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2014-10-22 02:00:46
10 votes, rating 4.9
10 votes, rating 4.9
Basic Things about CR
This is in response to this thread. https://fumbbl.com/index.php?name=PNphpBB2&file=viewtopic&t=25570
Do you always lose CR if you lose a game?
Yes. But if you are the underdog the amount you lose can be quite low.
Do you always get CR if you win a game?
Yes, but if you are the better coach, the amount you get can be quite low.
Do you always get CR if you tie a game?
No, the coach that is considered the underdog will get a little bit CR and the coach who is considered better will lose a bit.
What's the average CR I lose/win from a game?
If both coaches are equal it should be around 1 CR. If your opponent is much weaker it can drop to 0.15 or even lower. If you win a game you are a massive underdog in you'll not get much more than 2 CR (conjekture).
If I get only little CR sometimes, is it CR wise even worthwhile playing somebody much weaker than me?
CR wise probably not. The luck aspect of the game is too big as that you would be able to win 5 times as much just because you choose worse opponents. On top of it do you lose significantly from ties and avoiding ties is a really tricky thing to do.
The CR will probably reflect best on your abilities if you focus on coaches within 10 +- CR of your own.
Is there a racial factor in CR?
A racial factor was implemented back in LRB4 times, it wasn't biased but accounted accurately for the probability at which a racial matchup would work on a certain level of team rate based on all previously played games on Fumbbl.
With the switch to the new rules those tables disappeared. With CR being made secret it's impossible to tell if Christer ever adapted those tables. What we can tell for sure is that the site is tracking racial CR now, so it is a save bet that it is somehow factored into the formular.
It is also save to say and proven many times that the racial factor isn't significant enough to really account for the deficits of the weaker races. This is because.. I believe you mainly have to win a lot to increase your CR, lol. With some races you just don't win a lot. Even if you absolutely excell with Flings you'll never be able to keep your CR stable using them.
How exactly is CR calculated?
I don't know, Christer never made it public. There is just an old formular in the help section but I'm too lazy to look for it now. Suffice to say it was complicated.
CR difference was and is supposed to be the most relevant aspect, but TV-difference should be a factor too. It certainly was in the old days, the way how and if inducements are factored in however, I'm not aware of.
Why do I need CR?
You don't. But you can look at it, the way it develops and get an idea of your progress.
What are the ranks for? (Superstar etc)
CR is pretty unstable. The ranks were introduced to show more clearly different classes of abilities to distinguish.
How do the ranks work?
There is a shift area in which you could be either a lower or a higher rank (possibly based on the percentage of coaches on the site who are better or worse than you. Once you get past above shift your rank increases and you won't just fall back down unless you drop below the shift again. So for instance a coach with a CR of 167 might be listed as a Superstar or as a Legend. Depending on whether he recently lost CR (then Legend) or won CR (then Superstar).
I only played one race but it's racial CR is different from my overall CR, how is this possible?
All kinds of things are possible there because those two CR are just calculated differently.
Is the CR gained by one coach always the same amount as the CR lost by the other coach?
Christer said on the forum that the CR system is based on the ELO system and that that means yes, you lose the same amount the other coach gains.
No CR is ever truely lost. He remarked that this has two sideeffects. The top coaches consume some of the CR from new coaches who then quit. And new coaches will always tend to fall below their starting CR. This seems to be unfixable in ELO.
Why am I so tired?
You aren't, I am.
Do you always lose CR if you lose a game?
Yes. But if you are the underdog the amount you lose can be quite low.
Do you always get CR if you win a game?
Yes, but if you are the better coach, the amount you get can be quite low.
Do you always get CR if you tie a game?
No, the coach that is considered the underdog will get a little bit CR and the coach who is considered better will lose a bit.
What's the average CR I lose/win from a game?
If both coaches are equal it should be around 1 CR. If your opponent is much weaker it can drop to 0.15 or even lower. If you win a game you are a massive underdog in you'll not get much more than 2 CR (conjekture).
