Calculating better auction prices with "Pre-Inflation"

A while back I was paging through a post about some pro-league draft results, and noticed something strange about the auction prices. Here, in graphical form, is what I saw, as illustrated by my Big Board values for a typical 5x5 league vs. Yahoo's "Average auction values":

Two things should immediately jump out at you. Highly ranked players go for way more than the projections say they should. If you've ever done an auction draft, you've seen this happen first hand. The second? Way, WAY more $1 and $2 players in reality.

This phenomenon of inflation at higher ends, deflation at lower ends, is commonly accounted for by most draft softwares (including the Big Board) by calculating how much money is left vs. how much player-value is left, and adjusting values accordingly. But when the first player is put up to bid (and the 2nd, 3rd, etc.), you have no idea how much inflation is going to show up in the draft. That means that if you adhere strictly to your $ values, you will ALWAYS miss the first X number of players auctioned - let's say, the top 20 or so. It can also make calculating Keeper values very difficult. Have you been there? I know I have. Plotted another way, you can see the discrepancy between the two sets of values here:

So then let's say you want to 'anticipate' the inflation happening in your draft... enter "Pre-inflation". By applying a fairly simple adjustment to the calculated auction values, you can almost perfectly replicate the value curve that happens in-practice during a typically inflated auction draft. To calculate the adjustment factor for the nth ranked player, I used the function:

where n equals the percentage inflation you want to apply to the top-ranked player. Pre-inflated player value is equal to the projected player value times the adjustment factor, A. You can play around with the function yourself to see how it effects values, but essentially top players are worth up to (1+n)x their original value, with A linearly decreasing down into players in the bottom half, who will be worth less than half what they are originally projected for. I also set a minimum value of $1 for all players (so that the adjustment factor doesn't create negatively valued players). The value of n that I found to be most effective is 0.5, but your mileage may vary and you may want to compare the pre-inflated values vs. past seasons of your league.

So of course, the question is whether the adjustment was effective - take a look for yourself:

Yes! I was somewhat amazed at how well this relatively simple adjustment works (Rsq=.9945!), to the point that I'm wondering if I've modeled some other behavior that I'm unaware of. But in any case, it's very effective. I've tested this against a few different sets of auction values (note, *real* auction values, not projections) and it works great.

You can apply this factor yourself, or do it in the Big Board. The Pre-inflation factor in the Big Board allows you to set the value of 'n' from the Adjustment equation shown above.  If you test it out and find it works, or doesn't work, let me know what you discover either way. Happy auction drafting, all!