Batting Leadoff: Marginal Win Value and Dollars Per Win

This post originally appeared on Batting Leadoff. Batting Leadoff is a website dedicated to providing readers with premium baseball content. Posts from the site will appear regularly on the Sports Business Society Blog (view the information in the sidebar for updated information).

It is quite natural to spawn opinions on offseason moves that eventually manifest into conclusions that the general manager of Team A is a moron for signing Player B to Contract X. No matter our qualifications or level of knowledge of baseball, there are multiple times per winter us fans are left with the notion that yes, we absolutely have to be smarter than the GM of Team A.

What we do not take into consideration is that within every front office in Major League Baseball, there are dozens of bright analytical and scouting minds who are far more conversant than us. Their scouts can see how one player’s bat speed may be diminishing. Their analytical department knows how a free agent’s skill set will fit in their ballpark far better than we do. Their doctors have medical reports on players that we could only dream of seeing.

The information accessible to these bright minds is far more than we can find on MLB.TV, Fangraphs, and Baseball-Reference. Essentially, front offices make educated decisions dependent on a wealth of knowledge that the public lacks.

There are a multitude of factors that drive every transaction. The Mariners did not invest $240 million dollars in Robinson Cano because they thought he was a pretty damn good second baseman. Inside that decision came scouting insight, statistical analysis, and economic evaluation that indicated it was sensible for the Mariners to blow every single team in the market out of the water.

Of course, there are rudimentary differences in each front office’s valuation of every player. If each team valued every player equally, the market would be far different. Some teams put more weight into the scouting aspect of evaluations, while others rely on regression models to project players forward. Another large factor that is not touched on nearly enough is the marginal value that each player provides his employer.

For a number of years, analysts have looked at the contracts signed by free agents, quantified the value of the free agent, then depicted how much money the market demanded for a single Win Above Replacement ($/WAR). This number has risen annually for the past decade for reasons such as inflation and an influx of TV money among others.

The number for this off-season’s contracts was generally pegged at $6 to $7 million dollars per win. That is to say that if a team is going to sign a player who has consistently posted 2 WAR seasons (league-average), the market values him at around $13 million per season. These numbers are pretty consistent with how the market has played out so far.

However, the money per win valuation has numerous caveats that must be considered. First of all, $/WAR is not a good way to project salaries among elite players. As godly as he is, it’s unlikely that the 10-WAR man Mike Trout would be paid $70 million per year if he were on the open market. Robinson Cano posted a 6 WAR season in 2013, meaning if the market always held true, he would have found a contract that paid him an AAV of around $40 million dollars.

The second caveat is that while WAR is an extremely useful and powerful tool to evaluate players, front offices look far beyond that metric while putting a dollar sign on the value of a player. Another caveat, one which I find most interesting, is that a win is worth a different amount to every team. This in a nutshell is marginal win value.

The basic concept of marginal win value goes like this: a team filled with AAA players wins about 47 or so games in the major leagues while costing around $12 million dollars. From 47 wins on, the team is buying wins in hopes of accruing more revenue from being good. However, if the team buys one win at the market rate of $7 million dollars, the revenue added from increasing their win total from 47 to 48 is worth far less than $7 million dollars. From 47 wins on, it takes marginal analysis to decide if buying more wins is profitable for the team.

A single win carries far different value for teams who are on opposite sides of the spectrum. Several extremely smart people such as Phil Birnbaum and Nate Silver have looked at the marginal win value curve, creating the following graph to depict its true worth.

(Click to enlarge)





This graph is from 2005, so it is fairly outdated. In 2005, Silver found a win to cost around $2 million on the open market. To adjust to inflated contracts and revenue, we would simply raise the graph’s Y value to equate it to today’s contracts, keeping the shape consistent. The graph shows that it is an inefficient allocation of money to keep buying wins from around 60-85. This makes sense because barring a team slipping in one of the wildcard slots, it’s unlikely a team makes the playoffs with 85 wins.

However, the theory states that at 86 wins, the value of the revenue a team makes from extra ticket sales or whatever revenues are driven by playoff excitement begins to exceed the money you are paying for a win. Looking at the graph, you can see that you acquire surplus value buying wins from 85-95 because the marginal value is higher than the $2 million dollar cost of a win in 2005. From 95 on, the value decreases due to the fact that you likely have the division title in the bag and spending money to win upwards of 100 games is rather gluttonous.

