Marginal Payroll
by Sky Kalkman on Dec 18, 2008 2:25 PM EST
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PrintThis post is required of all sabermetric web sites, comparing the marginal cost of each team win above replacement level. I think you've all seen this before (thanks, Doug Pappas) so I'll skip right to the table.
| Lg | Team | Total Payrol | Adj W | Marg $$/Win |
| N | Florida Marlins | $21,811,500 | 82 | $291,142 |
| A | Tampa Bay Rays | $43,820,597 | 99 | $631,361 |
| A | Minnesota Twins | $56,932,766 | 90 | $1,093,255 |
| A | Oakland Athletics | $47,967,126 | 77 | $1,253,210 |
| A | Kansas City Royals | $58,245,500 | 77 | $1,628,363 |
| A | Texas Rangers | $67,712,326 | 81 | $1,719,516 |
| N | Arizona Diamondbacks | $66,202,712 | 80 | $1,726,201 |
| N | Milwaukee Brewers | $80,937,499 | 88 | $1,749,683 |
| A | Cleveland Indians | $78,970,066 | 83 | $1,946,804 |
| A | Los Angeles Angels | $119,216,333 | 102 | $2,007,796 |
| N | Philadelphia Phillies | $98,269,880 | 90 | $2,083,814 |
| N | Houston Astros | $88,930,414 | 84 | $2,154,914 |
| A | Toronto Blue Jays | $97,793,900 | 88 | $2,177,510 |
| N | Pittsburgh Pirates | $48,689,783 | 65 | $2,237,182 |
| N | Chicago Cubs | $118,345,833 | 95 | $2,277,213 |
| N | Colorado Rockies | $68,655,500 | 72 | $2,421,175 |
| N | St. Louis Cardinals | $99,624,449 | 84 | $2,475,267 |
| A | Boston Red Sox | $133,390,035 | 97 | $2,508,059 |
| A | Baltimore Orioles | $67,196,246 | 70 | $2,543,606 |
| A | Chicago White Sox | $121,189,332 | 91 | $2,593,571 |
| N | Cincinnati Reds | $74,117,695 | 72 | $2,654,602 |
| N | San Francisco Giants | $76,594,500 | 70 | $3,018,435 |
| N | Los Angeles Dodgers | $118,588,536 | 82 | $3,191,274 |
| N | New York Mets | $137,793,376 | 87 | $3,275,869 |
| N | Atlanta Braves | $102,365,683 | 70 | $4,222,695 |
| A | Detroit Tigers | $137,685,196 | 76 | $4,587,051 |
| A | New York Yankees | $209,081,577 | 91 | $4,648,150 |
| N | Washington Nationals | $54,961,000 | 57 | $4,938,046 |
| N | San Diego Padres | $73,677,616 | 61 | $4,974,001 |
| A | Seattle Mariners | $117,666,482 | 63 | $7,337,950 |
Payroll data from the USA Today salary database.
Note that I've added two wins to all AL teams and subtracted two from all NL teams to account for the difference in league talent. Although, depending on how you interpret the numbers, that's not necessarily a good choice. Some thoughts:
- Surely sinking $30MM more (mostly payments to arbitration-eligible players) into an 84-win Marlins team would pay for itself after a 10-win increase and playoff birth, no?
- The average payroll was $89.5MM in 2008. Without the Yankees and marlins, it was $87.7MM.
- The average cost of a marginal win was $2.4MM. Keep that in mind when we congratulate teams who sign free agents for just under the average of $4.8MM per win. Free agents are really only good deals relative to other free agents.
- Make fun of the Yankees' $200MM payroll all you like, but they were still more efficient than three other teams last year.
A further analysis that might be interesting would be to use Pythagorean record or third-order wins instead of actual wins. Both would better hold teams accountable for acquiring talent, instead of simply winning games. I'd be happy to share my spreadsheet with payroll information and win totals with anyone who wants to tackle those questions.
Lastly, this analysis isn't actually a great way to judge the effectiveness of general managers. Spending the first $25MM over the leaugue-minimum (mostly money to first- and second-year arbitration players) is MUCH more efficient than the $100MMth dollar (mostly on free agents by that point). What we really want to do is ask, "Given a certain payroll level, how many wins would we expect a team to have, and which teams outperformed that number?" That requires a non-linear estimate of dollars-per-win, and another post. Stay tuned.
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What happened to the Mariners?
