THE BOOK--Playing The Percentages In Baseball

Wednesday, April 13, 2011

Sabermetrics is the Cahill of our Discontent

Kahrl makes the case that maybe Cahill is worthy.

Monday, March 21, 2011

Longoria no longer the best deal in… (which year)?

The day Longoria signed his monster deal, which happened just days after he was put on the 25-man roster, which happened just days after he would not qualify for 172 days of service, I called that move by the Rays brilliant.  That his future WAR will generate far more than the Rays are going to pay.  And that was in 2008.

And since then, I have said that Longoria Properties has the highest net asset value (i.e., value of property minus mortgage value) in baseball.  Three years later, he still has that tag.

At some point, this will no longer be true.  And Dave asks when?  Longoria still only has 40MM$ of payroll coming to him as of today.

Entering the 2014 season, he’ll have about 90MM$ of value, and it’ll still cost the Rays only 30MM$ for him.  I think by then, someone will have overtaken Longoria for giving his team the biggest deal.

Three years later, and I’m still in shock.  And three years from now, I’ll still be in shock.  The deal was that good for the Rays.

Monday, March 07, 2011

Recent historical salaries

Jake gives us some historical context.

Personally, I prefer showing salaries as a percentage of the average team payroll.

Friday, March 04, 2011

MLBPA should consider allowing buyouts

There’s a thought that guaranteed contracts are the perfect thing for players.  Let me tell you why that’s not true.

Suppose you are a company, and you want to retain talent.  You offer someone a 3 year guaranteed contract for a total of 300,000$.  Suppose instead it was not a guarantee, that you are allowed to walk out of the deal, without penalty, at any point.  This person would not accept a 3 year non-guaranteed deal for 300,000$.  He might instead ask for a 3 year non-guaranteed deal for 360,000$.  He wants the extra money to make up for the fact that he can get cut loose at any time.

Now, suppose that the penalty to walk out on a deal is 10% of the remaining value of the contract.  So, say one year in, you want to cut the guy loose.  He has 200,000$ still coming to him, so you pay a 10% penalty of 20,000$, and that’s it.  In that case, this person would likely accept say a 330,000$ contract, non-guaranteed, with a 10% penalty.

In all cases, we’ve reached an optimum point for both the employee and employer.

I think the way people think of it, with respect to sports, is that the team would always pay the player say 36 million dollars, regardless of the guarantee or not.  But in actual fact, the team is paying the player 30 million dollars because it’s guaranteed, and if it were not guaranteed, they would pay the player 36 million dollars.

***

The NHL lets teams buy out contracts at two-thirds of the remaining value.  This has a good impact on the fan side, because it allows a team to get rid of albatrosses, without the fans thinking that it’s always hanging over their heads.  It gives teams options in terms of roster flexibility.

As I said, there’s an optimal point for the players and teams regardless of the guaranteed salary and buyout parameters in place.  It’s just a matter of figuring out what kind of system both sides want.  In my view, I’d like to see the buyout provision at around 33.3%.

If say Barry Zito has say 66MM$ due to him over the next 3 seasons, then the Giants can pay him 22MM$ to leave.  They would do this if they don’t think he can get them 44M$ of value in performance.

Had this provision always been in place, Zito, and all the other free agents, would have signed BIGGER deals.  This would have happened because the teams know they can save themselves by buying out the deals.  In the end, they’d have paid for all the free agents, as a group, the same amount.  It’s just that the risk of having a really bad deal got reduced.

***

So, the discussion point is: how much would you set the buyout level at?

Monday, February 28, 2011

Spending for playoff spots

I like RJ’s recent historical recap of the Indians.  Basically, how much they spend is indicative as to how much they expect to make a run for the playoffs.  Obviously, a team that spends more on free agents are getting less bang for their buck, so it would look like they have a better chance than they do.  Ideally, service time information, and player development costs would also be pieces of information that are routinely provided by MLB.  In any case, it’s a good way to at least look at within-team thinking year-to-year.

Wednesday, February 23, 2011

Forget about “average annual value”

Let’s say you have a pitcher who is forecasted(*) for 2 WAR, and the going rate is 4.675 MM$ per win.  That means he’ll be paid 9.35MM$, plus the 0.4MM$ minimum salary for a total of 9.75MM$.

And let’s say that next year (as of today), he’s forecasted for a 1.3 WAR, and the going rate is 4.885MM$ per win.  So, 4.885 x 1.3 + 0.4 = 6.75MM$.