There are uncertainties when using marginal win value to dictate your offseason. It is extremely hard to project how many wins a player is worth, especially with the volatility of pitchers or injury-risk players. That, along with other possible variations, makes it extremely difficult for a team to forecast its win totals while entering a season.

The standard deviation between true talent and performance is about six wins in the best projection models, meaning that a team with the talent of an 81 win team could win anywhere from 75 to 87 games. That being said, marginal win value is absolutely something that front offices take into account when deciding if it is profitable to keep spending on their club.

In Part 2, I am going to take a look at some of the most questionable moves that were made this offseason, and try to find each front office’s motives behind the moves. While marginal win value is going to play a large role in this exercise, I’m also going to use a number of other explanations to decipher why these transactions were made.

A lot of this piece was made possible by the fantastic work of people such as Dave Cameron, Lewie Pollis, Phil Birnbaum, and Nate Silver. These articles are fantastic reads and quite informative. Special thanks to Matt Swartz for the correspondence and help in equating Silver’s 2005 graph to the inflated contracts of this offseason. 

This post originally appeared on Batting Leadoff. Batting Leadoff is a website dedicated to providing readers with premium baseball content. Posts from the site will appear regularly on the Sports Business Society Blog (view the information in the sidebar for updated information).

Daniel Schoenfeld is a senior in high school in Evanston, Illinois. He plans on studying business economics while pitching in college next year. He is interested in scouting and statistical analysis, and hopes to use Batting Leadoff as a platform to break into the industry. He’s currently working on a large scale project detailing the indicative factors involved in injury projection of pitchers and is always willing to learn and share. Contact him at dschon711@aol.com and follow him @DanielSchoe. 

The Weekly Rant: Arbitration and Bullpen Construction

There has been a ton of recent discussion about teams over/undervaluing closers. Most of this comes from the high-profile bullpen additions made by the Tampa Bay Rays and the Oakland A's. Some have asked if the Rays/A's know something we don't know about relief pitching. Others have concluded that these teams were paying at or slightly below market rate for players that could readily improve their rosters.

That's a pretty reasonable conclusion to reach if you look at the acquisitions in isolation. Grant Balfour on a 2-year, $12 MM deal is rock solid with his projected WAR. Jim Johnson on a 1-year $10 MM contract in exchange for Jemile Weeks? Seems reasonable. A couple of duds for set-up men? That's what win-curve sensitive teams should do when they can't upgrade their roster easily at other positions, right?

I think all of that is logical, and in itself could explain these uncharacteristic relief expenditures. But I also think something else could be going on here. We should probably take another factor into consideration when considering these deals. Here's what Matt Swartz wrote on MLBTradeRumors about arbitration eligible relievers:

Relievers get paid by role. An elite closer with a history of saves gets paid far more than a set-up man, who gets paid far more than a middle reliever, even with similar performances. Andrew Bailey is slotted for $3.5MM this winter, but turn his 24 saves into 24 holds and he’d only get $2.1MM with the same elite ERA of 2.07. Even with his 51 career saves prior to 2011 still on his record. Take all those saves and holds away, and he’d get under $1.0M with 174 career IP of a 2.07 ERA.

According to his model (This was written in 2011, so the model has changed since then. Also, the dollar figures are a little low.), changing a pitcher's usage for one year from a closer to a set-up man could save the team $1.4 MM. Those savings would persist throughout the pitchers arbitration seasons, meaning a small role change could mean real money over the period of team control. This applies to a lesser extent to pre-arbitration eligible pitchers, whose career stats influence their salary during their first run through arbitration.

This is a definition of a market inefficiency. The arbitration process overvalues the differences in leverage between relievers. Arbitrary stats(holds and saves) largely account for the differences in salaries of relief pitchers in arbitration. Additionally, the arbitration process lags behind the market in valuing closers, meaning guys with big save numbers aren't coming at a discount through arbitration. It will take some years for the relatively diminished free agent market value of closers to trickle down and influence prices for arbitration players. Until then, elite closers will continue to make more than good starters.

So how would a team take advantage of a situation like this? The answer would be keeping the pre-arbitration pitchers and especially the arbitration eligible pitchers out of the closer role (and to a lesser extent, the set-up role). Bumping these "role-sensitive" pitchers as far down the bullpen pecking order as possible would result in the biggest cost savings.

