Prying Open the Black Box
Hi Everybody!
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.
You’re sure?
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.
(silence)
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.
Bad Cleric!
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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Amazing. Genius.
Formula for Jack Steele was missing the .25:
(.75*$512,600) + (.25*5428.589) * (100) = $520,165
Thanks for catching that! I fixed it there and another spot.
The .25 also slightly changes each week which is why it will never be 100% accurate throughout the season
Hi Pete. Is is not the .25 that changes. I’m pretty sure the effect you are seeing is from the multiplier.
hmmmmmm. Great stuff FD. A few thoughts to follow at some point 😉
Looking forward to them!
There’s something I’ve been wanting to write about this for a while, too… but I’ve got to get the AFLW leaderboard stuff finished first. Watch this space 😉
I’m dizzy
Hi guys,
The article is correct as to prices at start of season (magic number ~ 5.43), but in error for price changes during season (magic number varies each week, I use ~5.1 as a rough estimate).
This means that a player averaging 100 will plateau to a price of about $510k, not $543k.
But that same player, if they average 100 for the year, will get inflated to $543k to start the following year.
Ever wonder why everyone feels so damn expensive to load into your team in the pre-season, but rapidly drop in price once they start playing? This is the reason.
Hence you should calculate that starting a player who will average the same as last year will cost you about 6% of their price.
That’s the multiplier in action. As Father Dougal notes further down in the article, Champion Data wants to keep the sum of all player salaries more-or-less equal throughout the season. To compensate for the (massive) price increases experienced by rookies, they use a multiplier, which puts downwards pressure on all prices, but is whose effect is especially pronounced on premiums and mid-pricers.
The magic number doesn’t change, it’s the multiplier that changes as FD rightly points out. Moustachio, you’re actually talking about something else. You are right that premo’s relative value drops over time, but this is based on the multiplier factor changing on a weekly basis and NOT the magic number.
An Example.
Last year, by the time Rd9 came around a player who started the year at $549,800, based on his previous year’s average of exactly 100 (the magic number was larger last year), he would have been priced at $496,500, had he played every game and scored 100 pts each week. That’s an 9.7% relative drop. By Rd14, his price would have dropped further to $489,100 (11%). After the byes it tends to plateau but even increases a fraction the odd week and there are reasons for this that I’ll explain later.
The Salamander is spot on and I will try and explain a bit more .
Every player who played 8 games or more (bar nobody) is priced at their previous season’s average x the magic number. Anybody who played less games than that (or none at all) receives a discount based on their previous average, but we won’t go into that here. Then there are those who have never played an AFL game before (rookies) who are priced based on ludicrously low est’d ave. scores from 19 (base rookie price of $102,400) to Sam Walsh (#1 draft pick, priced at a 38 average).
What we do know is that we have a finite number of players, a finite number of points that get divvied out each week and a fixed total player price (the aggregated price of all players in the game). This last figure has actually been compromised this year, by the PSSP (supplementary picks) such as Gibbons and Stack and this will have added (albeit miniscule) effects on downward price pressure. If they play the early rounds the system will have to adjust to ‘factor in’ their salaries that weren’t considered when initial prices were set. This is evidenced by looking at say Gibbons on your teamsheet (should you have him 😉 ) and pressing the Stats projection button. Rather than having a BE of 17, it states that he has a BE of 0 and an est’d price change of -$102,400. The system needs to find that money from somewhere. They can’t rectify it now, since every other players’ price would have to come down $100 or so to accommodate the three of them (currently, but there could be more). The system will just swallow it at that first price change in Rd3 and to the detriment of all relatively under-performing players.
I’m waffling. Back to it.
So how does it work?