I mean I know what happened, but how? They were supposed to at least win near 80 games last year. How pathetic that they are nearly double any other team.
by Brendan Scolari on Dec 18, 2008 2:42 PM EST reply actions
They spent their money on players like Vidro, Sexson, Silva, and Washburn
That’s $42m right there
by JI on Dec 18, 2008 6:51 PM EST up reply actions
It really is unbelievable.
Webmaster of Driveline Mechanics
http://www.drivelinemechanics.com - An Unconventional Look at Scouting
They were only supposed to win near 80 games according to, like, ESPN.
And they don’t pay attention to anything beyond the most surface level evaluations.
Imagine some quick upgrades to the Marlins like Tex at 1st or Derek Lowe to anchor the rotation. 30MM a year and probably an 8-9 win upgrade. The marginal gains would seem to be tremendous.
That $30MM/10 wins comment was a throwaway, but now I'm thinking more about it.
$30MM would buy about 7 wins on the free agent market. But if it went towards paying 2nd and 3rd-year arbitration salaries (instead of trading those players for lesser talent), it would buy 10-12 wins, maybe.
Do teams that make the playoffs see $30MM revenue increases?
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
that's a tough question to determine, due to the obvious unknowns.
not if they just make the playoffs. but if they go to the world series, especially with series going the full slate, i could definitely see revenue getting to that point or beyond (not sure about profit, though). and you’d get the “season after bounce” that has been shown to exist.
Yeah.
I believe Nate Silver’s done some good work in that regard. Can’t remember where or if I’ve even read it before. Anyone know what I’m talking about?
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
Yes...
And I just spent 10 minutes searching for it and can’t find it. Frustrating.
by Peter Bendix on Dec 18, 2008 3:42 PM EST up reply actions
Just found...
This, which isn’t what I was looking for but is still extremely interesting.
by Peter Bendix on Dec 18, 2008 3:50 PM EST up reply actions
maybe it's this.
http://www.baseballprospectus.com/article.php?articleid=4618
"They will surely make fewer home runs," Guillen said. "Defense players and worthy pitchers will likely take over the protagonist's role."
Yes!
Money quote:
How all of this translates into optimal team strategy is not immediately obvious, and requires us to introduce a couple of additional economic concepts. The first of these is marginal revenue. The research that I conducted for Baseball Between the Numbers suggests the following:
* An additional regular season win is worth about $750,000 in marginal revenues, before accounting for its effect on the probability of a playoff appearance.
* A playoff appearance is worth about $30 million dollars.
A projected 77-win team that buys a five-win player, for example, can expect an increase of about $7.4 million in marginal revenues: $3.75 million for the extra regular-season wins, and $3.65 million for the roughly 12% improvement in the probability of reaching the playoffs. Meanwhile, a 77-win team that sells a five-win player can expect about a $5.8 million reduction in its revenues.
by Peter Bendix on Dec 18, 2008 4:05 PM EST up reply actions
Good stuff.
As others have pointed out below, I’ve sure those numbers drastically change depending on the team and frequency of making the playoffs.
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
gotta work on those search skills, pete
were you at the BP site? in case it’s helpful for future searches, i found it by searching under nate’s name and using ‘playoffs’ and ‘revenue’ as my search terms. no need to waste ten minutes in the future. the BP search engine is usually pretty user-friendly.
"They will surely make fewer home runs," Guillen said. "Defense players and worthy pitchers will likely take over the protagonist's role."
I failed miserably at researching.
Funny thing is, that’s EXACTLY what I did (I even used the exact words “playoffs” AND "revenue") and yet I somehow missed it.
Fail.
by Peter Bendix on Dec 18, 2008 4:31 PM EST up reply actions
So we need to pro-rate that $30MM bonus over the range of wins that takes a team from 0% playoff odds to 100% playoff odds.
Has that been done?
And, doesn’t that $750K number pretty much mean we should be subtracting out that much per marginal win of all free agent signings? Maybe only in certain analyses?
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
we should probably take into account that nate wrote that in 2005, too.
"They will surely make fewer home runs," Guillen said. "Defense players and worthy pitchers will likely take over the protagonist's role."
Yes.
And I really think that every team is goig to see a drastically different revenue increase per win.
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
by Sky Kalkman on Dec 20, 2008 10:40 AM EST up reply actions
season after bounce
It has been proven to exist, I am not so sure it exists the Marlins
by baseballandpi on Dec 22, 2008 8:33 PM EST up reply actions
something i've wondered about these payroll figures.
obviously, cash is often sent in trades – to which teams’ payroll should that cash be “charged”? for example, the phillies sent the white sox something like $7M last year. that player cost is charged to the white sox payroll. but they’re not paying it. the phillies are. and i don’t think it’s being counted in the phillies’ payroll – even though it’s obviously a cost to them that presumably prevents them from paying other talent (of course, they likely received what they considered more talent in the trade because of the cash).