So if there is a "proven closer" on the market for a reasonable price who is equal to or better than your best reliever, he's going to be worth significantly more than the improved performance of the bullpen. He could save the team a couple of million dollars on the team's "closer-in-waiting" arbitration eligible player in the future. And the trickle down goes all the way down the bullpen. Guys who were in the set-up role are now not getting holds. Read what Swartz says about the savings for that potential pitcher:

Tyler Clippard had 38 holds this year for the Nationals, which boosts him up to a $1.7MM salary estimate. Take away 33 of those 38 holds to make him a middle reliever, and he only projects to get $1.3MM.

And remember, these savings are basically carried over every additional time a player goes through arbitration. Depending on the service time makeup of a team's bullpen, adding a free agent closer for just one season could save the team several millions dollars each year come arbitration season. A free agent "proven set-up" man could mean a few more hundred thousand dollars in savings.

Everybody wants their team to have an awesome young pre-arbitration eligible bullpen. But that pre-arb bullpen would get very expensive, very fast. Adding a good closer through free agency could pay off even before considering marginally better performance.

Overall, I don't think the effect on other reliever's future salaries is getting enough consideration when analyzing free agent reliever deals. In fact, I think the potential cost savings in arbitration could be a driving force in bullpen construction. The Nationals signing of Rafael Soriano on a big 3-year deal makes a lot more sense when considering the cost savings on their talented young bullpen.

The other way to take advantage of this would be to extend young relievers before they rack up saves and holds. Once they are cost controlled, the team can use them however they wish without affecting future payroll. Again, the Nationals may have been ahead of the curve on this, locking up Craig Stammen for two arbitration years before last season.

Not all teams have the right pitchers to take full advantage of this market inefficiency, but generally, the interconnectedness of arbitration costs and bullpen construction needs to be examined thoroughly for any transaction.

The Weekly Rant: Possible Outcomes of the Tanaka Deal

Masahiro Tanaka's contract with the Yankees has gotten a lot of attention already.  Dave Cameron at Fangraphs had a nice overview of it.  I wanted to look more in depth at the specific possible outcomes for the deal.

The contract is interesting for reasons besides being one of the largest ever for a pitcher, at 7 years, $155 MM. (There's some disagreement on how to rank the pitcher mega-deals. MLBTR's Tim Dierkes has a great read on how they should be analyzed.) The contract also includes a $20 MM "release fee" and an "opt-out" after four seasons. Here's how the contract breaks down cost-wise with and without the "opt-out":

Years Cost Cost/Year w/ opt-out 4        $108 MM $27 MM w/o opt-out 7        $175 MM $25 MM

It's a ton of money either way.  The Yankees are going to be seriously hoping Tanaka opts-out though. The reason is that it is nearly impossible to imagine a situation where Tanaka both a) does not pitch well in his first four seasons and does not exercise the opt-out and b) pitches well enough in years 5-7 to be worth $67 MM.

Even if salary inflation bumps the value of 1 WAR over $9 MM by 2020 (Year 7), Tanaka would need to put up 2.5 WAR per season over years 5-7.  If he's likely to produce at that level, he will have just opt-out.  Overall, this deal would be pretty terrible if for the Yankees if Tanaka doesn't opt out.

Let's say he averages 2 WAR per year over the entire 7 seasons.  Maybe a little above 2 WAR for his 4 younger seasons and a little below for his 3 older seasons.  That's not great production, and not what the Yankees are expecting, but it's also not a complete bust. And let's assume some significant salary inflation, so that the overall $/WAR rate over the contract's duration is $8 MM/WAR. Here's how the contract would look:

Total	Total	Total	Surplus	$/WAR
WAR	Value	Cost	Value
14	$104 MM	$175 MM	­-$71 MM	$12.5MM

I guess that wouldn't crippling (for the Yankees), but its pretty bad.  Now lets see what would happen if Tanaka is a 3 WAR pitcher through his 4 seasons.  He would likely opt-out if this is the case.  If the going $/WAR rate is at just say $7 MM, he should be able to find a deal with more years and similar average annual value to what amounts to a 3-year, $67 MM option.  He would be entering his age-29 season at that point, so he'd be in line for a nice payday if healthy.  So I think as long as he's about 3 WAR pitcher through year 4, he'll opt-out. Now let's say $7 MM is the market rate over those four years and see what the contract looks like:

Total	Total	Total	Surplus	$/WAR
WAR	Value	Cost	Value
12	$84 MM	$108 MM	-$24 MM	$9 MM

Now it looks at least reasonable.  Since the "release fee" is getting spread around 4 years as opposed to 7, the average annual value goes up a couple million.  And remember this is guessing that Tanaka is about about as good as Hiroki Kuroda.  That would be a pretty nice projection for Tanaka, and he still doesn't provide positive return on that contract.  What does he have to pitch like for this deal to break even?