This pitcher therefore would either sign a 1/9.75MM$ deal or a 2/16.5MM$ deal.  Forget about that in the 2yr deal, the “average annual value” is less than the one year deal.  We don’t care about that, and you should never ever think like that.  Don’t ever do any of your math based on it.  Don’t even treat it as a shortcut.  Don’t do it, because that’s not reality.

Joe is reporting that when Carl Pavano signed his 2/16.5MM$ deal, Pavano had on the table a deal from the Yankees for 9.75MM$ for one year.

Basically, if (and this could be a big if, based on how Pavano perceives himself) the above illustration is correct, then Pavano would be ambivalent in which of the two deals to choose.  He was basically offered identical deals.

You should always think of these deals on a year-by-year basis, and how much he can earn and how much he’d get paid in those years.  If the deal with the Twins was structured as a 6.75MM$ per year, with a 3MM$ signing bonus paid in the first year, then it’s easy that they paid for expected performance.  But, if it’s a flat 8.25MM$ per year, then he’s being underpaid the first year and overpaid the second year (such that it balances out).

(*) Alert to language police: Firefox spell-checker says this is not a word.

Linear wins

Dave brings up the comparison of Pujols against two good players, of how they both contribute the same amount and (will be) paid the same amount.  So that all the extra things, scarcity, risk, non-linearity cancels out.

One of the things these discussions always brings out is the 2-for-1 comparison, and so, we also have to talk about roster management.  Let’s agree that this is an issue, and in the future, make it a 2-for-2.  I suggest that next time you want to do a 2-for-1 comparison, make the 4th player someone like Lastings Milledge (or Melky Cabrera, etc), a player young enough and seemingly with enough potential to be given a chance to play 120 games every year, but who always produces 0.5 WAR a season.  So Pujols+Milledge v two good players (say Rios/Dunn).

***

Also note that if you put the replacement level too low, you won’t get a linear wins to dollars conversion.  We talked about this way back when Nate Silver had a very low replacement level.  He and I ended up with the SAME dollar values for the same (above-average) players, except he had an exponential growth for wins to dollars, while I had a linear fit.  How is that?  Because where I’d have 6 WAR, he’d have 7.5 WAR.  And where I had 3 WAR, he’d have 4.5 WARP.  We both agreed that the better guy should get paid twice as much.  And in my case, it was simple enough: 6/3 = 2 times.  For him, it was 7.5/4.5 = 1.67.  So, he needed to add an exponent to turn that into 2 times.  Where we disagreed was on the very low end (the guys I had below 0 WAR but that he still had as a positive WARP).  Anyway, all that is moot now because BPro has increased their replacement level to around the level we’ve espoused.  And as a result, they’ve gone to a linear model as well.

Anyway, it’s an important critical part to point out that where you set the baseline will determine if you get a linear fit or not.

Let’s presume that’s still not clear, and I’ll give you a better example.  Think of win percentage for a pitcher (or better, the win% implied by a pitcher’s RA9).

Let’s say I ask you this question: how much do you pay for these three pitchers?

The first pitcher is your standard #1 guy, and you’re giving him 20MM$.  The second pitcher is your standard #3 pitcher, and you’re giving him 8MM$.  The third pitcher is your #6 pitcher, and you are giving him the league minimum (effectively 0$).

So, you look at that and think “well, obviously wins are not linear”.  The .600 pitcher only gets 1.2 times more wins per game, and he’s only pitching 205/150 (1.37 times) more than the .500 pitcher.  Their W/L records look like this:

So, I’m only going to pay the first pitcher 13.8/8.3 = 1.64 times as much (which you can also get from 1.2 x 1.37).

Ah, but we are not saying that ALL wins are linear.  We are saying the MARGINAL wins at the level we are interested in are linear.  More accurately, all the wins below a certain level of worth ZERO dollars, and then all wins above a certain level are worth 4MM$.

Let’s remove from each pitcher .380 wins.  So, we now have this:

Our first pitcher is now +.220 wins per game, the second one is +.120 wins per game, and the third one is +zero wins per game.  All the wins that we took out (the .380 wins per game) are worth zero dollars.

Now, let’s do the same thing and multiply the marginal win% by IP/9 to give us wins above the baseline.  We get this:

And if we multiply each win by 4MM$?  You get 20MM$, 8MM$, and 0MM$, respectively.  And that’s exactly what you (through me) said you would pay.