If I get only little CR sometimes, is it CR wise even worthwhile playing somebody much weaker than me?
CR wise probably not. The luck aspect of the game is too big as that you would be able to win 5 times as much just because you choose worse opponents. On top of it do you lose significantly from ties and avoiding ties is a really tricky thing to do.
The CR will probably reflect best on your abilities if you focus on coaches within 10 +- CR of your own.
Is there a racial factor in CR?
A racial factor was implemented back in LRB4 times, it wasn't biased but accounted accurately for the probability at which a racial matchup would work on a certain level of team rate based on all previously played games on Fumbbl.
With the switch to the new rules those tables disappeared. With CR being made secret it's impossible to tell if Christer ever adapted those tables. What we can tell for sure is that the site is tracking racial CR now, so it is a save bet that it is somehow factored into the formular.
It is also save to say and proven many times that the racial factor isn't significant enough to really account for the deficits of the weaker races. This is because.. I believe you mainly have to win a lot to increase your CR, lol. With some races you just don't win a lot. Even if you absolutely excell with Flings you'll never be able to keep your CR stable using them.
How exactly is CR calculated?
I don't know, Christer never made it public. There is just an old formular in the help section but I'm too lazy to look for it now. Suffice to say it was complicated.
CR difference was and is supposed to be the most relevant aspect, but TV-difference should be a factor too. It certainly was in the old days, the way how and if inducements are factored in however, I'm not aware of.
Why do I need CR?
You don't. But you can look at it, the way it develops and get an idea of your progress.
What are the ranks for? (Superstar etc)
CR is pretty unstable. The ranks were introduced to show more clearly different classes of abilities to distinguish.
How do the ranks work?
There is a shift area in which you could be either a lower or a higher rank (possibly based on the percentage of coaches on the site who are better or worse than you. Once you get past above shift your rank increases and you won't just fall back down unless you drop below the shift again. So for instance a coach with a CR of 167 might be listed as a Superstar or as a Legend. Depending on whether he recently lost CR (then Legend) or won CR (then Superstar).
I only played one race but it's racial CR is different from my overall CR, how is this possible?
All kinds of things are possible there because those two CR are just calculated differently.
Is the CR gained by one coach always the same amount as the CR lost by the other coach?
Christer said on the forum that the CR system is based on the ELO system and that that means yes, you lose the same amount the other coach gains.
No CR is ever truely lost. He remarked that this has two sideeffects. The top coaches consume some of the CR from new coaches who then quit. And new coaches will always tend to fall below their starting CR. This seems to be unfixable in ELO.
Why am I so tired?
You aren't, I am.
Comments
Posted by Dominik on 2014-10-22 03:42:35
"If I get only little CR sometimes, is it CR wise even worthwhile playing somebody much weaker than me?"
I've seen it among certain top coaches, that they tendentially choose skill-wise much weaker opponents but with their slightly stronger teams so that those top coaches still benefit sufficiently from a win.
I've seen it among certain top coaches, that they tendentially choose skill-wise much weaker opponents but with their slightly stronger teams so that those top coaches still benefit sufficiently from a win.
Posted by DrPoods on 2014-10-22 04:48:30
Nice concise blog post mate.
6 for info!
6 for info!
Posted by pythrr on 2014-10-22 05:12:19
lovely
Q: what is the point of CR?
A: isn't one. It's like giving yrself gold stars at elementary school.
Q: what is the point of CR?
A: isn't one. It's like giving yrself gold stars at elementary school.
Posted by Verminardo on 2014-10-22 09:42:32
Didn't Christer just say in the forum thread that racial modifieres were removed entirely?
Posted by Wreckage on 2014-10-22 09:46:35
If he did I must have missed it/ Can't find it.
In which of his posts did he write that?
In which of his posts did he write that?
Posted by Wreckage on 2014-10-22 09:58:28
Ah I think you might be referring to how the scheduler works in blackbox.
