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Price Fixing: Commentary

An Empirical Attempt at Reverse Engineering the Current Process
- contributed by Doug Taylor

December 30, 1997

I've been trying to figure out the Smallworld pricing scheme. My main sticking point right now is the following: The TOTAL value of the ENTIRE roster of available players, that is, the sum EVERYONE on the "Player Prices" page... that Total Value seems to increase over time, although some days it actually drops a bit. (Note: I have excluded the IPO players in coming up with these figures, only players as of November 10 are included).

For example, the total value on November 10 was $1,445,480,000. As of December 29 (excluding all IPOs), it was $1,482,670,000.

This is an increase of $37,190,000. Not a lot percentage wise, but almost 50 days have passed, so this is an average of about $750,000 per day. I want to know why. I will come back to this figure later.

If buys and sells are weighted equally, you'd figure you'd see little or no change in price. Now, on a daily basis, the $1.5 million cap might cause a temporary increase or decrease in the total due to the artificial price constraints, but assuming there is a 1-for-1 carryover of surplus buys and sells to the next day, then it is a temporary effect, and in the end (probably the following day) it should all balance out (i.e., up $1,000,000 one day, down $1,000,000 the next).

The only exception to this would relate to the $200,000 price floor.

Idea #1:
(NOTE: From this point forward, for the purposes of illustration I am going to assume that 1 buy or 1 sell = $10,000 price change.)

For example, suppose on Monday Penny is priced at $5,000,000 and is on the roster of 750 different managers. He sits out a game with a sore knee, and 200 managers sell.

So, next day's price: $3,500,000. Now another 50 managers decide they're going to drop him as well. Add to those 50 the carryover 50 from the previous day, and Penny drops $1,000,000 to $2,500,000 on day 3 (Wednesday) and he is still active on 500 SW rosters.

That night he sits out another game, and people realize he's going to be out a while. So 400 more managers sell him that night. Next morning, Penny is at $1,000,000. The remaining 100 managers are deadbeats and not keeping up their teams, so he is never sold off their rosters (Hey, I'm trying to make this as realistic as possible while keeping it simple.)

Finally, Friday rolls around and Penny bottoms out at $200,000... but there are still 170 "surplus sells". What happens to them? Do they magically disappear at $200,000? Or do they float around still? In the latter case, it would be as if Penny's "Virtual Price" was -$1,500,000, so that even if 150 managers repurchased the now-bargain-basement-Penny over the weekend, his price would still stick at $200,000, because his net buys and sells would still be at a -20, and thus his "Virtual Price" would still be only $0 (but being held artificially at $200,000).

I think it is more likely they do the magical disappearing trick... and in this case, those surplus sells which are "evaporating" still get turned into buys, and so for the example above, we'd see a net increase of $1,700,000 due to Penny's bottoming out.

However, EVEN if this explains a bit of the situation... there have only been two players who have dramatically bottomed out like this (to my recollection) all season... Penny and Travis Knight. All the others were guys who were in the sub-$1,000,000 range, and probably not on enough rosters to really make much of an impact.

But the price fluctuation happens EVERY SINGLE DAY. And the fact that it is overall an increasing amount suggests that something beyond the price caps of $1,500,000 is at work here.

Idea #2:
So I thought perhaps it was the continual influx of new owners that was making the difference... as each new owner means 12 additional buys without their accompanying sells (unless the owner is a flake). But the evidence from this weekend would seem to contradict this idea... case in point, Bobby Jackson. We know a lot of 2nd chance teams picked him up.

Of the 60 or so teams that I surveyed, he was listed on over half (33). If this was an accurate sample, then that would make about 70-90 total buys... yet his price dropped $260,000.

But let us think about this. I would assume that there are at least several thousand rosters out of the 50,000+ rosters out there that are being actively managed, or at least semi-actively managed. So it is not inconceivable that out of these couple thousand that 100 or so decided to sell Bobby Jackson over the weekend.

Let us consider that he was at his HIGHEST price of the entire season. So there was probably some profit-taking going on. Add to this his performances on Tuesday and Friday of last week... both 22 SWPoint games... not terrible, but by no means stellar... all of a sudden profit-taking seems like a pretty good idea. Now, he did have a nice 39 SWPoint game on Saturday, but by then many may have already taken their cash and run. Again, he WAS at a season high price.

So if we assume that a net of 100 existing managers sold him, and about 74 of our 2nd chance managers bought him (and their buys DO count), we still end up with a net of 26 sells... which under my system means -$260,000.

So maybe our buys DO count after all! Hold on a sec. If they did... that would mean a collective increase of about 1000 buys over the weekend, due to many of our 150+ managers selecting up to 11 players. This would cause the total value to increase about $10,000,000, at least according to my scale.