Hmm, the Sox definitely should not be taking that payroll hit.
I’m not sure how that would be counted with this data. We’d also really like to know operating expenses. If teams take money out of major league payroll and put it into scouting and development, it should still count.
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
Are you actually working on ...
“Given a certain payroll level, how many wins would we expect a team to have, and which teams outperformed that number?” That requires a non-linear estimate of dollars-per-win, and another post. Stay tuned.
because this is something I have thought a lot about given the sever limitations on a constant dollars per win figure. It seems fairly complex given a multitude of ways it could be approached.
Yes, and while my answer is decent, it's only a small step towards what we want.
And, honestly, I pretty much stole the answer from Tango/David Gassko. Which isn’t that uncommon of an activity.
There should be a MUCH better answer if we could model everything from the ground up.
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
Zep
Let’s talk about what the curve would look like. What factors are in play that make the curve non-linear? The obvious point that comes to mind is that 4 wins is easier to add to a 70 win team than an 88 win team. A 70 win team will have big holes where if you just add a league-average player, you’ve improved your team substantially, while an 88 win team likely won’t have holes. Maybe to add 4 wins to an 88 win team, you need to replace two 2 WAR players with two 4 WAR players, and 4 WAR players cost a hell of a lot.
Since we’re assuming the value of a win is non-linear, I think we’ll need to decide how the market will value wins. You asked, “are you trying to figure out which teams are the best run (which seems to be the point of this post) or is this an entry into the question of how much is a player worth?” I’m not sure these questions can be solved separately. Marginal wins will be most valuable to the best teams since these wins will greatly impact the chances of making the playoffs and winning championships. But these won’t have big holes, so they’ll need to acquire only the best players.
Let’s say a marginal win for a 90-win team is worth twice as much than a marginal win for an 80-win team, but the 90-win team’s biggest hole is a 2-WAR player while the 80-win team’s biggest hole is a 1-WAR player. If a 4-WAR player is on the market, the 90-win team would stand to add 2 wins by acquiring this player, while the 80-win team would stand to add 3 wins, but because the 90-win team values marginal wins twice as much, the 90-win team is willing to bid 33% higher than the 80-win team is willing to bid for the same player.
I’m already confused. What else is going in here?
I think we’ll need to decide how the market will value wins
this is really one of the stumbling blocks… are we trying to predict how the market WILL behave, or are we determining how the market SHOULD behave.
The WILL behave part is very difficult because it implicitly requires us to understand how teams value and forecast players, and if Moneyball taught us anything, we know teams suck at that, thus making a very inefficient market.
So back to how should they behave… well, I just don’t know, but I think approaching it from the revenue value of marginal wins is the right avenue to pursue.
MP / MW
Sky – posted on this subject last week (linked below). The problem with MP / MW is that each team works on its own economic scale; i.e. with all other things being equal, an additional win earns the Yankees more than it earns the Pirates. So it’s almost inevitable (and no less efficient) that the Yankees spend more per win than the Pirates.
This might be where you’re going with your next post. I think we can all agree that the Marlins aren’t the best run team in baseball, and the Astros aren’t better run than the Red Sox. The best way to look at it is: how much does Team X earn per marginal win, and how much do they pay for each marginal win.
Remember also that not all marginal wins are created equal; going from 91 to 92 is much more valuable than going from 67 to 68. This complicates things a bit, but Nate’s chapter in BBTN does a pretty good job of breaking it down.
Any ideas on how to measure MR/MW on a team-by-team basis?
Is it a function of fan-base?
Is the playoff-bonus a function of the last time the team made the playoffs?
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
this begs the question
are you trying to figure out which teams are the best run (which seems to be the point of this post) or is this an entry into the question of how much is a player worth?
That is kinda my point from the post above… there is value to knowing who the good GMs are, but isn’t the much bigger question how do you get better? How should you value a player? A linear $/win doesn’t do that well at all.
I honestly don't have much of a point with this post.
It’s a discussion starter, let’s say. The next post will be more along the lines of measuring organization abilities, given their payroll. Although it will still miss in some ways, because it’s based on best-fitting historical data, not building a model from the ground up.
