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Free Agency Project


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#16 CubChymyst

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Posted 03 April 2013 - 02:09 PM


If WAR is negative you could add extra cost to the contract, because the team actually paid someone to make them worse.


I thought about calculating the cost per WAR for all of the other contracts in baseball and using the total contract plus that amount. Now that I am typing that out it makes more sense than when I first thought of it. That should encapsulate the additional cost required to get a useful player, on average.

What I don't like about that, though, is how it benefits the guy who got -.1 WAR vs. .1 WAR. While both of them equal, roughly, the same amount of wasted money, the .1 WAR guy is going to negatively impact the overal calculation more.

Example:

The Braves signed Kenshin Kawakami to a 3/$23M contract in 2009. He proceeded to give them -.2 WAR over his contract. At the same time, the Cubs signed Milton Bradley to a 3/$30M deal and gave them (sans Carlos Silva) .2 WAR.

Now the calculation would put Bradley at $150M per WAR (which would be correct, you'd have to sign 5 Milton Bradleys (which might actually be hilarious) to achieve 1 WAR. However, the "best" way to calculate Kawakami's cost/WAR would put him at $33M to achieve 1 WAR (which would be technically impossible no matter how many of him you sign). Now, Bradley was .4 WAR more productive than Kawakami but cost ~$120M more? This also applies to the handful of guys that achieved replacement level.

I could take the worst deal possible and add it to the contract cost. (The worst deal ever, so far, was Kei Igawa. 5/$20 and provided .1 WAR - $200M per WAR.)


I thought about it some and here is what I came up with. It could serve as a solution for any player who has less than 1 WAR. Set their contract as the cost for 1 WAR, then add the necessary WAR to get up to 1 WAR. Using the examples you already mentioned.

Bradley: achieved 0.2 WAR on 30 million contract; 1 WAR = 30 million. Cost equals 30 + 30(1-0.2)= 30 +30(0.8) = 54 million per war

Kawakami: achieved -0.2 WAR on 23 million contract; 1 WAR =23 million. Cost equals 23 + 23(1- (-0.2)) = 23 + 23(1.2) = 50.6 million per WAR

Linebrink; achieved 0.1 WAR on 19 Million contract; 1 WAR = 19 million, Cost equals 19 + 19(1-0.1) = 19 +19(.9) = 36.1 million per WAR

Igawa; achieved 0.1 WAR on 20 million contract; Cost = 38 million per WAR

Bradleys contract still ends up worst despite being a positive war because the other guys signed for a lower amount (this sentence is definitely a downer).

Not sure if this will work for what you are doing but it will avoid outlandish numbers like 150 million per win (though 50 million is bad as well). It also involves calculation price per WAR different for players with less than 1 WAR than ones with greater, but I think it would work out okay based off of some random numbers I did for players with greater than 1 WAR.

#17 hansman1982

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Posted 03 April 2013 - 02:56 PM



If WAR is negative you could add extra cost to the contract, because the team actually paid someone to make them worse.


I thought about calculating the cost per WAR for all of the other contracts in baseball and using the total contract plus that amount. Now that I am typing that out it makes more sense than when I first thought of it. That should encapsulate the additional cost required to get a useful player, on average.

What I don't like about that, though, is how it benefits the guy who got -.1 WAR vs. .1 WAR. While both of them equal, roughly, the same amount of wasted money, the .1 WAR guy is going to negatively impact the overal calculation more.

Example:

The Braves signed Kenshin Kawakami to a 3/$23M contract in 2009. He proceeded to give them -.2 WAR over his contract. At the same time, the Cubs signed Milton Bradley to a 3/$30M deal and gave them (sans Carlos Silva) .2 WAR.

Now the calculation would put Bradley at $150M per WAR (which would be correct, you'd have to sign 5 Milton Bradleys (which might actually be hilarious) to achieve 1 WAR. However, the "best" way to calculate Kawakami's cost/WAR would put him at $33M to achieve 1 WAR (which would be technically impossible no matter how many of him you sign). Now, Bradley was .4 WAR more productive than Kawakami but cost ~$120M more? This also applies to the handful of guys that achieved replacement level.

I could take the worst deal possible and add it to the contract cost. (The worst deal ever, so far, was Kei Igawa. 5/$20 and provided .1 WAR - $200M per WAR.)


I thought about it some and here is what I came up with. It could serve as a solution for any player who has less than 1 WAR. Set their contract as the cost for 1 WAR, then add the necessary WAR to get up to 1 WAR. Using the examples you already mentioned.

Bradley: achieved 0.2 WAR on 30 million contract; 1 WAR = 30 million. Cost equals 30 + 30(1-0.2) million = 54 million per war

Kawakami: achieved -0.2 WAR on 23 million contract; 1 WAR =23 million. Cost equals 23 + 23(1- (-0.2) = 23 + 23(1.2) million = 50.6 million per WAR

Linebrink; achieved 0.1 WAR on 19 Million contract; 1 WAR = 19 million, Cost equals 19 + 19(1-0.1) million = 36.1 million per WAR

Bradleys contract still ends up worst despite being a positive war because the other guys signed for a lower amount.

Not sure if this will work for what you are doing but it will avoid outlandish numbers like 150 million per win (though 50 million is bad as well).