Total	Total	Total	Surplus	$/WAR
WAR	Value	Cost	Value
16	$112 MM	$108 MM	$4 MM	$6.75 MM

Basically, assuming some inflation, the Yankees are betting on Tanaka being a 4 WAR pitcher. He doesn't have to pitch like Yu Darvish to make this work, but he does have to very good.  And if he's only pretty good, the deal doesn't look good at all. And if he's not that good, this deal will be a 7-year disaster.  Tanaka is set-up exceptionally well to optimize his earnings no matter how he pitches.  But the Yankees are taking a big risk, knowing that Tanaka will have to pitch like an ace for this deal to be a winner.  

From the Booth #3: Big Red Advanced Stats

This is the third post in a six post series featuring the Cornell At Bat broadcasting team. These posts will appear throughout the Fall semester. For part one of the series, click here. For part two, click here. 

Here at Cornell At Bat, we are devoted to delivering the Big Red fans with the  latest and most in-depth analysis of the baseball team. This year, analyzing statistics will be at the forefront of my duties with Cornell At Bat. Sabremetrics, or advanced stats, have taken the baseball world by storm over the past few years, especially after Michael Lewis’ book Moneyball and the film that followed it. However, advanced analysis  of NCAA baseball has little to no existence. I thought it would be interesting to preliminarily derive one of the most basic and popular sabre stats for the Big Red: WAR, or Wins Above Replacement.

WAR attempts to assess the overall value of a team’s players compared to the average player (the replacement). Batting WAR attempts to minimize the habit of simply looking at traditional and less valuable stats, such as AVG and RBIs, in an effort to get the most accurate assessment of a player’s talent and value. WAR is at the forefront of analyzing MLB players and their success. This has especially been seen with the debate of the American League MVP, where proponents of Mike Trout receiving the award claim that he has the highest WAR of any player in recent years. Determining WAR for an NCAA team is a lot harder however, for certain statistics that equate to a very precise WAR do not exist. My WAR for the Big Red is a very rough and basic form, as the stat really isn’t developed for anything besides MLB at the moment. Stats like park adjusted stats for average OBP and SLG don’t exist for the NCAA, and neither do other advanced stats that would make the calculations more precise.

My calculations for the Big Red WAR values were accomplished using an online calculator. For the calculator, I needed to input the critical stats for WAR of the average, replacement player (OBP and SLG). I used the averages from the whole Ivy League for the 2012 season for this facet. I then inputted individual stats from the Big Red team last year for all of the other categories, as well as the players’ positions (certain positions have higher values). For fielding and base running, they ask for a scale from best to worst, and I came to conclusions using fielding percentage and steals/ caught stealing percentages. I compared each player’s stats against each other to come up with the scale.

Although not completely precise, these WAR values will still accurately assess the players’ values. Also included is RAR (Runs Above Replacement), which is the sum of all the run components (Batting, Fielding, and Base Running). WAR is derived from RAR by dividing it by a runs per win constant, which is standardly set at 10/game for MLB (I couldn’t change this, but if I eventually calculate the Ivy League’s runs per win, I can redo the computations). Here are the WAR and RAR values for the 2011-2012 Big Red:

Returning members with over 20 games played, in order of most valuable to least:

 Brenton Peters: 1.6 WAR, RAR 15.8

 Chris Cruz: 1.5 WAR, RAR 15.2

 Ben Swinford: 0.6 WAR, RAR 6.1

 Tom D’Alessandro: 0. 6 WAR, RAR 6.0

 JD Whetsel: 0.1 WAR, RAR 1.0

 Kevin Tatum: -0.1 WAR, RAR -0.8

 Matt Hall: -0.2 WAR, RAR -2.0

Departing Starters, in order of most valuable to least:

Brian Billigen: 2.6 WAR, RAR 26.6

Brandon Lee: 1.2 WAR, RAR 12.2

Frank Hager: 1.0 WAR, RAR 10

Marshall Yanzick: 0 WAR, RAR 0.2

For more information about this post, please contact Alex Garcia at asg232@cornell.edu. 

For more information on Cornell At Bat or if you want to get involved, contact Alex Gimenez email at ajg322@cornell.edu. For previous Cornell At Bat adventures, look here, here, here, here, and here.  

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