As far as player-value goes, and this is really only relevant to free agents, cost should pretty much be linear. There IS some value to acquiring players who pack a whole lot of WARs into one guy (because there are a maximum number of positions you can spend money on), but it’s not all that significant and really only matters to teams on the upper end of the payroll rankings.
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
i disagee
cost should pretty much be linear
thats pretty radical from an economics standpoint… the supply of 1 WAR players versus the supply of 3 WAR players is not equal, and thus should not be valued at the same rate.
but it’s not all that significant and really only matters to teams on the upper end of the payroll rankings.
yes certain teams only buy expensive FAs, but smaller teams do spend on some too. The Royals do pay Gil Meche 55 mil and Jose Guillen 36 mil…
Teams need to buy WINS, though.
Why would you spend more money on a 5 WAR and a 1 WAR player than two 3 WAR players? You wouldn’t, given two openings. Well, maybe you would just a little bit, because you want to leave that 1 WAR spot open to prospects or break-throughs surpassing 1 WAR. It’s the stars and scrubs approach.
Also, while I know you aren’t saying this, I’m not trying to say a 1 WAR player and a 3 WAR player are equally valuable. I’m saying their WARs are equally valuable. The second guy is three times more valuable. I wonder if the supply of 3 WAR players is about 1/3 the size of the 1 WAR supply pool?
And I shouldn’t have said that small market teams should care less about scarcity. Bad teams should care less about scarcity. When you have tons of positions that can be upgraded, you’ll take a lot of average players. When you have just a few position that can be upgraded, you need the WAR you’re going to be to be concentrated into one player, making them more attractive, if you really are set on spending the money.
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
i think we are on the same page more or less
teams do need to buy wins, no question there, and they want to do that in the most efficient way possible.
Obviously, there is a limit on roster size (and players that can impact a game) which is the key here. If a team wants to buy more wins, they cannot do so by buying more players. This is exactly what you are saying. So if you want to buy wins, you have to demand higher WAR players.
This is a very simple supply-demand game at this point, and economics says that the WAR at the higher margin is valued greater than the lower one. If a 1 WAR player is worth 5 mil, a 3 WAR player cannot be worth 15 mil (lower supply and higher demand) unless the market is extremely inefficient (certainly possible). You aren’t buying the player, like you said you are buying the WAR.
Yeah, the question becomes exactly how non-linear is it?
I don’t think it’s much at all, which makes it effectively pretty linear. We agree.
An interesting question is how do you go about measuring the cost-per-win at differe supply-demand points. You’d need to measure the opportunity-cost of filling up roster spots. And the expected off-season supply of X-WAR players. I’m no economist, by the way.
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
i am an economist
and i don’t have a good answer either :P
but its something I have been thinking alot about, maybe someday it will all make sense
you're a Royals fan, and after the Winter meetings
you think it’s “possible” that the market is extremely inefficient?
(winky face)
response:
OMG Banny. FWIW I am only crdtng u w/3 runs allwd bc of DDJ OMFG
by Matt Klaassen on Dec 18, 2008 5:05 PM EST up reply actions
i was so down about the winter meeting comments until
the futurama pic, god i love that show
dude, when’s you next driveline mechanics post coming?
heh
after I get back from Christmas vacation. I’ve got something that’s been simmering for months that hopefully other people will find entertaining and maybe a bit informative (insert line from the Fat Albert intro).
Yeah… I went to bed during the Winter Meetings thinking “I guess if the Royals can get Farnsworth for $1M, it wouldn’t be the end of the world.” The the next morniing I go to RR, and “wildthang” had posted a Prof. F. Pic with a simple “Good news, everyone!” subject line… then I heard the contract details… and then all hell broke loose at RR.
heady days, man… heady days…
OMG Banny. FWIW I am only crdtng u w/3 runs allwd bc of DDJ OMFG
by Matt Klaassen on Dec 18, 2008 5:26 PM EST up reply actions
Yeah, I guess I skipped over that.
(TmPayroll – $12MM) / (TmWins – 48)
The $12MM is about 30 times the league-minimum salary of $400K (no team gets by on just 25 players). 48 is the number of wins a .300 win % would have, which is a pretty good estimate of a replacement-level team.
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
What am I doing wrong?
Lets just go with Arizona:
66,202,712 Payroll-$12 mil=54,202,712.
80 wins – 48 = 32 wins.
54,202,712/32 = 1,693,835, no?
I took 2 wins off NL teams and added 2 to AL teams.