Currently blackbox seems to be only based on TV. There is a debate ongoing whether to match popular races more against each other. There used to be at least a bias regarding mirror matches.
It has also been suggested to use CR as a factor in box scheduling. However this incentivises playing poorly to gain an advantage in team development. So Christer assessed that this isn't a great design choice.
Overall they are just two different matters entirely.
Currently blackbox seems to be only based on TV. There is a debate ongoing whether to match popular races more against each other. There used to be at least a bias regarding mirror matches.
It has also been suggested to use CR as a factor in box scheduling. However this incentivises playing poorly to gain an advantage in team development. So Christer assessed that this isn't a great design choice.
Overall they are just two different matters entirely.
Posted by the_Sage on 2014-10-22 10:38:49
Is the CR gained by one coach always the same amount as the CR lost by the other coach?
Posted by the_Sage on 2014-10-22 10:44:32
Ooh, a versatility bonus which schedules you more against less-played races if you play more often AS less-played races. That could be a great way to soft-enforce versatility.
Posted by Wreckage on 2014-10-22 11:05:39
"Is the CR gained by one coach always the same amount as the CR lost by the other coach?"
Christer said on the forum that the CR system is based on the ELO system and that that means yes, you lose the same amount the other coach gains.
Christer said on the forum that the CR system is based on the ELO system and that that means yes, you lose the same amount the other coach gains.
Posted by Verminardo on 2014-10-22 11:07:37
"But in terms of the ranking system, team strength isn't related to the strength stat on players. It's a reference to an alternative way that FUMBBL used to estimate how good a team is (basically, a custom team rating/team value type system). It's not in use anymore."
https://fumbbl.com/index.php?name=PNphpBB2&file=viewtopic&p=614106#614106
https://fumbbl.com/index.php?name=PNphpBB2&file=viewtopic&p=614106#614106
Posted by Wreckage on 2014-10-22 11:28:16
Well, you've been around since 2006, so you should know what Team Strengh is. :P
TV is used to replace the former TR. Because TR was so inaccurate Fumbbl invented its own measuring system for strengh, called TS. In the old CR calculation, TS was the basis for assessing the level of threat a team posed. The difference in TS of both teams was slightly less relevant than the difference in CR. (about 4/7 as important for the formular)
With the introduction of TV, TS has become obsolete. TS was the more advanced measuring system still, but in order to recreate it, it would need a complete overhaul but TV as well as the inducement system has been accurate enough that there was no real need to focus on recreating TS.
TS did not account for racial differences. For instance an amazon team could have significant TS yet still perform poorly against a dwarf team.
That's where the racial modifiers came into place (post TS) in terms of calculating CR.
TV is used to replace the former TR. Because TR was so inaccurate Fumbbl invented its own measuring system for strengh, called TS. In the old CR calculation, TS was the basis for assessing the level of threat a team posed. The difference in TS of both teams was slightly less relevant than the difference in CR. (about 4/7 as important for the formular)
With the introduction of TV, TS has become obsolete. TS was the more advanced measuring system still, but in order to recreate it, it would need a complete overhaul but TV as well as the inducement system has been accurate enough that there was no real need to focus on recreating TS.
TS did not account for racial differences. For instance an amazon team could have significant TS yet still perform poorly against a dwarf team.
That's where the racial modifiers came into place (post TS) in terms of calculating CR.
Posted by Verminardo on 2014-10-22 12:05:04
Ah jetzt ja.^^
Posted by Beerox on 2014-10-22 16:19:01
All I know is that once upon a time I played like 5 Halfling matches in the box, lost 3, tied 2, and my CR dropped about 7 or 8 points.
At that point I stopped trying to understand it.
At that point I stopped trying to understand it.
Posted by Cavetroll on 2014-10-22 21:02:01
Here's some intersting data that I've only ever encountered once on FUMBBL.