Basically, rather than having two lines as we do (0$ per win up until a win% of .380, and 4MM$ per win for each win past the .380), a typical statistician would try to have ONE line that best-fits through all the data, and he’d have some exponential or quadratic equation to try to describe the data.

That’s why, when I say the wins to dollars is linear, it’s only linear above a certain point.  And I set that point at around .380 win%.

Friday, February 18, 2011

Free agency for all

What would happen if everyone signed one-year deals?

I know what you are thinking: 5MM$ per win x forecasted wins = 35MM$ for Pujols.

But, no.  The $ per win is set presuming that MLB is operating efficiently in signing their free agents.  What if instead MLB teams are simply spending to budget? 

Let’s say that MLB has decided that to turn the profit they want, they want to spend 3 billion $ in salaries, as they are doing right now, plus say another 1 billion $ in “development” costs (minor leagues, scouting, signing bonuses, etc).  I totally made up that 1 billion$ figure.  If you were to make every player a free agent after his first year, MLB would have to reorganize so that the feeder system would be some sort of MLB controlled academy.  Instead of teams individually adding up to 1 billion$ in development cost, they’d pool their money for that.

Anyway, you’ll still have 1000 wins above replacement.  That’s going to remain fixed.  With 3 billion$, that means that each win is going to cost 3MM$.  (A bit less because of minimum salary consideration.)

So, if everyone is a free agent, and if Pujols is say 7 wins above replacement, he’d sign a series of 21MM$ (present-day) contracts.  Sounds like he’d take a hit from the 30-35MM$ he should get in current free agency, no?

Don’t forget though that in the first 6 years, he played at a deep discount.  If let’s say he was a 7 win player each of those years, he should have gotten 147MM$ (present-day dollars), but instead got less than 40MM$.  So, he’s been playing at over a 100MM$ discount over the first 6 years.

Overall, this “Free agency for all” system would benefit anyone who has a career that was less than 6 years, and likely benefit anyone with a career of under 10 years.

Wednesday, February 16, 2011

Cashing in your chips?

Dave takes a look at Bautista.

Friday, February 11, 2011

Help me with my financial math: Pujols share of Cardinals should be 15%?

According to Forbes, the Cardinals are worth close to (present day) 500MM$.  According to me, Albert Pujols has some (present day) 200MM$ to 250MM$ of baseball life left.  If the Cardinals simply gave Pujols 40% equity stake, is that a fair deal?  I presume no, because of the tax implications.

The after-tax value of the Cardinals (if Pujols were to simply flip the shares, with presumably a cost-basis of 0 dollars) would mean say 20% of the value is lost (or whatever the tax rate would be).  His present-day salary would be more like 100MM to 150MM$ in after tax money.  So then, would 25%-35% be the fair price?

Let’s say that’s how it works.  So, MLB has a total valuation of say 15 billion $, of which after tax it would be 12 billion$.  Total player payroll is 3 billion$, of which after tax it would be say 1.6 billion $.  This would mean that the players can forego their salaries (for this year alone) in return for 13% share in MLB.  That after 8 years, MLBPA can own MLB.

But it gets better (maybe).  If MLB has no player payroll to worry about, the valuation of the teams would skyrocket, giving them the best ROI since Microsoft’s early days.  Instead of being worth 15 billion$, cutting 3 billion in expenses (annually) must increase the value of the company by, what, 30 billion$?  So, now MLB is worth 45 billion$, but only because the players have salaries.  Anyway, now, the players would only get 3.5% share (each year), and so, after 30 years, they’d own all of MLB.

This part makes more sense.  It’s like the paying rent v mortgage conundrum. 

Anyway, the only reason this works out so well is because of the guarantee of non salaries for players, and this is going to sustain itself.  In the case of Pujols, his non-salary is only going to last while he’s playing.  So, the Cardinals would receive a huge boost in franchise value for not having to pay his salary, but that value will die when Pujols retires.  I’m a little stuck here.  The Cardinals are worth 500MM$ because of expected expenses over the life of its company.  If Pujols doesn’t take his 200MM$ in present-day salary, but provides that value, is that going to at least increase the Cardinals value to 700MM$? 

Now, the new calculation for Pujols’share would be 100MM$/700MM$, or about 15% share of the Cardinals.  (Bobby Orr was once offered 18%).

Did I do all this correctly?  I’m a complete novice at this, so walk me through how a financial analyst on Wall Street would work this out.

