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A question about projection equations...

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Postby Wozzyck » Thu Jan 27, 2005 9:25 pm

xeifrank wrote:The way I'd do it (using this formula) is to calculate the values for all players. Break the players into groups, based on what position they play. Next determine how many players at each position will be drafted. In a 5 OFer league of 12 teams, with no bench there would be 5*12=60 outfielders in the OF draft pool, and the 61st player would be the replacement level. Let's say the replacement level player had a value of 500 using the formula. You would then subtract 500 from all the outfielders and this would be their replacement level value. Do the same for all positions. If you have bench slots, you may have to do a little guess work on how many players at each position would be drafted, but this should give you a rough idea of how to do it. This method will let you compare replacement values of players at different positions, to get an idea on who ranks higher or lower due to position scarcity.

vr

Xeifrank


I don't know; I've got a couple of issues with this way of assessing position scarcity. Suppose I'm in a 12-team league, and I've determined that Phil Nevin is the 13th-best 1B. Thus, assuming that my leaguemates agree with me on Nevin and there are no CI or UT positions to fill or a bench, Nevin is not a player that will be drafted in our league. However I will be determining the value of my top 12 first basemen based on how good they are relative to Phil Nevin, a player who isn't part of our limited draft universe.

Now suppose Nevin and almost all of the 1B ranked below him are suspended for some odd reason, leaving Ken Harvey as the 13th best 1B. Our player universe (for the purposes of our league), hasn't changed at all. It seems clear that I shouldn't value any of these players any differently, however using this system the values of the top 12 1B have gone up tremendously. It stands to reason that they've been valued against an irrelevant benchmark.

I think the broader problem is that alot of information is being ignored. Suppose instead that I value my players relative to the 12th best player at their respective position (i.e. a player whose value should have some relevance in my league). It's been determined that the top 12 1B have raw values of:

12,11,10,..,3,2,1

The top 12 2B have raw values of:

12,1,1,...,1,1,1

According to this new evaluation system the best 1B is deemed to be as valuable as the best 2B (each having a value of 11). However a glance at the values shows that this new system isn't doing much better at evaluating position scarcity.
I think the issue is that position scarcity is a composite of how a player rates relative to all players at his position. In other words, how a 1B compares to the 5th best 1B is perhaps as relevant as how he compares to the 12th best. So I simply don't think these are the sort of benchmarks that should be used.
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Postby Wozzyck » Thu Jan 27, 2005 11:26 pm

I'd like to amend one thing I said above. The value of the "13th best 1B", or any other such replacement player, isn't entirely irrelevant (as such players could be forced onto rosters due to injuries, etc.). But since their inclusion into the player universe is contingent on the performance/health of those above them, their value has less significance than that of draftable players and shouldn't, in my opinion, be so privilaged as to be the baseline for comparison.
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Postby xeifrank » Thu Jan 27, 2005 11:28 pm

It's one of the standard methods for determining player value taking position scarcity into consideration. Here is another example for you (though simplified).

Imagine a league that has 3 outfielders and 3 shortstops to draft, with three owners getting to select one from each of those two positions.

Your make believe outfielders are...
Player A (Value = 20)
Player B (Value = 16)
Player C (Value = 14)
--------------------------------
Player D (Value = 11)
Player E (Value = 6)

Your 3 make believe shortstops are...
Player F (Value = 15)
Player G (Value = 9)
Player H (Value = 6)
------------------------------
Player I (Value = 3)
Player J (Value = 2)

The dashed line shows you where the replacement level is for each position. The value of the first player above the dashed line is the replacement value for that position. That is the minimum value any owner should be able to draft at that position (14 for outfielders and 6 for shortstops). Keep in mind this is just an example to show you how the calculations work, the value distribution is not very likely.

Now, to calculate the Replacement Level Value for each player, simply subtract from his value the replacement level at his position.

Player A (RPV) = 20 - 14 = 6
Player B (RPV) = 16 - 14 = 2
Player C (RPV) = 14 - 14 = 0
Player D (RPV) = 11 - 14 = -3
Player E (RPV) = 6 - 14 = -8

Player F (RPV) = 15 - 6 = 9
Player G RPV) = 9 - 6 = 3
Player H (RPV) = 6 - 6 = 0
Player I (RPV) = 3 - 6 = -3
Player J (RPV) = 2 - 6 = -4

You can see from this example, that Player F has the highest RPV (replacement value) of 9. If you had the first pick in this 6 player draft (3 OFs, 3 SSs) your best bet would be to draft Player F. You are atleast gauranteed Player C in a snake draft at the other position. This would give you players of value 15 + 14 = 29, which couldn't be beat as long as everyone drafted the best available player.