I recently played a game and tied, my end game CR was 161.64
https://fumbbl.com/p/match?op=view&id=3605915
The next Ranked/Blackbox game I played (it was Ranked) also resulted in a Draw, and my CR remained 161.64. The coach had a CR of 159.02, and he also ended the game with the same CR he started with
https://fumbbl.com/p/match?op=view&id=3607129
Here is that coaches previous game to verify his CR didn't change
https://fumbbl.com/p/match?op=view&id=3601832
We somehow hit on this sweet spot of difference in CR (I was higher) vs. difference in TV (his team was higher) that meant a draw game resulted in no change in CR.
I recently played a game and tied, my end game CR was 161.64
https://fumbbl.com/p/match?op=view&id=3605915
The next Ranked/Blackbox game I played (it was Ranked) also resulted in a Draw, and my CR remained 161.64. The coach had a CR of 159.02, and he also ended the game with the same CR he started with
https://fumbbl.com/p/match?op=view&id=3607129
Here is that coaches previous game to verify his CR didn't change
https://fumbbl.com/p/match?op=view&id=3601832
We somehow hit on this sweet spot of difference in CR (I was higher) vs. difference in TV (his team was higher) that meant a draw game resulted in no change in CR.
Posted by Cavetroll on 2014-10-22 21:05:55
As to the_Sage's question about CR loss/gain being equal between both teams, I have seen several examples where it was not perfectly equal but it is always close (if not identical). I've often wondered why this is so, and I suspect it is the CR system 'normalizing' itself based on some things Christer said in the thread.
Posted by Wreckage on 2014-10-23 10:27:21
Actually I gotta say I thought too that win and loss wasn't equal. Don't think the original formular implied that either.
I decided to have a look at it and see what I can figure out.
Ok... if I read this correctly the alteration in CR per game would read something like this:
for wins:
CRchange = 2* (1 - ((1/(1+10^(DeltaCR/40 + DeltaTV/700)))))
for losses:
CRchange = 2*(0 - ((1/(1+10^(DeltaCR/40 + DeltaTV/700)))))
Things of note:
The term in the breaks looks like it's going to be smaller than 1, only the divident ever changes, so if the term was subtracted from 1 (game won) the outcome should be smaller 1.
If the term was substracted from 0 (game lost), the outcome should be between 0 and -1. That is not factoring the 2 times multiplier in yet.
The 2 times multiplier is called k value.
The term in the breaks is called p. p = ((1/(1+10^(DeltaCR/40 + DeltaTV/700))))
For simplicity sake we will call the power breaks: DeltaA = (DeltaCR/40 + DeltaTV/700).
And the area that is undergoing the most changes simply 'y'. y = 10^(DeltaCR/40 + DeltaTV/700)
Y is what we are going to have to understand.
Problems:
What impact does it have that we have two added deltas in the power section?
Probably none, the DeltaTV is probably actually more neglectable. Principially if both terms are positive DeltaA will be positive, if one is positive the other negative, the negative will substract appropriatly. No funny buisness, two additiive terms that behave exactly like you would expect it.
Extreme Points:
If TV difference or CR difference goes towards infinity, DeltaA will go towards infinity, if TV difference or CR difference is close to 0, the respective term will add close to 0 to DeltaA and be neglectable. If both Deltas go towards 0, DeltaA becomes close to 0 entirely.
Pretty much what you expect, but what does that mean for the entire equation?
We defined y as 10^DeltaA. If DeltaA is moving towards 0, y will be moving towards 1. (10^0 = 1)
So if 2 equal teams would play, p = 1 / (1 + y[=1] ) = 1/2. So in case of a win, basically normally 0.5 CR would be added, in case of a loss -0.5CR.
With the k value always being a double multiplier the CR change with equal teams would be +1 or -1 instead.
So far the easy part.
I decided to have a look at it and see what I can figure out.
Ok... if I read this correctly the alteration in CR per game would read something like this:
for wins:
CRchange = 2* (1 - ((1/(1+10^(DeltaCR/40 + DeltaTV/700)))))
for losses:
CRchange = 2*(0 - ((1/(1+10^(DeltaCR/40 + DeltaTV/700)))))
Things of note:
The term in the breaks looks like it's going to be smaller than 1, only the divident ever changes, so if the term was subtracted from 1 (game won) the outcome should be smaller 1.
