The formula is linear, and based on net buys and sells ("net trades). Net trades are adjusted to approximately eliminate the initial drafting of new teams during the pricing period.

	Buys	Sells
Apr 14	540,959	317,542
Apr 21	610,766	452,037
Apr 28	570,036	454,882
May 5	491,490	406,576
May 12	555,505	461,819
May 19	427,950	359,983

I've always suspected this was the case, but wondered how Smallworld distinguished between an "initial buy" and a "trade buy". As it turns out, they don't track these buys individually. Instead, they reduce the buys for each player proportionately so that the total of the "reduced buys" equals the total sells for the week. Since draft buys won't likely be proportionate to "trade buys", especially as roster values increase during the season, it isn't quite fair to say that draft buys after opening day have no impact on pricing.

By forcing buys to equal sells, there is no upward bias on player prices. Aside from the stated price change limits (and rounding), gains and losses in any week should offset.

This factoring down of buys explains why some players seem to show a price decline in a week with positive net trades. The table shows how buys and sells compare, week by week. Even as late as week #6, total buys exceeded total sells by 18%. So, the price change for week #6 is based on 84% of buys less 100% of sells.

The system has no "memory". If net trades would have caused a price to change by more than the weekly limit, the excess is not carried over to the following week.

This was the most surprising discovery for me. And it is probably the most noteworthy, because it refutes some of the symmetry that I had always thought existed.

Assume, for example, that 10,000 net buys are just sufficient to produce a $1 million gain. Let's say that Player "A" has 10,000 net buys in each of the first three weeks, pushing his price up from $2 million to $5 million. Then, in the following week, he gets injured, and sustains 30,000 net sells all in that week. His price drops the max of $1 million, to a level of $4 million, which now effectively becomes his new floor price (assuming that no one owned him before the first week).

The asymmetry can work in the other direction as well. If everyone buys a player in one week, then sell him more gradually over several week, then the price can go below the starting point.

I haven't yet studied some of this season's big movers to see whether this has already been happening - in either direction.

This lack of carryover means that there is no inherent safety in holding a maxed out player, other than the safety implicit in owning someone who has been hot.

The other significant implication is that a player with slow, sustained buying has more price upside over the long term than a flash-in-the-pan.

By the way, the lack of a carryover effect is neither good nor bad. There are valid reasons for either formula. The key is to understand how the system works, and plan accordingly.

The price sensitivity of a trade varies from week to week, based on overall trading activity.

This helps to explain why price changes late in the season seem to maintain a similar overall volatility vs. early season changes, in spite of the inevitable decline in activity as the season wears on. Once again, this means that a net trade will tend to have an increasing impact as the season progresses.

This changing sensitivity also works against the symmetry of price changes. 800 net buys might push a player's price up by $100,000 this week, but a month from now it may only take 400 net sells to push the price back down by $100,000. So far, the number of "adjusted net buys" required to produce a $100,000 price change has ranged from a high of about 1060 (week 2) to a low of roughly 790 (week 6).

The price sensitivity of a single trade is so small that the potential for an individual manager to manipulate prices (through trading on multiple teams) is extremely remote.

I've heard the suggestion that perhaps there are managers running dozens of teams in an effort to produce enough simultaneous trades to influence prices. This now seems highly unlikely. Currently, it requires roughly 1000 net buys just to produce a paltry gain of $100,000. Unless someone has figured out an automated way to trade, an individual just can't make a meaningful impact.

What's it all mean?

Understanding this doesn't really change my strategy, or my general trading approach - at least, I don't think it does. But it does substitute facts for impressions. And there may be times when this leads to better decisions.

It may be useful to know how many times a player has been bought or sold. I haven't summarized this data this way yet, but I guess that should be the next step. Having a better feel for the relative ownership of a player - particularly the ones which are heavily owned - may help identify those players who are most vulnerable. I'm not sure whether this additional information, above and beyond the raw price change data that Gurupies have had access to all along, really adds a whole lot, though.

But it is cool to really know how this all works, isn't it?