As you may have noticed, the GMTR player rankings contain information on monetary values for auction leagues. In addition, we’ve produced an NBA fantasy cheat sheet specifically for auction leagues. If you have ever wondered how these auction dollar values are created (no, they aren’t COMPLETELY made up, just mostly), then this is the post for you. I will warn you now. This post contains math, unfortunate amounts of math. You have been warned.

First, let’s just say that calculating auction dollar values is an inexact science. There are a lot of variables that go into the calculations, some of which are completely unknown (like how each owner in the league likes to spend their money). But just because we can’t hope to accurately measure something doesn’t mean we stop trying. No, much like the local weatherman, the hopelessness of the endeavor only makes our resolve stronger.

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Let’s forge ahead by defining some important league variables.

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This judge looked an inmate square in the eyes and did something that left the entire courtroom in tears:**League scoring**: H2H or roto, 9 statistical categories**Amount of money per team**: $200 (a commonly used amount, although this can be anything in theory).**Number of teams**: 12 (other typical setups include 10 or 14, or the dreaded 30 Man)**Number of starters per team**: 10 (using a PG, SG, G, SF, PF, F, C, C, UTIL, UTIL setup, although this can vary as well).**Number of bench players per team**: 4 (guess what? This can vary too).

Good to see there is so much in common between fantasy basketball leagues out there…

Ok, with that out of the way, here comes the more complicated stuff. First up, we need to figure out the average amount a team will spend per starter. Why? This will define the mid-point of our player value distribution. Typically, teams in auction leagues spend the majority of their money on starters, since they are the most important part of a team. Online auction leagues require that a team keep at least $1 per remaining roster spot, so the most a team could spend on starters in our league with 4 bench spots would be $196 (leaving $1 left over for each bench player).

Now, in my experience, it is a good idea to leave more than $1 per bench player for the end of an auction so that you can grab a decent sleeper or two without an opposing team screwing you over by bidding $2. So, let’s leave $10 for the bench (or $10 / 4 = $2.50 per bench player) which would give us $190 for the starters (or $190 / 10 starters = $19 per starter).

This amount can range from $19.60 per starter to $14.29 ($200 / 14 players total). Although good luck to you and your team if you plan to spend an equal amount on your starters and bench players.

Anyway, we have our (somewhat debatable) answer: the average starter in our league is worth $19.

Now that we’ve figured out what the average starter is worth, it’s time to figure out who the heck the average starter is. That sounds easy enough – and it would be – if player value was linear. However, at the very top of the league are guys like Kevin Durant and LeBron James who are so much better than everyone else that they skew the average towards the high end. (It’s why trying to build a winning fantasy team out of mid-round picks is tougher than it seems).

Therefore, in a league that starts 120 players (12 teams * 10 starters per) the average player is not guy #60. If you take a look at the GMTR player rater, the average starter in a 12 team, 10 starter league is around player #55 in 9-cat leagues (due to the effect of the first round draft picks). Here is a graph of fantasy value for the top 200 players for 2009-10.

Again, the “average” player will vary depending on the makeup and size of the fantasy league. For our purposes, we will make player #55 “Mr. Average” and lock in his value at $19, or the average amount of money being spent per player in the league.

With our mid-point defined, now we just have to define our two end points. The low end of the distribution occurs when players basically become “free” or can be had for the minimum bid ($1 in this league). This will vary quite a bit depending on how the auction plays out and how owners like to spend their money, but it will almost always happen somewhere between the first bench player (player #121 in this league) and the last bench player (player #168 in this league) when teams run out of money. For lack of a compelling reason otherwise, we’ll set this endpoint between those two numbers, around player #144. This is the point where player value becomes $1.

Again, this $1 point is a moving target which depends on the league. In a league full of aggressive owners, teams might be out of money by the time the first bench players show up. I’ve also been in auctions where tightwad owners horde so much money that, by the end, guys like Mike Conley start going for $15 because teams have so much money to blow.

The final step is to calculate the upper end of the distribution, aka Kevin Durant’s value. It’s outside the scope of this article (believe it or not), but on a per game basis, LeBron and Durant’s 2009-10 fantasy season was about 3.5 times better than the “average” starter in a 12 team, 10 starter league. It’s not that LeBron and Durant deliver 3.5 times the amount of stats, rather a team with LeBron or Durant is 3.5 times more likely to win in either a H2H or roto league compared to a league average starter.

So, as long as you accept that leap of faith, it means LeBron and Durant were worth about $19*3.5 = $66.5 last season (not adjusted for games played). This season, LeBron’s stats are expected to drop slightly in Miami, but it’s safe to say that Durant will be at least as good as he was last year, if not a little better. So, taking Durant’s value last season ($66.5) and projecting a 5% improvement this season results in a value for Durant at the high end of the distribution of around $70*.

Easy enough, right? With the upper, mid, and lower points of the distribution, we can calculate the remaining players’ dollar amounts based on the distribution of player value found in previous seasons (see the graph above for the shape of that distribution). Oh and as a final step, it’s important to normalize the dollar amounts so that they equal the total amount of money available to all teams (12 teams * $200 per team = $2,400 total for the top 168 players). Otherwise, it’s possible to get dollar amounts that wouldn’t jive with the amount of money available for teams to spend.

Of course, before any of this can happen, we actually need to create a ranked list of players in order of their expected fantasy value in 2010-11. And we at GMTR just made up that list.

* The actual calculation for Durant this season came out to $69.

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Thanks to a couple readers who emailed with fascinating observations and discussion about the auction values we calculated for our player values. And special thanks to one reader who pointed out that my first attempt at calculating auction values was incorrect.

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