Another season, another explanation of prices with the new numbers
( This season I steal from my past self and rewrite last year’s post, since little has changed, and this saves me time I can use for other research. )
Firstly, every season the Gods of Supercoach (mock them at your peril) come up with a magic number for that season. When you multiply the magic number by a player’s average from last season you get their price for this season. Well, you get it after rounding to the nearest $100. How do we know this? First we can prove it with math. Second, this was stated explicitly on an official AFL podcast a while back!
Some players get a discount applied based on the whims of the Gods. In theory they have “A System” but in practice they do not always follow the rules as we know them. You can figure out if a player has been discounted and by how much if you multiply their average by the magic number and subtracting their real price from that. If the difference is less than $50, it is from rounding. If it is more, that is the discounted amount.
Once the season starts, prices start to change. New prices are based on the current price and the average of the last 3 scores, and the magic number. The base formula is [ (Current-Price * .75) + (Average-of-the-last-three-scores * .25 * Magic-Number) * Weekly-Multiplier] So the current price counts for ¾ of the new price and the last three scores average counts for ¼. The weekly multiplier changes week to week. As best as I could determine from reading my hamster’s entrails, The Gods of Supecoach want to keep the total of all player’s salaries the same each week. Since prices as a whole tend to rise over the season, thanks to cow growth, that means in order to keep the total the same, every week all prices need to be scaled back. This is why premium player prices drop over time even if they keep the same average as they had the previous season.
How much do players drop from the multiplier? At the start of Week 10, 2016 all player prices were around 5.5% lower than they would have been without it. Exactly how far varies a little; I think from repeated rounding.
I have yet to figure out exactly, or even mostly, how this is affected by the byes. It is one of those things that I want to know, but I don’t want to spend the time on that when there are more useful things I can work on.
Note that at least in past seasons, the breakevens provided by Supercoach Gold do *not* take the multiplier fully into account and are therefore a little bit low. Since the multiplier can’t be calculated until after a round finishes it makes sense that it can’t be completely accounted for. That means all of the breakevens SC Gold provides are a little bit low. I have run into cases of players exactly making their breakeven and then not actually breaking even, which was a Big Clue.
Oh, almost forgot. 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 $458. With the multiplier, I would use $450, 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. Also, the multiplier seems to be newly calculated every single week. For season projections I will probably use what the week to week multipliers from last/a past season, even though they won’t be exact, they will be close enough to use. 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 to calculate this season’s magic number
Last season I wrote in detail about how I figured out how to do this. This season, I’m just gonna explain how it works and those of you who care about the experimental process can look it up! I’ll still show my work of course.
To do this at home – and you can try it at home, math is good for you – Take the twenty five players with the highest price who also played 21 or 22 matches. For each one, divide their total points from last season by their matches played last season to get their average. Do NOT use the average shown in Supercoach because it is rounded enough to mess up the results; you have to do the math yourself to lots of decimal places, with the aid of a spreadsheet of course, we’re not barbarians! Anyways, take their price and divide it by their real average you just calculated. That would be the magic number if prices were not rounded to the nearest $100. Since they are, do that for all twenty five players we picked. Then add those together and divide by 25. That’s gonna be pretty close. To check, we reverse the process to see if it generates correct prices. Multiply the magic-number you just came up with by the accurate season averages of the twenty five players, one by one, and round to the nearest $100. The results should be exactly the same as the published prices.
Except that fails! Fyfe is not only life, Fyfe is truth. Because 5497.794462 * 2248 / 21 = 597950.5977. Which rounds up to $598,000. And his price is $597,900. Bugger. The real magic number is just far enough off this average to require some adjusting.
One thing to look at is how far from the real price the reverse calculated prices are. The highest difference in the other direction is Oliver, at 46.8. So a small move won’t push him over. But now I have to think…..that took a while……as did that…..and I am thinking I need to check a big pile of averages vs the number we came up with and see how that goes. And by big pile I mean adding another 10 to the list and rerunning the same thing with 35 and seeing how that comes out. And it comes out fine, with all thirty five players producing the correct value. Fyfe is Fine, and Oliver is closer to but not over the line in the other direction.
While I initially panicked, I remembered how tolerant the numbers are for the way we use them. I can’t handle a wrong number, but I’m good with a close enough number that’s not actually wrong. I also tried, just to see if maybe the SC gods had picked a really round number, using 5497.75. but that put players out of bounds, so no reason to fiddle further.
Anyways, that means as far as I am concerned, the magic number this season is 5497.763. I’m dropping the 044 from 5497.763044 because the change is too small to notice and using more digits is a huge pain.
Oh, I forgot to say, we use the highest priced players because they are most sensitive to changes in the magic number. We do not use players who played less than 21 matches because they might have a games-played adjustment made to their price, which would really mess things up.
When I run projections, such as the Cow Growth Reference Tables, I use the formulas above, week by week, with educated guesses based on past seasons for the multiplier. Since $100 either way does not change what we learn from projections, works well enough.
If you have any questions about all this, ask in the comments and I’ll do my best to answer!
Leave a comment / Scroll to bottom