Thursday, February 10, 2011

Weaver: to Lincecum or not to Lincecum, that is the arbitrator’s question

Jered Weaver, Felix Hernandez, Justin Verlander, and Josh Johnson are all each other’s comparables.  In their first year of arb-eligibility, Felix, Verlander, and Johnson got between 3.675 and 3.800MM$.  In their second year of arb-eligibility, they got 6.85 to 7.75MM$.  Clearly MLB thinks of the three as interchangeable.  Their two year contracts for their first two seasons of arb eligibility: Felix: 11.0, Verlander: 10.5, Josh 11.5 (though Johnson signed as part of a longer term deal).

Weaver however is a bit ahead of them according to his salary. His first year of arb-eligibility had his salary at 4.265MM$, or about 14% higher than his other three brothers.  In their 2nd year of arb eligibility, the three of them averaged 7.27MM$, and 14% higher would be 8.28MM$.

The Angels put in 7.375MM$, squarely in the middle of Felix, Verlander, and Josh Johnson.  Obviously, they are going to use those three as their main comps.  Weaver put in 8.8MM$, which is substantially higher than what those three got.  How is Weaver going to justify that amount?  He’s going to have to bring in Tim Lincecum as his comp as well as those three.

If we make Weaver’s comps the three obvious plus Lincecum, then their 4yr average in their 1st year of arb eligibility is 5.06MM$, far above what Weaver got his first year.  In their 2nd year, the three obvious + Lincecum averaged… 8.7MM$.

So, that’s what Weaver’s camp is shooting for, that Jered Weaver has four comps: Felix, Verlander, Josh Johnson, and Tim Lincecum.

Given Lincecum’s relatively down year (in relation to his two Cy Young years), this is a great opportunity for Weaver to use Lincecum in his comp group.  The interesting thing is that Lincecum’s 13MM$ was “earned” from his 2008-2009 performance, but “counts” side-by-side with his 2010 performance.  Weaver’s group is going to say “hey look… look at what Linecum did in his 2nd year of arb eligibility to earn 13MM$”.

Therefore, if Weaver prevails, you know the arbitrator accepted the Lincecum argment.  If he doesn’t, then the arbitrator stuck with the three main comps and ignored Lincecum.

***

I also presume this is a prelude to a 5-year contract.  If the arbitrator rejects the Lincecum argument, then he’ll sign for what Felix and Verlander signed (close to 5/80).  If the arbitrator however accepts the Lincecum argment, and awards him 8.8MM$ instead, then 5/80 extension goes out the window.  The 8.8MM$ is 20% higher than what his non-Lincecum comps got, so that would push Weaver long-term extension to close to a 5/100 deal.

Let’s see how this plays out…

Ohlendorf’s arbitration case

Nice presentation.

Thursday, January 27, 2011

Sign Vlad to limit Abreu?

Dave makes the case that to limit iron-man Abreu to not vest his 2012 option, they should sign Vlad for 2011.

This is the tradeoff:
A. Sign Vlad for 7MM$ in 2011, and some other one-year DH for say 8MM$ in 2012 (total 15MM$).
B. Let it ride with Abreu (9MM$ option in 2012).

So, that’s the trade, that by doing this, it costs you 6MM$ to have someone other than Abreu as your DH in 2012, and you gain the platoon advantage in 2011 (but limit your bench).

Someone else can work out the estimates to see if it’s a net gain or net loss.  The proposal is interesting anyway.

Friday, January 21, 2011

Budgets

This is how it works in the real-world, be it baseball or corporate America:

With a projected Opening Day payroll of $113 million, they insist they have reached their limit. Insiders say Carl Pavano’s contract actually pushed them over budget, requiring special approval from CEO Jim Pohlad.

You can have 15 teams be able to reasonably justify the INVESTMENT of Carl Pavano’s 2 years and 16MM$ contract as having a positive RETURN ON it.  (That is, a positive ROI, and preferably exceeding the T-bill rate.)

But, more than that, you have to have an owner that BELIEVES this is an investment, not an expense.  The fact of the matter is that it is hard to see an ROI on any one player signing.  He could have a bad season, just by luck, and it’s going to make you look really bad when you tell the owner: “Uh, hi, remember me?  I asked you for 50MM$, and, well, this guy did perform bad for two years, but, really, it was bad luck.”

You end up with situations where the Mets had the chance to sign Vlad, but they chose to not, because of their poor ROI on Mo Vaughn, and insisted on a health clause for Vlad, one that Arte Moreno was glad to not include.

So, getting back to Pavano: teams are only going to be able to bid on him if they’ve been allocated the budget room for it.  If you don’t have the budget room, you have to beg for it.  And now, your a$$ is on the line, and “random variation” is not a reason an owner will want to hear.

