Friday, February 18, 2011

Viewing Transactions Like a Drunken Gambler

The Cubs fan base (and any fan base, I would imagine) spends a good deal of time talking about the transactions a team can make and then also making judgements about the transactions that actually happen.

Right now, the potential transaction du jour to talk about is Albert Pujols in a Cubs uniform.  He's been one of the best players on the planet pretty much since he came into the league, so it's hard to deny that some team somewhere won't come up with something like $30 million per season to get him.  There are many folks on Twitter who believe the Cubs should be the team that gives it to him.
MB21 at ACB estimated Pujols' projected value assuming a standard value of Wins Above Replacement, inflation and Albert's assumed decline in production:

Using the Fans 7.5 projected WAR in 2011, $4.5 million per win, 7% annual increase, -.5 WAR per season, I get Pujols being worth $223, $250, $275, and $297 million over 7, 8, 9, and 10 seasons beginning in 2012.

So if Pujols actually becomes a free agent, the Cubs actually make a run at him, and actually sign him to something like 10 years and $280 million, there will be all sorts of reactions.

Most people who don't want to be "Negative Nellies" who ruin optimism will take a wait and see approach, as in, "We'll have to see how Pujols ages to determine whether the Cubs paid too much for him." Some will immediately cry about how the Cubs are idiots because they didn't learn from the mistake of signing Soriano to such a long, expensive deal.

Both groups are not viewing a transaction appropriately.  How can fans judge a transaction with the benefit of knowing how things actually turned out, when the person who made the move clearly did not have that same ability.  Why do we expect our general managers to have some sort of crystal ball to foresee circumstances that are completely unknowable?

On the flip side, how can we judge a deal based on an event that has absolutely no impact on the current deal?  How does the failure of one contract make any future contract more or less likely to be succesful?

Let's say you go to Vegas and are playing blackjack. Let's say you get dealt a fourteen and the dealer is showing a five. The smartest, most statistically viable option for the player is to stay on fourteen, thus guaranteeing that you don't bust when the dealer is quite likely to bust and thus making a fourteen good enough to win.  Staying is the right move.  Based on the information available at the time of the decision, any action besides declining a card is a mistake.

Ideally, the dealer will proceed to turn over their down card to show a ten or face card, and then they will draw another large card to bust.  Then everybody at the table exchanges high fives and life is good.  Unfortunately, sometimes a dealer ends up making his hand.  Sometimes the dealer pulls out a bunch of twos and threes to salvage their hand and make you a loser.  That does not make your decision to stay a wrong one.  Sometimes correct strategy fails.

If this player had made the correct decision at the time of the decision, the dealer would have drawn the 6 and gotten 21.  This lucky result doesn't make the decision any more correct than if he had lost.
When Jim Hendry made the deal for Soriano, the projected production put Soriano's value for an eight-year deal at somewhere between $172 and $212 million (thanks again to MB for doing the math).  Hendry got him for $136 million.  So at the time he made the deal, it was actually a pretty decent value, even if you figure in a discount on the per year average to get the security of an eight year contract.  But then injuries precipitated a dramatic decline in Soriano's production that couldn't have been foreseen and the result now is we all hate the contract.  But the results can't change the fact that the decision made at the time were correct.

Basically, Hendry stayed on fourteen like the guy in the photo and the dealer made his hand to make it a losing situation. 

Well, let's say you get pissed off at the blackjack dealer for pulling that 21 out of his ass when he should have busted and you wander over to the roulette table to win your money back.  You look up at the past results that are posted and notice that the last ten spins of the wheel have all landed on a red number.  Surely, you think, it can't possibly land on a red space for an eleventh time in a row!  I should put my money on black!

Now, aside from the fact that gambling is always a poor decision because you can't beat the math, this particular reasoning to make the decision is entirely wrong.  The odds of a black result on a standard American roulette table is 47.6%.  The odds of a black result on that same table after the previous ten results had all been red is 47.6%.  Nothing about the past results makes any sort of difference in how the future result will turn out.

Why would Soriano's injuries and subsequent precipitous decline have any impact on whether Pujols would similarly decline?  There is just as good a chance that Pujols beats the projections as there is that he underperforms his projections.  In fact, given that Pujols' value comes overwhelmingly from his bat, he is probably easier to project than someone like Soriano, whose value was based on his bat and speed.

I know we are fans and we are prone to our emotions.  I am no different.  Deep down, I do truly believe that the Bartman incident occurred because my buddy in Seat 106 yelled to a beer vendor one pitch prior, "Hey Steve! I'll see you at the World Series!"  I'm certain that the Harry Caray commemorative pin was the reason the Cubs went on a 15-0 run when I wore it to the ballpark in 1998.  To this day, I remain convinced that I caused the 1984 NLCS collapse by accepting a $5 bet with a junior high friend that the Cubs still wouldn't make the World Series when they were up two games to none.