Let's look at how the draft would go using RPV. Each owner must draft 1 player at each of the two positions, of course in a real league there would be more than 2 positions involved, more fantasy owners and a larger player pool. That is why it's important to have a computer do all the calculations for you.

Owner #1: Selects Player F (Value = 15)
Owner #2: Selects Player A (Value = 20)
Owner #3: Selects Player G (Value = 9)
Owner #3: Selects Player B (Value = 16)
Owner #2: Selects Player C (Value = 6)
Owner #1: Selects Player H (Value = 14)

Owner #1: Team value of = 15+14 = 29
Owner #2: Team value of = 20+6 = 26
Owner #3: Team value of = 9+16 = 25

By using the Replacment Value Algorithm Owner #1 was able to draft the strongest team of the three, even though he passed on the player with the highest value (Player A) with the first overall pick.

vr

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Postby RynMan » Thu Jan 27, 2005 11:35 pm

So Frank, question:

How do you calculate the value for each of those guys? !+)
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Postby Wozzyck » Thu Jan 27, 2005 11:47 pm

I understand that there are situations in which this sort of algorithm will lead to optimal results, but that's not a good test of an algorithm. I imagine with all slightly reasonable drafting strategies one could concoct a situation in which it leads to an optimal result. It's the fact that it that it can fail rather badly that should be troubling. I question the principles.
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Postby Tavish » Thu Jan 27, 2005 11:53 pm

I realize it was just a quick example, but wouldn't the replacement level player be the first one below the dashed line being that is what you could expect for a replacement player? Not that it really matters exactly where you set the replacement level, I'm just being pedantic.
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Postby xeifrank » Fri Jan 28, 2005 12:02 am

Wozzyck wrote:I understand that there are situations in which this sort of algorithm will lead to optimal results, but that's not a good test of an algorithm. I imagine with all slightly reasonable drafting strategies one could concoct a situation in which it leads to an optimal result. It's the fact that it that it can fail rather badly that should be troubling. I question the principles.


Give me an example where it fails.

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Postby LBJackal » Fri Jan 28, 2005 12:12 am

Tavish wrote:Not that it really matters exactly where you set the replacement level, I'm just being pedantic.


You're only allowed one user name... you cheater. Besides I thought Pedantic was younger.

:-D
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Postby Tavish » Fri Jan 28, 2005 12:13 am

LBJackal wrote:
Tavish wrote:Not that it really matters exactly where you set the replacement level, I'm just being pedantic.


You're only allowed one user name... you cheater. Besides I thought Pedantic was younger.

:-D


You calling me old you hoser??? ;-)
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Postby Wozzyck » Fri Jan 28, 2005 12:13 am

Here's a quick example where it fails to give an optimal solution:


Your make believe outfielders are...
Player A (Value = 15)
Player B (Value = 15)
Player C (Value = 5)
--------------------------------
Player D (Value = 0)
Player E (Value = 0)

Your 3 make believe shortstops are...
Player F (Value = 12)
Player G (Value = 12)
Player H (Value = 1)
------------------------------
Player I (Value = 0)
Player J (Value = 0)

Now, to calculate the Replacement Level Value for each player, simply subtract from his value the replacement level at his position.

Player A (RPV) = 15 - 5 = 10
Player B (RPV) = 15 - 5 = 10
Player C (RPV) = 5 - 5 = 0

Player F (RPV) = 12 - 1 = 11
Player G RPV) = 12 - 1 = 11
Player H (RPV) = 1 - 1 = 0

If Owner #1 uses the Replacement Player Algorithm (others using a greedy algorithm) you get:

Owner #1: Selects Player F (Value = 12)
Owner #2: Selects Player A (Value = 15)
Owner #3: Selects Player B (Value = 15)
Owner #3: Selects Player C (Value = 5)
Owner #2: Selects Player G (Value = 12)
Owner #1: Selects Player H (Value = 1)

Owner #1: Team value of = 12+5 = 17
Owner #2: Team value of = 15+12 = 27
Owner #3: Team value of = 15+1 = 16

By using the Replacment Value Algorithm Owner #1 wasn't able to draft the strongest team of the three; he could have had the best team by using a greedy algorithm.
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