I know Matt is going to come around and tell me about economic theory.  I just don’t think that particular theory considers the situation at hand in the way I’ve laid it out.

***

Note: I have no insider knowledge as to the relationship between owners and GMs, and budget allocation or request to increase budget.  I just think I’ve made a good guess.

Tuesday, January 18, 2011

Gil Meche

Meche was paid 43MM$ for his four years with the Royals and is now retiring, leaving 12MM$ on the table (unless of course the Royals induced him to retire by paying him some settlement fee).

According to Fangraphs, he had 11 wins for the Royals, and according to B-R.com, he had 9 wins (partly because of higher replacement level).  BPro has him at 10 wins (partly because of lower replacement level).  Anyway, some 9-11 wins for 43MM$ means that the Royals made out fine.

They overpaid for him, but he turned in two excellent seasons to kick off the deal.  This is one of those deals where either the Royals played with fire, or their talent evaluators knew more than the other 29 teams in the league.

On one deal, you can’t tell, and so, no conclusions can be drawn.

Monday, January 10, 2011

Minor league farm value

And Evan Longoria is worth more than half of these systems:

Tuesday, December 28, 2010

Do low-talent teams overspend on free agents?

Matt had a pretty good Q&A from the saberfreak article.  He also said this from Question 36:

Matt: Teams don’t appear to PAY less for wins when they have smaller fan bases or are further behind on the projected win curve, but that’s because they are outbidding teams who are in the sweet spot of the win-revenue curve and/or from big markets. Small market teams and below average teams certainly pay for a lower quantity of these players, but they pay what it costs when they do buy those guys’ services. Sometimes they are doing it because of a splash effect, sometimes they are doing it because they think the rest of the league is undervaluing the player, sometimes they do it because they just overestimated the player’s talent, sometimes the player has a unique value to the town or is willing to take a discount. But the market is set by above average teams from big cities, and the prices are driven by that part of the demand curve even when they are signed by other teams.

So, what he’s saying is that rather than teams pay for their specific marginal $ per marginal win, all teams are forced to pay up to the “trend setters”, and that is, the teams in the sweetspot of the playoffs, those teams with say 85-90 wins of talent.  Whatever they pay, they set the market.  And, if you want to play with the big boys, you’ve got to pay like the big boys.

This would mean that a team with a low talent level, say 75 wins and under, if they pay like the big boys (say Gil Meche with the Royals), they are, overall, going to get burnt, as they will have overpaid by say 25% to 50%.  In a rational market, Meche would never be bid on by the Royals, because he can never have the same impact (monetarily) with the Royals as he could with the Redsox.

Theoretically, this makes sense.  If we had the knowledge required to make those deals.

But, what are we really talking about here in terms of impact? It’s not like God tells us what a team’s true talent level is.  We know that one SD = .060 wins in talent level among the teams, but our uncertainty level is going to be high.  Taking a guess, I’ll say that it’s one SD = .040 wins of uncertainty (this includes the chance that the player won’t play as often as he should because of injuries). 

Furthermore, with only 162 games to play, it will happen on a more than rare occasion that a team that we think is a true talent of 75 wins (meaning that we think are 75 wins +/- 6.5 wins) is going to win 85-90 games.  Or on the flip side,a team that is a true 87 win team (i.e., true 87 +/- 6.5) is going to win 72-77 games.

So, I’m ok with Matt’s point as a point of general principle.  But I think you are going to be severely constrained to apply that as a more general rule within the context of what we actually have to work with.

Will MLBPA be begging for revenue sharing?

Hello?  Why is no one talking about this:

Total end-of-year salaries totaled $2,911575,488 – nearly $3 billion dollars. MLB has said that gross revenues totaled $7 billion in 2010, meaning player salaries accounted for 43 percent of the total.

NHL I think is at 57% (fixed as per CBA), and I think NBA is around 55% (also fixed as per CBA).  I don’t know what the NFL is.

So, now, we are supposed to believe that a “free” market (not that it’s actually free) for a small percentage of its union members somehow benefits the MLBPA as a whole?  Even though they only get 43% of the revenues?

I seem to remember that back in the collusion days, the players would get close to 40% of the revenue.

The difference between then and now?  GMs got smart.  And young players lock themselves in to huge discounts.

