Prying Open the Black Box
Hi Doctor Nick! Dr. Dougal! Father Nick! Whoever!
So, time for the yearly explanation of pricing and price changes. Almost as exicting as Father Jack’s yearly bath, of which we shall not speak
You just spoke of it
Which we shall not speak of again.
Anyways, pricing is pretty simple. Every year the SC gods come up with a magic number. You can do a magic trick with the number. Multiple a player’s average by it, round to the nearest $100, and you get their price.
That trick never works!
What are you a flying squirrel? ‘Cause I am definitely not a Moose!
I love that I made you say you are not a Moose? Feeling defensive about your Mooseness? Perhaps someone protests too much?
I, um….Yeah, ok, that trick does sometimes not work. Players get a discount if they miss enough games. I ran number down to 15 matches where it still worked, and then got bored and stopped. But, for players who do not get a discount, it is dead on.
Yeah. Very. And, by the way, I did not figure this out the hard way, I read about it on the Google. I did, however check it and check it again every season as part of Cow Talk’s Mr. Magic Spreadsheet creation process.
Oh, so you can cast 6th level Magic User spells? I though you were a Cleric?
….You’ve run rings around me logically. Shut up and let me explain more.
Right, so starting prices. Figuring out the magic number each year is easy, even more so if you are not too worried about precision. Take the most expensive player in the game who played a lot of matches, I just use 22 even though I don’t need to, and divide their price into their real average. Not the one rounded off that is shown on the SC site. So, for Titch: Price of $700,800 / (2840/22) = 5428.732394. If we stopped there that would work ok, and dropping a few numbers past the decimal wouldn’t matter much either for anything quick and dirty. But, if you take 5428.732394 and multiply it by Max Gawn’s average, you get $692,163, which rounds to $692,200, which is not his price. The Great Bearded One only costs $692,100.
So to get a better number for use when we care, I did the same calculation on 19 other players and then averaged the results. That came out to be 5428.5890015908. I love that number, because I can just use 5428.589! When I plug that back in to all the 20 players, plus my random sample of player with less than 22 games, they all come back correctly. Using 5428.59 does too, and is no more than a dollar different, so you are pretty safe just using that if you like.
So, all that for starting numbers?
Yeah, I want to be sure it is clear and show my work, and that I am not making this up. On to price changes.
Again, I found this with the aid of the Google. I have also checked it, tested it, and used it for Cow Talk. It works, every week, for many weeks. Other methods are inaccurate heresy! Unless they can prove to be more accurate, in which case I will pretend to have always know that and change. But, not expecting that at this point.
At the beginning of each week every player has a value. After three rounds, a new price is calculated each round. The *base* formula is:
(.75 * current price) + (.25 *Magic Number * (average of last three rounds))
So if Jack Steel scores a ton each of the first three rounds, his price after R3 would be:
(.75*$512,600) + (.25*$5428.589) * (100) = $520,165. Rounded off to $520,200. If he keeps scoring 100 every week, his price will slowly get closer to (100*5428.589) = $542,858.
A player who scores what he was priced to average every week would stay at the same price, unless rounding to the nearest $100 made it change $100 at some point.
Breakevens are the number that when plugged into the above formula, will result in no price change.
Say Jack Steele goes for 130 and 130 the first two weeks and sets a record for “corrective” trades in. What does he have to score for his price to not change?
(.75*$512,600) + .25*((5428.589) * ((100+100+BE)/3)) = $512,600
It turns out to be 43.278. Since BEs are round numbers, it would be shown as 43. Have you ever noticed that sometimes when a player hits the BE, they go down in price anyway? That can be due to rounding error if it is a $100-200 difference. If Jack Steel scored a 43 in the above example, using the base method he would go down $100. ($512,474 rounded up) If he scored 44 using the base method he would go up $300. But, sometimes the difference is bigger.
Now, you may have noticed I said *base* formula with the base all “*’d” and stuff. That is because, for some reason, the SC gods want the total price of all players to add up to the same amount every week. More players go up in price then down in price each week, for more total money. That means every player’s price is scaled down each week, by the same percentage. What SC seems to be doing is:
(Total $ value of all players in previous round / total $ value of all players new round) * player’s updated $ value.
So, if the total value of all players before R5 is $1,000,000 and the total after running the base formula on all players is $1,014,000 then $1,000,000 / $1,014,000 = 0.98619239. Keeping with the Jack Steele example, his actual SC price would be:
(.75*$512,600) + .25((5428.589) * ((100+100+43)/3)) = $512,474 * (1,000,000/1,014,000) = $505,399.
This effect and adjusting for it when making predictions makes the Cow Talk calculations a real pain!
Let’s look at a real life example from last season.
(In which I watch FD get increasingly confused, and he does not include the example.)
Ok, now let’s look at that example using last year’s magic number in the calculations. Brodie Grundy this time.
His actual prices are on the left. His prices as projected by the base system, (rounded) are ones the right. Next to that is the percent and amount different, and then the week by week percent change
The week to week numbers fit how we know the season words. On round 3 we get the first price changes of the season. All the cows get their biggest price increases their first week, and sure enough there is the biggest overall drop. Round 4 has the next highest drop, followed by steady and slowly decreasing drops until the mid season, where things are pretty even. Which also fits cows, since there are few showing up and the ups and downs are more balanced.
Of course to make things complicated, not all players are off by the same amounts. I blame rounding, possibly incorrectly. But, the overall trend is the same. Below is the same chart but for Max Gawn.
As you can see, same basic pattern.
These price adjustments matter a lot, since even premium players doing well are likely to come down in price over the early part of the season. Or, as in the two cases, here, their prices rose far less than they otherwise would have.
Because he is lazy, he stole this bits from last season’s write up and just changed the numbers.
I am often asked how much is one point worth within the price change calculation? Using math we know it is 1/12th of the magic number each week. If next weeks number is 3/4 the existing price, and 1/4 based on the three most recent scores, then each of those most recent scores is 1/4 * 1/3 = 1/12. This season, without the multiplier, a point would be worth about $452. With the multiplier, I would use $445 or so, remembering that the exact amount changes every week. (Arrgh!)
Oh, and I did check if the magic number itself changes, but the data fits a multiplier and does not fit the magic number changing. The fact that Supercoach changes the multiplier each week is a big reason Cow Talk is not a quick-to-math post each week, and why those numbers are only “close enough” and not exact.
How sure I am of all this? Well, it is mostly all put together from sources, and can be used to make projections that work pretty well. We know that Breakevens are not exact, the Supercoach site even says so. From the FAQ:
“There are however certain factors that impact the Break Even calculations that make it impossible to determine a 100% accurate Break Even figure before the whole round of matches has been played and the scores processed. Projected Break Evens for rounds beyond the next one are projections based on an analysis of the projected scores for those rounds and the corresponding projected price changes.”
Oh, now doesn’t that just fit well with what I just went over!
I will note that is anyone has alternate methods, I would love to take a look and try to validate them. I encourage people to test out the above and not take anything on faith.
Well, not as far as math goes at least!
Ok, my brain is empty and I am gonna stop here. I’m going to follow up with a post about how the drops affect growth, and probably make a new set of cow growth reference tables using the average drops from a larger set of players.
Thanks for reading!
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