Let’s take Rd1 last year. 396 players played (22 x 18sides). 29,707pts were scored (=3300 x 9 games, give or take). That scenario is the same every week (except for the byes), BUT …
31 of those players were rookies (I don’t know how many were discounted players but) and their collective salaries accounted for 2.95% of all salaries to play, BUT they accounted for 5.89% of all the points divvied out, which means they basically took twice their relative share of the points (all other things being equal). This is particularly significant when you consider that it isn’t until Rd3 that we see our first price changes. It’s like a perfect, closed market having 8% of sellers (rookies) turn up and offer the same product (points) at half the price of everyone else! Leads to massive and immediate downward price pressure, a constant deflationary market, until a new steady-state (at a lower market price) is reached. Around Rd14, when c. 98% of the total rookie price growth for the season will have already occurred. By now some will be falling, some won’t be playing anymore and most will have reached their peak.
Given that we see more rookies play their first game in Rd1 than in any other Round AND the fact that we have to take a combined three rounds of scores into that initial price change, the multiplier effect is significantly bigger in that Rd3 price change than in any subsequent round. Of course it is. The whole idea of the multiplier is to alter a player’s price to better reflect their ongoing average, over time (games played). It takes an average of approx. 10 games for a rookie to do this (within +/-5% of his steady-state).
Now, the top 18 rookie performers of those initial 31 who played in R1 last year, increased by an aggregate of $3.81mn. in value as they coursed their way to their respective peak prices. That money has to come from somewhere.
To reiterate, the market is being flooded by relatively cheap newcomers forcing huge deflationary pressure on the market, but it will always tend to its steady-state (as the multiplier tends to 1). It will never quite get there, because every round there is always one player playing their third game of the season, but you get the point.
To conclude.
The impacts of the multiplier are particularly strong at season’s start, but will forever diminish from there until such a time that it is negligible.
There are ways to calculate it each week, but not PRIOR to the fact, because it will always depend on who precisely scores the points, and how they are priced that week relative to their average (ie are they relatively under- or over-priced and to what degree?).
Hope that helps make some sense of what to expect. For me, it also has implications on my starting structure. If people are keen to hear my thoughts on that, let me know below and I’ll waffle (I mean rustle) summit up.
The sentence in the middle of that was bang on – “I’m waffling”.
But so was the content – cheers.
Thanks to you and the The Salamander for explaining my explaining!
I hadn’t thought about the players added late; they will indeed push prices down a bit more than usual the first price change.
Follow up post about the prices changes coming soon. Talks more about the price drops and the implications of them.
Allsaints,
Does this mean you will seek to field more rookies/cows/mid-pricers, keep cash in bank, and trade up to premiums as they experience deflationary pressure/cop a bad score or two?
Note: I’m looking at league only and might cop a few losses early but should build a very strong team.
Thoughts?
hey mate. you can read more about my thoughts this year here:
http://supercoachtalk.com/the-team-2019-rookies/#comment-770428
can’t fit it all in a twitter post 😉
But Jack steele wont even score 130 once. so the entire article must be wrong. maybe if it said Danger would score consecutive 130’s I could have faith in it
I’m presuming that’s a joke.
Hey Father Dougal, I copy and pasted your formula for Jack Steele into Excel and got (0.75*512600)+0.25*((5428.589)*((100+100+43)/3)) = $494,379.
Also seems to spit out different figures for Grundy and Gawn’s base price.
Would you be able to explain what the issue is?
The percentage reduction to the players weekly increase/decrease change in price to accommodate the constant salary cap of around $245 million is also affected by non players and less than 3 game players who played in that round.
In 2018 the first price increases following round 3 and and in the following five to six rounds were unusually affected by the large number of high priced players who had not completed 3 games or did play that round. Ten of top 18 salaried players missed all of or a large chunk of games during this period.
Up to the bye rounds the weekly multiplier correction reduction is generally around the 2.5% mark, however, last year it reached lows of 1.78% and 1.86% before getting back to 2.53% as of round 9.
I’d like to see all non-playing players price drop by a set %, this may remove the need for the multiplier. Maybe eliminate the multiplier all-together and balance each week’s rise against the drops to non-playing players.
This would challenge the approach of buying cheap non-playing rucks if you knew that if you needed to trade them out, you’d have lost 10-20k (more?) whilst having them sit on the bench as loopholers.