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So a few people asked for something on BEs and price changes, so I wrote something up.
Its a bit long, so take that as a warning if you don't want to read about maths and price changes but for those that are interested, here it is.
Putting it behind spoiler tags ot hide it from those who just want to scroll past easily
Its a bit long, so take that as a warning if you don't want to read about maths and price changes but for those that are interested, here it is.
Putting it behind spoiler tags ot hide it from those who just want to scroll past easily
- many many paragraphs on price changes:
Will also copy this into the sticky thread for future reference
Before we talk about BEs, we need to know a little about the Magic Number.
Essentially this number represents the amount of money it costs to buy 1 fantasy point.
The value changes slightly throughout the year (more on that later) but for now all we need to know is that it started the year at 8935.
That means that the starting price for players is their initial average * 8935
Eg Cameron Smith averaged 61.53 in 2015. 61.35 * 8935 = $548,162 Smith's starting price (rounded to the nearest $1000)
Players receive a discount for playing less than 10 games.
Rookies are priced at an average of 14.5.
Guys who come from Super League/Union/Jail etc basically just get a random price of whatever Fanhub feel like (it will be loosely based on their Super League stats, or their stats the least time they played NRL, but its a bit of a crapshoot)
During the season the magic number is recalculated for each round.
Its the total cost of all players playing that round divided by the total fantasy points scored that round.
In Round 1 $83,193,000 worth of players played, and scored 9003 points, giving MN of a bit over 9000
Onto actual price rises.
Prices change each week based on existing price and a 5 game weighted average. What that means in maths terms is
New Price = (75% Old Price) + (25% * MN * 5 game weighted average)
There are other slight considerations, but Fanhub don't publish the exact formula, and this is close enough for our purposes.
For the 5 game weighted average, the oldest game in the average (lets call it G5) is given a weighting of 1
The 4th oldest game, G4, is twice as important
G3 is three times as important as G5.
G2 is 4 times as important
And G1, the most recent game (ie for the purposes of BE calculations the game that is about to be played) is worth 5 times as much as the oldest game
Mathematically, the weighted average (WA) looks like this
(G1*5 + G2*4 + G3*3 + G4*2 + G5*1) / 15
For the start of the season, or any time a player hasn't yet played 4 games this year, all old games are assumed to be their priced average (eg their original price divided by 8935)
Due to pricing discounts there can be a difference between last seasons actual average and the average they are priced at.
BE/ Price Change calculations use the priced average.
Now, because the magic number is the sum of everyone's prices divided by the sum of everyones scores, if you add all the prices changes together you'll find the the total price changes each week add up to $0.
If you are mathematically inclined you can go and prove that. If not, just take my word for it.
What this means is every time someone gains $1, someone else has to lose $1
Now, it doesn't always add up to exactly $0 for 2 reasons.
1. Prices are rounded to the nearest $1000, so you can be off a couple thousand here ad there due to rounding.
b) Players can't drop below $128,000, and any money dropped below that is ignored.
But its pretty close to $0, in a normal round total price changes normally sum to a couple thousand dollars.
Back in 2014 when players could drop below base price, and prices weren't rounded - the price changes for a round were always exactly $0.
Now, to convert the price change formula into a BE, we just have to swap the equaltion around.
Remember the prioce change equation is
NP = 0.75 * OP + 0.25*MN*WA
Where OP = old price, NP = new price, MN = Magic Number, WA = 5 game weighted average
Now, when we say break even we mean no money gained or lost. So we know that OP = NP
For the 5 game weighted average, we know 4 of the scores, but we don't know G1, the most recent score, becasue that game hasn't been played yet.
But G1 is what we want to know.
Play around with the formula (it's high school maths, but if you don't remember it you can trust me) and we can work out what G1 can be for old price to = new price
Formula starts as
NP = 0.75 * OP + 0.25*MN*((G1*5 + G2*4 + G3*3 + G4*2 + G5*1) / 15)
and finishes as
G1 = 3 * ( OP/MN - (4*G2+3*G3+2*G4+G5)/15)
we know what OP, G2, G3, G4 and G5 are. Its the original price and the last 4 scores (or assumed scores if the player has not played 4 games yet)
But before the round is played, we don't know what the Magic Number is, so we have to take a guess.
Generally the magic number hovers around a certain set of values, so we can be somewhat accurate, but we can't know it exactly.
Note that this applies, whether the BE is generated by me, by Fanhub, by Renegades or by a thousand monkeys with a thousand typewriters.
Unless you can see the future, you don't know the MN so you can't give a 100% accurate break even.
If you look at our BE formula, we can work out that the higher the magic number, the lower the BE will be.
as Magic Number is total prices / total points, it will be bigger if
a) the total price is bigger than expected
b) the total points scored is lower than expected.
If either of these happens, then when the price calculations are done, the true BE will be a bit lower than whatever you calculated it at
Conversely if the total price is lower than usual, or there is a larger number of points scored than usual, then the true BE will be higher than calculated.