If the term was substracted from 0 (game lost), the outcome should be between 0 and -1. That is not factoring the 2 times multiplier in yet.
The 2 times multiplier is called k value.
The term in the breaks is called p. p = ((1/(1+10^(DeltaCR/40 + DeltaTV/700))))
For simplicity sake we will call the power breaks: DeltaA = (DeltaCR/40 + DeltaTV/700).
And the area that is undergoing the most changes simply 'y'. y = 10^(DeltaCR/40 + DeltaTV/700)
Y is what we are going to have to understand.
Problems:
What impact does it have that we have two added deltas in the power section?
Probably none, the DeltaTV is probably actually more neglectable. Principially if both terms are positive DeltaA will be positive, if one is positive the other negative, the negative will substract appropriatly. No funny buisness, two additiive terms that behave exactly like you would expect it.
Extreme Points:
If TV difference or CR difference goes towards infinity, DeltaA will go towards infinity, if TV difference or CR difference is close to 0, the respective term will add close to 0 to DeltaA and be neglectable. If both Deltas go towards 0, DeltaA becomes close to 0 entirely.
Pretty much what you expect, but what does that mean for the entire equation?
We defined y as 10^DeltaA. If DeltaA is moving towards 0, y will be moving towards 1. (10^0 = 1)
So if 2 equal teams would play, p = 1 / (1 + y[=1] ) = 1/2. So in case of a win, basically normally 0.5 CR would be added, in case of a loss -0.5CR.
With the k value always being a double multiplier the CR change with equal teams would be +1 or -1 instead.
So far the easy part.
Posted by Wreckage on 2014-10-23 11:45:30
So what happens if 2 unequal coaches play and DeltaCR gets really large?
As DeltaCR goes towards infinity, DeltaTV becomes neglectable. y = 10^DeltaA grows towards infinity too. (10^10000000000000000000)
What does this mean for p? p = 1 / (1 + 10000000000000000000000000000000000000), so if y goes towards infinity, p becomes infinitely small and goes towards 0.
So, the whole equation would now go like this:
For win:
CRchange = 2* (1 - 0) = 2
For loss:
CRchange = 2* (0 - 0) = 0
At first sight this looks a bit odd. These tables indicate that if the TV difference is especially high, the winning coach gets a lot of CR and loses nothing if he loses.
You'd expect sort of the opposite. If my CR is so much higher than my opponents I should rather gain nothing if I win and lose a lot if I lost.
However, we haven't really specified how the DeltaTV is calculated.
Just from looking at the numbers it is pretty save to assume that it is OpponentTV - OwnTV, rather than OwnTV - OpponentTV.
Note: The gain and loss here aren't actually those of the two coaches respectively but of the same coach, depending on whether he wins or loses.
So what we see here is what happens when the own team is vastly inferior and wins: The inferior team would gain about 2 CR. (by the old formular tho and pre other modifiers) If it lost however it would lose nothing.
Can we now make the reverse assumption for the own team being vastly superior by simply using an infinity negative for this equation OwnTV - OpponentTV?
Unfortunatly not. We are dealing with a y = 10^(-infinity) term, so we have to rather look at what is going to happen there.
A negative power is just like switching divident and divisor, so...
y = 1 / 10 ^ infinity = 0, or rather a really small number.
Now for p that means:
p = 1 / (1 + 0)
and for CRchange
for win:
CRchange = 2 * (1 - 1) = 0
for loss:
CRchange = 2 * (0 - 1) = -2
Amazingly those numbers indicate that an infinitely stronger team would actually lose precisely the same amount of TV, the infinitely weaker team would gain and vice versa.
However, that is a pretty extreme example, so lets have a look if that still remains true if we use smaller numbers.
Let's say a team has 10 CR less and wins at equal TV.