Compare for example to Ovechkin, who signed a 12yr 124MM$ deal with the NHL Capitals.  Note that in the NHL, revenues are less than half that of MLB.  So, a 124MM$ deal would be akin to a 248MM$ deal in MLB.  And Ovechkin signed that with less than 3 years of service.  Do you think Longoria or Tulo or Verlander or any of the other young players would be able to sign such a deal?  No, of course not.  Even in free agency that might not even be able to do so.

And let’s not forget that the minimum salary in MLB is LESS than the NHL, even though they have over twice the revenue!  The minimum salary should be at least a million, if not 1.5MM$.  Does the MLBPA not care for its young players?

The MLBPA has operated under the belief that owners pay out contracts like they have a gun to their head.  What they didn’t count on is that GMs would become smart, educated, and would learn.

Well, here we are.  They’ve learned that the slave-players and the arb-players offer an enormous discount a huge discount.  And they’ve learned that while free agents are overpaid, they can pay them normal prices if they sign them to just one year, maybe two year deals.  And all that learning means that only 43% of revenues goes to payroll.

And what do the agents say?  Collusion?  That’s laughable.  How about they scream “smarty pants”?  That’s far more plausible.

The MLBPA should be begging for revenue sharing, and payroll limits.  And if they are lucky, they’ll get free agency for all players by the time they hit 28 years old.  Don’t get me started on Carlos Ruiz.

***

Maury: can you give us a year-by-year percentage of revenue that’s gone to payrolls?

Wednesday, December 22, 2010

Multi-year relievers

Eric and Dave both gave us a list of relievers signed to multi-year deals.

Using Eric’s data, which excludes Mariano, we see that his list of 19 multi-year relievers signed for 50 years at 235MM$ (with of course 20MM$ of that being the league minimum).  The total WARP accumulated was 38 wins.  That’s an average of 5.7MM marginal $ per win.

Since WARP has a lower replacement level, the baseline $ per win is less than what we are used to, about 10-20% less (because there are 10% more WARP than fWAR and 20% more WARP than rWAR).

Anyway, no surprise that relievers are hugely overpaid.  But it might not be because they are relievers, because as Eric points out, all these guys are old.  So, it’s unclear if they are being overpaid because they are relievers, they are old, or they are old relievers. 

They should be paid about 30% less based on these results.

***

Eric also shows us some numbers for one year relievers.  He doesn’t show the total number of relievers, and it’s unclear if the overall average he shows is a simple average or multi-year average.  Nonetheless, it likely won’t matter much here: 2.2MM$ above the minimum for 0.8 WARP wins, or 2.75MM$ per win.  This is pretty much standard of what you’d expect from one-year deals at any position: a huge discount.

***

I’ll ask Eric for the total number of relievers in his one year group, we can come up with the aggregated total.

Saturday, December 18, 2010

Economics of Fantasy Valuation

Tango- I just read through this whole thread after I saw it referenced in two separate spots had I had two questions: 1. Are you still comfortable with the positions you took here? 2. Do you see your position as optimal or convenient? Thanks much.

I am ONLY comfortable to the extent that there is a continuous distribution of talent.  (We can assume this is pretty much true, and so what follows is a theoretical objection to my model, but one that is more relevant the more gaps there are in talent.)

I’ll tell you where I am not comfortable: say that there has to be 25 2B and 25 SS drafted.  And let’s say that the top 24 SS are all Jeter and Nomar and Trammell and Larkin and on and on, each of which is indistinguishable from each other.  And the 25th SS is Mario Mendoza.

And let’s say the 25 2B who are all the same, each indistinguishable from each other.

It would be insane to value the 24 SS relative to Mendoza (meaning they’d all be 20$ SS) , while you would value the 25 2B relative to the bottom guy, meaning they’d all be worth 1$.

This doesn’t make any sense.  Why would you bid 20$ for Trammell, if you can get Larkin or Jeter or… BUT, if it came down to two SS, and you had Nomar and Mendoza, then you would pay 20$ for Nomar.  So, you don’t want to be the last guy left to make the decision.  If you had Nomar and Trammell and Mendoza, do you bid 18$ for Trammell, and the guy who doesn’t up that bid does so realizing he’s only going to get a chance for 20$ of Nomar or 1$ for Mendoza?  Or, does Trammell get bid up to 20$.  And if he does, then what happens when you have Nomar, Trammell, Larkin and Mendoza available.  How much is Larkin bid?  17$?  15$?  or 20$?  How much does the first SS go for?  1$?  20$?

I would love to hear more about how economic theory would play a role here.  Teach me.