Better.

What if I were to only sample the players that provided 1+ WAR in a season, figured their $ per WAR ($WAR (Which for illustrative purposes we will set at $5M)) and set that as the cost basis for players with >.5 WAR. So (setting contracts to a fixed amount and years to act as a control):

Bradley's cost per WAR would be $30M + (1 - .2) * $5M * 3 (Length of contract (you would have to, effectively, buy up to 1 WAR each year)) = $42M

Kawakami would be $30M + (1 + .2) * $5M * 3 = $48M

Linebrink = $30M + (1 - .1) * $5M * 3 = $43.5M

Actual numbers (still using $5M per WAR for replacement player) (since that turned out as you would expect)

Bradley = $42M cost per WAR
Kawakami = $41M
Linebrink = $37M
Igawa = $42.5M

Does this seem better or worse?

Once this "Better Cost" (capitalization intentional) gets hammered out, then you add these back into the total cost and get a better estimate of how much teams actually paid per WAR.

One thing I didn't think of before, is that we are expecting 1 WAR over the life of the contract. Should we be calculating for 1 WAR per year? Then do similar calculations for <1 WAR players each year.

#18 CubChymyst

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Posted 03 April 2013 - 04:17 PM

I think either way you go you'll reach the same conclusion, with a contract for a bad player you end up paying a huge amount for 1 win. My assumption is your going to find out that their are a few different types of free agents. Ones that exceed their contract (less than 5 million per win), ones that match their expected value (5-7 million per win), ones that are that are bad (10-15 million per win) and then the albatross contracts (greater than 15 million per win). What I'm curious about is what percentage of contracts fall into each level and how the long term contracts stack up against the short term.

As far as expecting, your expecting the player to live up to the contract. The different formula for calculation war for players less than 1 is due the asymptotic nature of numbers when dividing as you approach 0 and the fact that some players have negative WAR. For players with WAR greater than 1 I would use the straight forward calculation ($$Contract)/(accumulated WAR for length of contract).

#19 hansman1982

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Posted 10 April 2013 - 02:44 PM

Alright, I finally got a minute to work on this a bit.

Using the calculations above, I calculated that GM's got around $6M per WAR from guys with some sort of positive WAR. To get that number I took the average of:

1. The cost per WAR provided by guys who provided at least 1 WAR over their contract. ($7.6M)
2. Blah blah blah, for guys who provided an average of 1 WAR per season of the contract. ($5.1M)

From there, I plugged that in above and ran out, with that formula or straight $/WAR for each year of a player's contract using AAV.

The cost per WAR was $11,383,609.10

The average free agent contributed 1.4 WAR the first year, .9 in year two, then: .7, .8, .9, -.1 in year six.

The only 2 FA classes that would take you to the playoffs would be 2010 (49 WAR) and 2012 (70.3 WAR). One other class would have gotten you above .500. The rest were below .500.

I shall do more digging, though. I am not satisfied I have quite answered the question, what is free agency good for?

#20 SirCub

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Posted 10 April 2013 - 03:37 PM

How about frequency distributions of players' $/WAR, broken down by contract year? That'd be pretty cool to see.

#21 hansman1982

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Posted 10 April 2013 - 05:53 PM

How about frequency distributions of players' $/WAR, broken down by contract year? That'd be pretty cool to see.


Ya, ill work on that. Get a distribution.

I also need to get their pre-contract war and start looking at that. I don't know how overpaid any of these guys were.

#22 Luke

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Posted 10 April 2013 - 07:38 PM

Using WAR as an exponent on a constant I think will solve the problem of WAR less than 1, including negatives, but that also rapidly devalues Dollar/WAR for good players.

I've played around with some options, but I don't have a complete solution yet.

Something like:

(AnnualContract/LeagueMinimum) /10^WAR

I think starts to get there, but it breaks down rapidly above 1 WAR.

Interesting problem.

#23 hansman1982

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Posted 10 April 2013 - 09:06 PM

Using WAR as an exponent on a constant I think will solve the problem of WAR less than 1, including negatives, but that also rapidly devalues Dollar/WAR for good players.

I've played around with some options, but I don't have a complete solution yet.

Something like:

(AnnualContract/LeagueMinimum) /10^WAR

I think starts to get there, but it breaks down rapidly above 1 WAR.

Interesting problem.


Could we have two separate solutions to the question of how much is a WAR worth? One for small amounts of WAR and one for large amounts of WAR?

Well, shoot. Einstein couldn't even help us here. I'm looking forward to jumping into this more tomorrow.

#24 hansman1982

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Posted 11 April 2013 - 03:06 PM

I looked at this again today, this time, breaking out the guys who signed 5 year or longer contracts and how they did in each year. Then I took those numbers, summed up by contract year (regardless of when a guy signed, what was his WAR in the first year, 2nd year, etc...)

From there, I took how many guys were in each "year" and divided the total WAR for that year by the number of guys. Basically WAR per contract year. Of the top free agents in each class, how did they do, on average, each year they were signed.

Year of Contract - Average WAR

First --- 3.076
Second --- 1.988
Third --- 1.66
Fourth --- 1.031
Fifth --- .908
Sixth --- -.1

The Fifth and Sixth years are skewed by small sample sizes.




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