CRchange = 2 * (1- ( 1 / (1+(10^(10/40)))))
for y = 10^(10/40) = 10^(1/4) = ~1.78
so:
CRchange = 2 * ( 1 - ( 1 / (1+ ~1.78)))
= 2 * (1- ( 1 / ~2.78))
= 2 * ~0.64
= ~ 1.28 CR
Amazingly the benefit would only be this much for the inferior team.
Would the superior team lose the same amount?
for y = 10^(-10/40) = 10^(-1/4) = ~0.56
for
CRchange(loss) = 2 * (0- ( 1 / (1+ ~0.56)))
= 2* (-1/~1.56)
= 2* (~ -0.641)
= ~ - 1.282
The numbers are oddly similar, but now it's a problem that I only approximated them, have to make sure they are really identical. If they are there must be some mathematical law behind it I don't see right now.
Precise:
CRchange(winner) = 1.28013
CRchange(loser) = -1.28013
We can make a converse test for the opposite case. The team with +10 CR wins.
CRchange (winner) = 0.71987
CRchange (loser) = -0.71987
Not really sure how this works. Guess the negative symbol in the power only turning divisor and divident around must somehow produce the reverse number. But I am not sure how this works by adding 1 to it in both cases.
Would be probably clearer if I restructured the formular, but there is really no point to this right now.
Lets just take note that the CR changes are really identical, at least by the old formular.
Possible explanations for a difference beyond that could only be that they are either a result of the way they are displayed after rounding - then it would also make them appear correct later on (if, what I assume for the calculations the correct CR is used, not the rounded one).
Otherwise the only explanation could be that they are a result of other equations injected into the formular post main calculation...
In any case, it's probably worthwhile checking if there is any actual evidence for a difference in won and lost CR in some game.
As DeltaCR goes towards infinity, DeltaTV becomes neglectable. y = 10^DeltaA grows towards infinity too. (10^10000000000000000000)
What does this mean for p? p = 1 / (1 + 10000000000000000000000000000000000000), so if y goes towards infinity, p becomes infinitely small and goes towards 0.
So, the whole equation would now go like this:
For win:
CRchange = 2* (1 - 0) = 2
For loss:
CRchange = 2* (0 - 0) = 0
At first sight this looks a bit odd. These tables indicate that if the TV difference is especially high, the winning coach gets a lot of CR and loses nothing if he loses.
You'd expect sort of the opposite. If my CR is so much higher than my opponents I should rather gain nothing if I win and lose a lot if I lost.
However, we haven't really specified how the DeltaTV is calculated.
Just from looking at the numbers it is pretty save to assume that it is OpponentTV - OwnTV, rather than OwnTV - OpponentTV.
Note: The gain and loss here aren't actually those of the two coaches respectively but of the same coach, depending on whether he wins or loses.
So what we see here is what happens when the own team is vastly inferior and wins: The inferior team would gain about 2 CR. (by the old formular tho and pre other modifiers) If it lost however it would lose nothing.
Can we now make the reverse assumption for the own team being vastly superior by simply using an infinity negative for this equation OwnTV - OpponentTV?
Unfortunatly not. We are dealing with a y = 10^(-infinity) term, so we have to rather look at what is going to happen there.
A negative power is just like switching divident and divisor, so...
y = 1 / 10 ^ infinity = 0, or rather a really small number.
Now for p that means:
p = 1 / (1 + 0)
and for CRchange
for win:
CRchange = 2 * (1 - 1) = 0
for loss:
CRchange = 2 * (0 - 1) = -2
Amazingly those numbers indicate that an infinitely stronger team would actually lose precisely the same amount of TV, the infinitely weaker team would gain and vice versa.
However, that is a pretty extreme example, so lets have a look if that still remains true if we use smaller numbers.
Let's say a team has 10 CR less and wins at equal TV.