But in reality, the total value of all players FELL $1,450,000. Now, some of this is due to the fact that 3 players maxed out at $1,500,000 increases (Brian, Donyell, Travis) and would have risen much higher were it not for the artificial constraint. On the other hand, one player (Brevin) bottomed out at a $1,500,000 drop. My intuition is that his bottoming out comparatively small... that is, he WOULD have dropped $2,000,000 maybe, whereas Brian Williams WOULD have increased $4,000,000 probably. Now, is this enough to make up the $11.5 million difference between what I predicted and what really happened? Maybe, but probably not. But what if 1 buy = 1 sell = $5,000 instead? Then the difference is only $6.5 million... and this is starting to sound more feasible.

It will be interesting to see what happens in the next couple days as Brian and Donyell reach their stable points (Travis should already be there, I think). If we have a day in the near future with nobody maxing out on daily changes or bottoming out at $200,000, then we'll have eliminated these factors. Should be interesting to watch.

Idea #3:
This brings me to my last idea. Rounding. What if, as I suggested just a moment ago, that 1 buy or 1 sell does NOT equal $10,000? What if it is $5,000? SW daily prices change in $10,000 increments... so is there rounding going on here? Do you round up or down? Depending on the exact figure for the 1 buy and 1 sell change, and how their rounding rules are determined, this could play a big role in the daily total value changes (especially if it is biased upward due to rounding up). Part of me now thinks, "Wouldn't it be nice just to ask them and see if they would tell me?" [note from Guru: They won't tell you. I've tried. Good for them!] Ahh, but that would take all the fun out of guessing at it...

Anomalous Observation:
Nov. 20, a day that will live in infamy.

For whatever reason, on Nov. 20 prices were allowed to change more than $1,500,000... Brevin went up $2,060,000, and Penny dropped $1,570,000. But even more noteworthy, and something I never picked up on until tonight... but for that one day a price floor of $500,000 was established. Many players' prices trickled down from that point again, but still, there was an artificial boost to that point. So, on that day alone, the total value of the player roster increased $9,000,000. However, approximately $8,540,000 of it was attributable to this $500,000 factor.

Bringing it all home:
OK, so let's get back to the total increase number of $37,190,000, which was $750,000 per day.

If we consider that there have only been 28 days where prices have changed, then this is actually an average of over $1,300,000 per price change (thus excluding days where prices don't change, and there is therefore no "rounding").

Divided amongst 416 players, this is $3,193 per player, per price change. Now, if we assume that the price changes themselves are "rounded up" (so a -$5,000 would become a -$10,000), then the rounding on both the buy and sell sides should more or less cancel each other out (with some statistical error). But if we first figure the new price, THEN round it up, a -$5,000 becomes $0 instead (For example, a $1,000,000 player changes to $995,000, but this gets rounded back up to $1,000,000). And if we assume that an odd or an even number of trades are equally likely, we would expect an average rounding up of $2,500 per player per price change, which isn't too far off from the $3,193 mentioned above. But in reality, the full 416 players aren't bought and sold each price change... some just sit there. So actually if we have an average of about 50 out of our 416 players who are completely inactive each day, then we would expect an average of only about $2,200 per player per price change (since some players are dead weight). This is a bit further from $3,193.

OK, now let's take out the $8,540,000 from the Nov. 20 anomaly. So our base increase is now only $28,650,000 . Our new figure would be $2,416 per player per price change, which falls right in between our adjusted and unadjusted estimates of $2,200 and $2,500.

Well, I don't know if you followed all that, but in essence what I'm saying is that if we use the 1 buy = 1 sell = $5,000 assumption, AND we assume that after calculating the new price each day it is rounded UP to the nearest $10,000... well then that would seem to fit our data pretty well.

But as beautiful as I think that analysis was... I have one last piece of contradictory evidence to overcome.

Through December 5, the average daily change in the total value of all players was almost $700,000 per day. Since December 5, the average daily change in the total value of all players has been over $2,300,000. Why this huge discrepancy?

My theory is the $200,000 price floor discussed in Idea #1. That weekend is when Penny started dropping like a rock. Hundreds of people sold him and bought other players instead, but it took a while for his price to catch up with all that selling. And then later that week, when you might have expected things to start normalizing a bit, along comes Travis Knight, also beginning his freefall to $200,000. Then the Smallworld database freaked out, then we had a two-day week, and now here we are. Also, Idea #2, the unresolved question (at least in my mind) of whether all our "new team" activity has had any effect on prices. Quite possibly it did not, but I think the next couple days will shed more light on the subject.

Oh, and FYI... I'm not crazy... I'm just analytical and I happen to love basketball. [note from Guru: I'm also analytical and love basketball, too. But I wouldn't go so far as to say I'm not crazy....]

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