makes replacement level a good target to calculate value off of. So, this afternoon, we’ll talk about replacement level and how that is defined.