CRchange = 2 * (1- ( 1 / (1+(10^(10/40)))))
for y = 10^(10/40) = 10^(1/4) = ~1.78
so:
CRchange = 2 * ( 1 - ( 1 / (1+ ~1.78)))
= 2 * (1- ( 1 / ~2.78))
= 2 * ~0.64
= ~ 1.28 CR
Amazingly the benefit would only be this much for the inferior team.
Would the superior team lose the same amount?
for y = 10^(-10/40) = 10^(-1/4) = ~0.56
for
CRchange(loss) = 2 * (0- ( 1 / (1+ ~0.56)))
= 2* (-1/~1.56)
= 2* (~ -0.641)
= ~ - 1.282
The numbers are oddly similar, but now it's a problem that I only approximated them, have to make sure they are really identical. If they are there must be some mathematical law behind it I don't see right now.
Precise:
CRchange(winner) = 1.28013
CRchange(loser) = -1.28013
We can make a converse test for the opposite case. The team with +10 CR wins.
CRchange (winner) = 0.71987
CRchange (loser) = -0.71987
Not really sure how this works. Guess the negative symbol in the power only turning divisor and divident around must somehow produce the reverse number. But I am not sure how this works by adding 1 to it in both cases.
Would be probably clearer if I restructured the formular, but there is really no point to this right now.
Lets just take note that the CR changes are really identical, at least by the old formular.
Possible explanations for a difference beyond that could only be that they are either a result of the way they are displayed after rounding - then it would also make them appear correct later on (if, what I assume for the calculations the correct CR is used, not the rounded one).
Otherwise the only explanation could be that they are a result of other equations injected into the formular post main calculation...
In any case, it's probably worthwhile checking if there is any actual evidence for a difference in won and lost CR in some game.
Posted by Wreckage on 2014-10-23 11:54:58
Just on a different note we can see that the entire CR change in every single case is 2 (or rather 1 before the application of the k value).
Ie. If I'd win 0.5 CR as I won, I'd lose 1.5 CR as I lost and vice versa.
So, it would be interesting to see if such predictions can still be made with the current formular or if we can make statements about how it might have changed.
Ie. If I'd win 0.5 CR as I won, I'd lose 1.5 CR as I lost and vice versa.
So, it would be interesting to see if such predictions can still be made with the current formular or if we can make statements about how it might have changed.
Posted by Wreckage on 2014-10-23 11:58:43
It's really a bit irritating that such a complex equation could spawn so simple results. It all hints that something much much simpler is going on with these numbers than it seems at first glance.
Can't help to feel very foolish here. :P
Can't help to feel very foolish here. :P
Posted by Wreckage on 2014-10-23 15:35:56
10^DeltaD = 1/p - 1
Restructuring I get this, that's actually a pretty interesting way to look at it. Taking the logarythm doesn't really do anything.
But the 10^DeltaD is really the key to understand this. The 1/p - 1 is actually constant. It is save to assume that the purpose of this construct is merely to force the outcome into a numerical corsett that can't fall below 0 or above 1.
Now what about this thing.
10^x isn't just any potence, it's incredibly common and easy to use.
I guess it makes enough sense to choose it.
Now we have 4 sections in the DeltaCR.
DeltaCR > 1 => Highly Unfavored(CRdiff > 40)
1 > DeltaCR > 0 => Unfavored (CRdiff < 40)
0 > DeltaCR > -1 => Favored (CRdiff > -40)
-1 > DeltaCR => Highly Favored (CRdiff < -40)
The distinction at a CRdiff of 40 is rather random, but lets look at its effects:
If the CRdiff is exactly 40, we get p = 1/11, respectively p = 10/11 on a CRdiff of -40.
Those seem awfully inconvenient key numbers. And also kinda random, the probably only point of this is to choose a very large number as basis for the calculation.
I guess if the potence exceeds 1, the sum in the divisor becomes too arbitrarily small to still make a significant difference on the equation.
In this case that would mean that as you approach a TV diff of 40, the impact of the formular gets really inconveniently small.