Looking at total price, as I mentioned earlier, total price changes always equal $0 (before rounding occurs)
So if every team played exactly the same 17 every week, then total price would remain exactly the same, as any $1 someone makes is lost somewhere else.
This isn't the case though. Players get injured.
Between round 1 and 2 this year, James Segeyaro, Michael Lichaa and Paul Gallen all got injured (and guys like Kade Snowden got straught out dropped).
These are all expensive players, and their replacements are generally quite cheap.
Next week they look to be joined by Nathan Peats and Shaun Fensom, who will also be replaced by cheaper players.
In this way, the magic number falls over the first few weeks of the season. Eventually injured players start returning, and prices sort of level out.
The big exception is bye rounds. Lots of the most expensive players in the game miss the bye rounds on origin duty, and are replaced by cheap players.
The end result is that last year rounds 11,14,17 had a magic number about 1000 less than the other rounds. This has a noticable effect on price change calculations
The other thing that changes the MN is points scored. This is harder to predict as scores could be anything any week.
Generally a fantasy game will score about 1200 points on average.
but round 1 last year and this year wer eboth closer to 1100. Extra mistakes because players aren't into the swing of things yet is one possible explanation, but for whatever reason, round 1 seems to score low.
Either way I'd expect fantasy averages to go back up to a bit over 1200 a game this round and stay around there most of the season.
After a few weeks, the prices and scores will settle down and we can predict a BE with some accuracy but never exactly, becaus the MN will not vary too much week to week.
If you have read this far and still understand what I am talking about, congratulations.
But we now know how price changes are calculated.
We know we can't predict exactly what price changes will be because not only do we need to know what a player will score that weekend, but what every other player will score too.
But we can have a reasonable guess, by using a Magic number similar to the past few weeks.
So, one of the biggest complaints about BEs is "My players scored 2 more than his BE, but lost money, how is this possible"
Well, now we know.
The BE calculation is this G1 = 3 * ( OP/MN - (4*G2+3*G3+2*G4+G5)/15)
If we use a magic number to work out our BE that is larger than what ends up occuring, the our esitame will be too low.
As the MN falls over the first few weeks of the comp, the tednency is to use a MN slightly higher than we should for BEs which is why this happens.
There is also another minor reason. Prices for buying and selling are rounded to the nearest $1000.
But internally to the system they are not.
So a player who costs $160,000 actually has a true value of somewhere between $159,500 and $160,499
This can also have an impact on BE calcs. Theoretically a guy could lose $1 in real value, but cost you $1000 if the rounding changes, and another player could gain $950 but stay the same price.
Last point
People often talk about points over BE being worth $x per point over BE
But this is not quite true for 2 reasons.
When we calculate a BE, we guess at a MN, but as we've seen this isn't the MN used for actual calculations.
So if someone has a pre-round BE of 20, and they score 30. The probably haven't scored exactly 10 points over their BE, more like 8-12 points over depending on the MN for the round.
If we could predict the MN perfectly then you could say that the price rise can be worked out as
8.33% x the MN * score over BE
This would ignore rounding errors but be close enough.
With the current magic number, a guess of $750 per point over BE is a pretty good guess, but won't be exact.
But its accuracy depends mainly on using the right MN for the BE calcs.
If you get that wrong (which you almost always will) then you won't know the right BE to know hoe many points over it they scored.
A more accurate formula to use would be
8.33% x the MN * score over BE + 16.666% * 4GWA * Diff
Where 4GWA = 4 game weighted average
and
Diff = the difference between the Magic Number you used for the BE calcs and the actual Magic Number
This also won't be completely accurate, unless you know the players true price (ie not rounded to the nearest $1000) but its better than $750 per point.
Final, final point.
All the above applies to Fantasy. If you play Supercoach or Dreamteam, its basically the same.
Except instead of a 5 game weighted average, they use a straight 3 game average.
Their Magic Number differs based on their salary cap and scoring, but the concept is still the same.
So for SC/DT
NP = 0.75*OP + MN * (G1+G2+G3)/3
Or for Break Even
BE = 3*OP/MN - (G2 + G3)
NP = New Price, OP = Old Price, MN = Magic Number, G1 = most recent game, G2 = 2 games ago, G3 = 3 games ago
OK, that's it for BEs and price changes for now.
Sincere congratulations if you read all of this. Even better if you understood any of it.
Hopefully I've improved the understanding of the game for a few people
Any questions feel free to go for it, I'm generally happy to talk about this kind of stuff for hours.
If you think I've made an error, please let me know. I'm far from perfect but always looking to improve so if you think you can improve on what I've said, please do so.
If there is something I didn't cover that you wanted to know, please ask. I'm genuinely happy to talk about this stuff.
Last edited by Milchcow on Sun Mar 13, 2016 6:52 pm; edited 1 time in total
