Does value change during an auction?

Unfortunately, due to time constraints, I did not complete my review of the best 108 A.L. pitchers versus the 108 A.L. pitchers purchased. So I did not have time to complete the analysis I did for A.L. hitters yesterday. I'll come back to that.

Instead, I'll look at sas4's comment from two days ago about player values:

Once upon a time, long, long ago, there was a fantasy league concluding its auction. Almost all of the rosters were filled and only two teams had any money left. Very few serviceable players were available excpet for one, George Brett, who was at the pinnacle of his career.

The bidding was fast and since owner A had $62 left and owner B had $59 left, Brett sold for $60 -- to owner A.

Owner B rounded out his team with a number of lousy players as the other owners shook thier heads.

We can agree that Brett was not worth $60? Maybe a dollar was not worth a dollar by the end of that auction.

The point being: we start the auction with a 'snapshot' of the value of all players, but maybe, during the course of the auction, the value of players changes depending upon who is left and how much money is available.

(And maybe another variable is roster spots neeeded to be filled?)

At the end of that auction, Brett was worth $60.

In order to respond thoroughly to sas4, I need to once again review auction theory.

Prior to a player auction, most owners distribute the money available to spend across the best players they believe are available. In almost every rotisserie league, the players frozen are worth more than the prices they are frozen at. This is known as inflation.

Using my American League as an example, this year there were 114 players kept at a salary of $1,233. Therefore, there were 162 players to buy for $1,887. These are cold, hard facts. No matter what you think the kept players or available players might be worth, there is no disagreement on this in any league.

In my opinion, the 114 frozen players were worth $1,525. This meant that the 162 players left to buy were worth $1,595. My inflation rate, as a result, was 18.31%, or $1,887/$1,595.

In theory, inflation does change with every player, which is what I believe sas4 is talking about. To illustrate this, I'll show you the first round of my American League auction from this year:

Round 1: 2007 Billy Almon Brown Graduate League

#	Player	Cost	Inf. Value	+/-
1	Joe Nathan	$45	$39	-6
2	Mike Piazza	$19	$21	+2
3	Mariano Rivera	$37	$38	+1
4	Alex Rodriguez	$42	$44	+2
5	Daisuke Matsuzaka	$40	$30	-10
6	Derek Jeter	$35	$35	0
7	Paul Konerko	$32	$32	0
8	Ben Zobrist	$7	$2	-5
9	Sammy Sosa	$6	$6	0
10	Francisco Rodriguez	$40	$38	-2
11	Bobby Abreu	$37	$38	+1
12	Kelvim Escobar	$22	$19	-3
	Totals	$362	$342	-20

The inflation value listed is the value of inflation assuming that the auction is linear. Which, for the purposes of the auction on the whole, is true. At the end of the auction $1,887 will be spent on 162 players. The "Inf. Value" column is a linear distribution of the $1,887 left to spend for the $1,595 worth of talent I believe is left.

However, inflation is actually not linear and changes every time a player is purchased. When Joe Nathan is purchased for $45 and I believe his inflation value is only $39, there is now $1,842 left to spend on $1,556 worth of talent. Believe it or not, the inflation rate actually goes up incrementally, from 18.31% to 18.38%. This is not a misprint. Even though Joe Nathan is overpriced, inflation goes up ($1,842/$1,556 = 18.38%).

At the end of this round, even though the 12 players purchased cost $20 more than their inflation value, inflation has gone up. My league has $1,525 to spend on $1,263 worth of talent. Inflation has gone up to 21.7%, or $1,525/$1,263.

So, in theory, value does change during an auction. In practice, though, you must maintain discipline and resist the tempation to start applying the "new" inflation rate after every player. At the end of the auction, if you don't resist this temptation, you will overpay for your team as inflation goes "up". Why? Because inflation will eventually revert back to what it was before the auction. Nothing will have changed. The $1,887 will be spent, and the talent in the pool will be worth $1,595.

And this is the problem with assuming that George Brett was worth $60.

In reality, inflation is a gauge of how much money is left to spend on the talent that is available in the auction. It is not a gauge of what a player is worth. That will not change during the season.

Inflation causes us to overpay for statistics. With one or two exceptions at the most, we know we're going to overpay for the stats we're buying in the auction. We accept that fact, and try to minimize this through savvy purchases. Nevertheless, we know that inflation is dragging our teams back toward par.

In the example sas4 provided, Owner A and Owner B didn't spend enough money on the rest of their teams. Owner A repaired the damage to some degree by purchasing George Brett. But, even if Brett earned $40 that year, his inflation value would only jump to $48 if league inflation was 20%. Brett would still result in a $12 loss for his owner. In all likelihood, Brett lost his owner more than $12.

In the context of that particular moment in that particular auction, Brett was a good choice. But both Owner A and Owner B should have spent their money beforehand. George Brett isn't "worth" $60. He will lose money for Owner A. Brett's value didn't change. The amount of money a team had to spend on Brett is what changed.

Brett would earn what he earned in this example. But Owner A should have been more aggressive early and filled out his team with fewer scrubs. Brett's price, in context, might be better than Owner B's strategy of filling in holes at the end of the auction with garbage. But it doesn't change the fact that Brett wasn't worth $60.