But when these kinds of deals get done by whoever is in charge of the team we love, lets at least try to understand the circumstances involved.  Otherwise, we are just the idiot at the table splitting kings all night.


Berselius said...

This was a fantastic piece, Tim. Thanks for writing it.

Kin said...

This is awesome and must be shared with everyone. Whether they agree with your viewpoint or think you're an idiot is out of my control though.

Aisle 424 said...

Thanks, guys. I'm still not happy with how I threw this together, but I haven't been able to concentrate on this much lately with other stuff going on. So I just went with what I had since, you know, I hadn't posted much lately.

Unknown said...

This is good stuff.

Anonymous said...

I certainly agree that decisions need to be evaluated based on expected value rather than how the results actually turn out. However, in the gambling instances referenced above those odds are well established. I don't really think that's as much the case here.

I will assume that the average player regresses .5 WAR per year after a certain age. There's enough data out there that we can assume that's reasonably accurate. However, the "average" player is worth 2 WAR to begin with, correct? So what do those numbers look like when you run them based on a 25% reduction the first year, 33% the second year, etc - which would be the case of an average player declining by .5 each year? Why are you using a fixed number decline rather than a percentage?

Aisle 424 said...

Yes, you can argue about how an expected value was reached, but you would still be debating the decision based on information at the time of the transaction - which was my point.

I used MB's computations because I was too lazy to do them myself and he's, frankly, smarter than I am.

GirlieView said...

You always bring such a voice of reason to all the craziness out there. I love the math!

braun said...

This is a great post,and i loved the way you used blackjack to prove your point.

mb21 said...

Excellent stuff, Tim.

The article about Soriano's value was written by berselius for what it's worth. I'll take credit for something he wrote though.

Anonymous, you're absolutely right that the talent level of the player affects how much he'll decline. A player who has been worth about 3-5 WAR on average over the last few seasons will decline at about -.5 WAR per season. A player who has been worth something like 2 WAR (league average) will not decline by -.5 WAR, but rather something like -.4, -.3 and so on. So yeah, a percentage would be better. Actually, it would just be better if we did something like this:

Previous 3-year average: 4 WAR (that's our 2011 projection)
You The next year your average WAR is again 4 so he'll be projected at 3.5 in 2012.
Now are average is a bit below 4 of course.

Anyway, you'd be best to re-calculate the 3-year average and use that number, but for someone of Soriano's caliber the -.5 WAR works out almost perfectly.

There is also some recent evidence to suggest that when players hit 32 the drop is more like -.7 WAR. In other words, the drop from 29-32 is more like the -.5, but after that it's a big more. I haven't seen that evidence tested thoroughly yet so I only occasionally use that. Plus, at the time Soriano signed the thinking in the sabermetric community was that the player would decline by about half a win each season. We can't expect a front office to know something that isn't yet known.

I should also point out that every organization is going to have their own projection system so what I like to do anymore is to use the overall value of the contract to figure out how much a team was expecting from the player. Then you look at that and see if the projection is reasonable based on what those of use who do not work for teams know.

I disagree with berselius somewhat. I've come out with Soriano being worth about 7 years and $17 million less. Basically, the Cubs signed him for one year too long based on what I've come up with. Then we factor in that we know McDonough took over for Hendry because Hendry wasn't going to go to 8 years. McDonough did. I think that's our extra year.

I'd also add that looking at one contract as evidence of someone being a poor GM is incorrect. Tim alluded to that as far as injuries go, but people make mistakes. We cannot reasonably expect a GM to have nothing but good signings. If that were the case, the value of the win would be less than it is. GMs, like every human, makes mistakes and his worth isn't defined by one good or bad decision, but the sum of those decisions.

I think some people have decided to say that no GM would give Soriano that contract (or Grabow) and therefore he's terrible. But what about the first Ramirez deal, the 3 deals for Dempster, Derrek Lee, Ted Lilly, Mark DeRosa and others?

Aisle 424 said...

Sorry, berselius. This blog is becoming almost as discredited as ACB.

Good points, MB. I wasn't trying to really make a judgement on Hendry based on one isolated incident, but rather showing how we can get wrapped up in emotion or conventional wisdom when discussing trades and signings, much like one can get wrapped up in Vegas when you're on a roll, or desperately trying to win back money because your luck "has to" change soon. It's not logical, but most people do it to some degree.

I just wanted to point out that having these 4 years of Soriano doesn't change the factors that were in play at the time Hendry made the decision. I used that one because his contract is pretty universally accepted as terrible, but depending on how one would assign value and projected worth, there is an argument to be made that the deal was not bad inherently, it just turned out that way.

mb21 said...

You did a great job, Tim. The gambling comparisons were perfect and I think something that a lot of people can understand.

I agree that arguments can be made Soriano's deal wasn't bad when it was signed and really that's all I care about. What happened after the fact is either fortunate or unfortunate. Jim Hendry shouldn't get any more credit for signing Lilly (terrible contract at the time it was signed by the way) than he should be bashed for signing Soriano.

Very well done.

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