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Originally posted by Ken
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Sour Masher, you hit on one of the key components that most people skip, which is considering the relative $'s not spent and nuking them for inflation.
But we can do that in a general formula, and it turns out some of the numbers cancel out.
Let's take a step back away from the problem for a second. What we really care is total value... at the end of the auction. Let's start by looking at what we would have if we don't keep anyone.
$260 (or placeholder, it works for any total budget) / (1 + inflation/100)
So we are talking about 260/1.25 here = $208. If you don't do anything with keepers that is your base.
And the key is your total EV if you keep a player, vs if you do not.
Lets say I keep player Z. Reminder Player Z is on a $14 contract and you believe he's worth $40.
So I will have my $40 of value, and then I will have ($260 - $14) remaining. But that remaining auction money will be worth less due to inflation. Specifically 25% less. (one interesting nugget here, is that we are seeing that the more a keeper COSTS, the less I'll be subject to inflation during the auction - this is counter intiutive in the general sense - we all want our keepers to be cheap - but in fact when comparing two keepers we need to keep in mind that the more expensive a keeper is, the less money I will have left at auction - which sounds like a bad thing, but that means I'll have less money that is subject to inflation!)
So my EV for keeping player Z is $40 + ($260 - $14) / 1.25 = $40 + $246/1.25 = $236.8. In other words, if I keep player Z and no other keepers, my expectation should be to come out of the auction with $236.8 of total value (which is not good, I want more than $260!)
The "keeper value" of player Z is the $236.8 EV - my base $208 = $28.80 ******** Note, this is the value correctly scaled that we should use when comparing the values of different players. It's truly the net profitability of keeping this player.
So, Sour Masher, at this point you are thinking, "but you said I'd answer in 1 step, and you took more steps than I did".
... but there's a trick. Let's change our values into variables and look at the total equation.
Lets call our price too keep the player (in this case $14) X
Lets call our valuation of the player (in this case $40) Y
And lets call our total budget (normally $260) Z
And lets call our inflation (our example was 25) i
The specific numbers don't matter. This formula works in all cases.
Above we said our base was 260/1.25. That is Z / (1 + i/100).
And we said our EV for our whole team was 40 + (260-14)/1.25 => in the general sense Y + (Z - X) / (1 + i/100)
And our "keeper value" which is the number we care about, is simply the difference in those two numbers.
[Y + (Z - X) / (1 + i/100)] - [Z / (1 + i/100)]
This simplifies down to:
Y - X/(1 + i/100)
40 - 14/1.25 = 28.80
So all I'm doing is taking my valuation, and subtracting the keeper PRICE of the player divided by inflation.
Everyone thinks you multiply the value by inflation (I used to think this too).
Nope.
We divide the price by inflation to get our true valuation.
Player X = 30 - 1/1.25 = 29.20
Player Y = 35 - 8/1.25 = 28.60
Player Z = 40 - 14/1.25 = 28.80
Surprise! Player X is the answer.
I picked examples that were really close so that I would not get generic answers (Feral!), and in this real scenario I'd obviously go with Player Z. Our valuations are not precise enough to go down to decimals like this.
But the takeaway here is a) surprise, the answer is Player X which no one got correct. b) there's a really simple solution to the question and c) use your inflation to reduce your PRICE not to increase your VALUATION!
Value minus (Price over inflation).
That's it. That's all you have to do. It takes everything into consideration and gives you that true "keeper value" that we are always looking for when comparing keepers at different price points. (Obviously positional needs, and contract - a/b/c/z - matter too, but that's not what I was trying to compare here).
Anyway, I hope this was as surprising to you guys as it was to me when I came across it!
Let me know if you disagree with anything here.
But we can do that in a general formula, and it turns out some of the numbers cancel out.
Let's take a step back away from the problem for a second. What we really care is total value... at the end of the auction. Let's start by looking at what we would have if we don't keep anyone.
$260 (or placeholder, it works for any total budget) / (1 + inflation/100)
So we are talking about 260/1.25 here = $208. If you don't do anything with keepers that is your base.
And the key is your total EV if you keep a player, vs if you do not.
Lets say I keep player Z. Reminder Player Z is on a $14 contract and you believe he's worth $40.
So I will have my $40 of value, and then I will have ($260 - $14) remaining. But that remaining auction money will be worth less due to inflation. Specifically 25% less. (one interesting nugget here, is that we are seeing that the more a keeper COSTS, the less I'll be subject to inflation during the auction - this is counter intiutive in the general sense - we all want our keepers to be cheap - but in fact when comparing two keepers we need to keep in mind that the more expensive a keeper is, the less money I will have left at auction - which sounds like a bad thing, but that means I'll have less money that is subject to inflation!)
So my EV for keeping player Z is $40 + ($260 - $14) / 1.25 = $40 + $246/1.25 = $236.8. In other words, if I keep player Z and no other keepers, my expectation should be to come out of the auction with $236.8 of total value (which is not good, I want more than $260!)
The "keeper value" of player Z is the $236.8 EV - my base $208 = $28.80 ******** Note, this is the value correctly scaled that we should use when comparing the values of different players. It's truly the net profitability of keeping this player.
So, Sour Masher, at this point you are thinking, "but you said I'd answer in 1 step, and you took more steps than I did".
... but there's a trick. Let's change our values into variables and look at the total equation.
Lets call our price too keep the player (in this case $14) X
Lets call our valuation of the player (in this case $40) Y
And lets call our total budget (normally $260) Z
And lets call our inflation (our example was 25) i
The specific numbers don't matter. This formula works in all cases.
Above we said our base was 260/1.25. That is Z / (1 + i/100).
And we said our EV for our whole team was 40 + (260-14)/1.25 => in the general sense Y + (Z - X) / (1 + i/100)
And our "keeper value" which is the number we care about, is simply the difference in those two numbers.
[Y + (Z - X) / (1 + i/100)] - [Z / (1 + i/100)]
This simplifies down to:
Y - X/(1 + i/100)
40 - 14/1.25 = 28.80
So all I'm doing is taking my valuation, and subtracting the keeper PRICE of the player divided by inflation.
Everyone thinks you multiply the value by inflation (I used to think this too).
Nope.
We divide the price by inflation to get our true valuation.
Player X = 30 - 1/1.25 = 29.20
Player Y = 35 - 8/1.25 = 28.60
Player Z = 40 - 14/1.25 = 28.80
Surprise! Player X is the answer.
I picked examples that were really close so that I would not get generic answers (Feral!), and in this real scenario I'd obviously go with Player Z. Our valuations are not precise enough to go down to decimals like this.
But the takeaway here is a) surprise, the answer is Player X which no one got correct. b) there's a really simple solution to the question and c) use your inflation to reduce your PRICE not to increase your VALUATION!
Value minus (Price over inflation).
That's it. That's all you have to do. It takes everything into consideration and gives you that true "keeper value" that we are always looking for when comparing keepers at different price points. (Obviously positional needs, and contract - a/b/c/z - matter too, but that's not what I was trying to compare here).
Anyway, I hope this was as surprising to you guys as it was to me when I came across it!
Let me know if you disagree with anything here.
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