How players are priced

Every lot in the sale carries a printed estimate — $17–27M, say — before a single bid is made. It is not a hint somebody typed in. It falls out of three numbers, and once you can see all three you can tell a bargain from a disaster in about a second, which is roughly the time the clock gives you.

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Why an estimate exists at all

A real saleroom prints an estimate against every lot in the catalogue, and it does it for one reason: without a number, a first bid is impossible. You are holding a hundred million and five empty slots, a player walks out rated 87, and you have no idea whether twelve million for him is theft or ruin.

The computer opponent has always known this number. It values every player against what is still gettable and bids accordingly. Printing it for the human simply stops the central decision of the game from being made blind. It is derived from the same curve the opponent bids from — which is what makes it arguable rather than asserted. An estimate you can beat is information; an estimate somebody typed in is a hint.

1. The curve: value bends upward

The first number is the player's rating, run through a curve that is deliberately not a straight line:

curve = ((rating − 60) ÷ 39) ^2.1

A rating of 60 produces zero. A rating of 99 produces one. Everything else lands in between, but not evenly — the exponent of 2.1 means value rises faster than rating does. That single choice is what makes the game a game.

An 80 is not "a bit worse" than a 99. On this curve he is worth a quarter as much. With only five slots to fill, one genuine star really does beat two solid starters, and the pricing says so out loud rather than leaving you to discover it in the simulation afterwards.

2. Replacement level: what you are actually buying

The second number is the one most people never think about, and it is where most money is lost. A player is not worth what he is. He is worth the difference between him and whoever else you could still get for that slot.

So the game looks at everyone left in the pool who can play the position, sorts them by rating, and takes the man about 40% of the way down that list. Not the best one left — somebody will outbid you for him — but the level still realistically obtainable once the obvious targets are gone. That is replacement level, and the player being priced is removed from the pool before it is measured, because a man cannot be his own alternative.

The gap between his rating and that level is his edge. A 93 in a pool where the next gettable centre is an 78 has an edge of 15. The same 93 in a pool stacked with other centres has an edge of 4, and is worth dramatically less to you — not because he got worse, but because you had somewhere else to go.

3. Scarcity: how much that edge is worth

Edge is converted into a multiplier that runs from 0.5 to 1.5:

scarcity = 0.5 + min(1, edge ÷ 20)

No edge at all halves the price. An edge of twenty or more — a genuine hole in the market at that position — multiplies it by one and a half. Between the two it is linear. A player with a big edge is worth three times the same player with none.

The whole arithmetic

Those three numbers, plus the budget spread evenly across a roster, produce the midpoint:

midpoint = curve × scarcity × ($100M ÷ 5 slots) × 2.2

The printed band is then 80% of that midpoint at the bottom and 125% at the top, with at least a million of daylight so it never reads as one price printed twice. Here is the whole thing end to end, with ratings given as effective ratings — a player gets +3 at his natural position and +1 at his secondary one:

Note what the top row means in practice. A maxed-out player in a thin position is estimated at over half your entire budget. You can afford exactly one of him, and then you are shopping in the bargain bin for four more. That is a real decision, and it is the decision the game is about.

The estimate is deliberately seat-blind

The number printed in the catalogue does not know whose turn it is, how much money you have left, or which holes are still open on your roster. It prices against a full paddle — the whole budget spread evenly over a whole roster — so that both bidders read the same figure off the same page.

The computer's own private valuation does none of that. It scales by its remaining budget over its remaining slots, which is correct for deciding what to pay and quite wrong for printing in a catalogue: the same player would carry two different estimates depending on who was looking at him.

This matters when you are reading the room. Late in a sale, when the computer bids thirty for a man estimated at eighteen, it is not being irrational. It is telling you it has money it must spend and holes it must fill, and that information is worth more than the estimate is.

The floor that shapes every bid

One rule constrains everything above it: every slot must be filled. The auction will not let you bid your way into a roster you cannot complete, so the most you can ever offer is your budget minus one million for each hole you still have open.

With five slots open, your true ceiling on the first lot is $96M, not $100M. It is a small difference on lot one and a decisive one on lot eight, when two holes and eleven million left means your real maximum is ten. Bidders who ignore this spend their way to a legal roster of one star and four minimum-priced bodies, and then lose to somebody who bought five 85s.

Where the estimate is wrong on purpose

It is a band, not a price, and a contested lot can run well past the top of it. Three situations reliably break it:

• The last man at a position. Replacement level collapses when a position is picked clean, so the final decent centre is worth far more than his rating suggests — and the estimate, measured against a nearly empty pool, will often say so before you have noticed.
• Endgame money. A bidder with forty million and two slots left has to spend it. Estimates assume an even spread; a cornered opponent does not.
• Position flexibility. A player who covers two positions is worth more than the band shows, because he is priced for the slot he was called for, not for the hole he lets you leave open.