And a few teams didn’t play 162 games, so you need to pro-rate.
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
by Sky Kalkman on Dec 20, 2008 10:42 AM EST up reply actions
Also, I used opening day payrolls.
If anyone knows a source for better actual payroll estimates, please share.
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
I'm cool with paying $2mil per win.
Esp. because the Sox probably make that much per win too.
Clutch: A measurement of how much better or worse a player does in high leverage situations than he would have done in a context neutral environment. http://www.fangraphs.com/blogs/index.php/glossary/
The Sox paid $2.5MM per marginal win...
… which is league-average. That’s pretty good, considering they spent so much money.
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
It'd be nice if Karma wasn't such a drag though.
Clutch: A measurement of how much better or worse a player does in high leverage situations than he would have done in a context neutral environment. http://www.fangraphs.com/blogs/index.php/glossary/
Best and worst...
Ran this using the data inthe lahman db
Bestand worst:
2007 White Sox $4.2M, D’Rays $0.73M
2006 Cubs $4.9M, Marlins $0.18M
2005 Yankees $4.3M, Indians $0.72M
2004 D’Backs $25.3M, Indians $0.81M
2003 Tigers* $??, D’Rays $0.74M
2002 Tigers $7.3M, A’s $0.62M
2001 Orioles $4.3M, Twins $0.50M
2000 Cubs $3.3M, Marlins $0.45M
1999 Cubs $3.1M, A’s $0.48M
1998 Marlins $6.7M, Expos $0.34M
1997 Cubs $1.9M, Pirates $0.21M
1996 Tigers $4.6M, Expos $0.33M
1995 Blue Jays $3.7M, Expos $0.40M
1994 Cubs $2.2M, Expos $0.40M
1993 Mets $3.4M, Expos $0.35M
1992 Dodgers $2.9M, Indians $0.22M
1991 Indians $1.7M, Braves $0.33M
1990 Yankees $0.97M, White Sox $0.14M
1989 Tigers $1.3M, Orioles $0.16M
1988 Orioles $2.0M, Pirates $0.11M
- The Tigers had below replacement level wins, so they’re actually in the negatives, which would equate to some huge number of $$$ per marginal win
by erosen on Dec 18, 2008 5:07 PM EST reply actions 1 recs
Nice.
Please come back to Lahman-ize my next post.
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
Can you normalize the seasons?
Find league-average $$/win and adjust seasonal numbers onto the same scale? That way we can compare across seasons.
Beyond the Boxscore // Calling BJ Upton lazy is lazy.
Here are the top and bottom 25,adjusted to 2007 levels
2003 DET ???
YearID TeamID $/Marg+
2004 ARI 29.99
1988 BAL 14.99
1988 ATL 13.26
1998 FLO 12.7
1996 DET 10.53
2002 DET 8.46
1993 NYN 8.41
1985 PIT 7.83
1995 TOR 7.6
1989 DET 7.58
1992 LAN 7.37
2003 NYN 6.98
2002 MIL 6.91
1991 CLE 6.05
2004 SEA 5.96
1987 ATL 5.94
1985 ATL 5.91
1987 BAL 5.47
1988 PHI 5.35
2001 BAL 5.12
2006 CHN 5.11
1986 CHN 4.95
1999 CHN 4.94
2002 TEX 4.92
…
YearID TeamID $/Marg+
1993 MON 0.85
2007 FLO 0.85
2003 TBA 0.85
1992 MON 0.84
1997 DET 0.83
1988 PIT 0.82
1995 MON 0.82
2005 CLE 0.81
2000 CHA 0.78
1999 OAK 0.77
1996 MON 0.76
2000 MIN 0.74
2007 TBA 0.73
2002 OAK 0.72
1990 CHA 0.72
1994 MON 0.67
2000 FLO 0.65
1998 MON 0.64
2001 OAK 0.62
2001 MIN 0.6
1992 CLE 0.57
1987 MIN 0.42
1997 PIT 0.41
2006 FLO 0.19
1987 SEA 0.11
Data Envelopment Analysis
This technique might be applicable if you’re trying to answer the question “which teams were most efficient in creating wins.” Essentially, the technique boils down to graphing Wins on the vertical access and Dollars on the horizontal, then connecting the “outermost points” to create an envelope. Then you can examine efficiency by comparing the actual wins to “efficient wins.”
The drawback to this method is that is extremely sensitive to outliers. A big benefit is that you do not need to make any assumptions about the relationship between “dollars” and “wins.”
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