This creates some interesting questions:
1. Does it even make sense that CR changes less as the gap in abilities gets wider and vice versa?
2. Shouldn't it rather be a constant?
3. What would a constant look like and what problems would that create?
4. What if I keep the formular and just alter the operational range drastically instead?
5. What would be the way to set the formular to have the maximum level of alteration with every small change of CR, considering that it will always be stuck between 1 and 0?
If I simply alter the CRdiff divisor of 40 to a higher number, I'll sort of probably have a really small alteration to the numbers as well. Let's say I took 400, the potence would probably get this small that 10^DeltaCR would just end up going towards 1, or 0 respectively in the reverse case.
So 40 was probably chosen because it is sort of in the middle. It is also the most likely value to be changed as a result of the CR overhaul.
That CR changes more slowly now means hm, good question. Is the value higher or lower? On the underdog side the CR boost is never going to exceed 2 either way. So it can't be more than twice as effective to pick on somebody better. So the lower CR diff can only be explained in the way that it's gotta be that boosting CR with weak opponents got a lot harder.
So if I was to tweak 40 to a lower value, lets say 20, that would have exactly that effect. Although 20 is maybe very low.
Lets make a test and see if we can figure out at what value Christer set the new CR.
Lets try 30. For minimum interferance, I'll choose a mirror match game. Can't be sure about that... and hh.. still the issue of TV... so... two rookie teams... perfect.
Restructuring I get this, that's actually a pretty interesting way to look at it. Taking the logarythm doesn't really do anything.
But the 10^DeltaD is really the key to understand this. The 1/p - 1 is actually constant. It is save to assume that the purpose of this construct is merely to force the outcome into a numerical corsett that can't fall below 0 or above 1.
Now what about this thing.
10^x isn't just any potence, it's incredibly common and easy to use.
I guess it makes enough sense to choose it.
Now we have 4 sections in the DeltaCR.
DeltaCR > 1 => Highly Unfavored(CRdiff > 40)
1 > DeltaCR > 0 => Unfavored (CRdiff < 40)
0 > DeltaCR > -1 => Favored (CRdiff > -40)
-1 > DeltaCR => Highly Favored (CRdiff < -40)
The distinction at a CRdiff of 40 is rather random, but lets look at its effects:
If the CRdiff is exactly 40, we get p = 1/11, respectively p = 10/11 on a CRdiff of -40.
Those seem awfully inconvenient key numbers. And also kinda random, the probably only point of this is to choose a very large number as basis for the calculation.
I guess if the potence exceeds 1, the sum in the divisor becomes too arbitrarily small to still make a significant difference on the equation.
In this case that would mean that as you approach a TV diff of 40, the impact of the formular gets really inconveniently small.
This creates some interesting questions:
1. Does it even make sense that CR changes less as the gap in abilities gets wider and vice versa?
2. Shouldn't it rather be a constant?
3. What would a constant look like and what problems would that create?
4. What if I keep the formular and just alter the operational range drastically instead?
5. What would be the way to set the formular to have the maximum level of alteration with every small change of CR, considering that it will always be stuck between 1 and 0?
If I simply alter the CRdiff divisor of 40 to a higher number, I'll sort of probably have a really small alteration to the numbers as well. Let's say I took 400, the potence would probably get this small that 10^DeltaCR would just end up going towards 1, or 0 respectively in the reverse case.
So 40 was probably chosen because it is sort of in the middle. It is also the most likely value to be changed as a result of the CR overhaul.
That CR changes more slowly now means hm, good question. Is the value higher or lower? On the underdog side the CR boost is never going to exceed 2 either way. So it can't be more than twice as effective to pick on somebody better. So the lower CR diff can only be explained in the way that it's gotta be that boosting CR with weak opponents got a lot harder.
So if I was to tweak 40 to a lower value, lets say 20, that would have exactly that effect. Although 20 is maybe very low.
Lets make a test and see if we can figure out at what value Christer set the new CR.
Lets try 30. For minimum interferance, I'll choose a mirror match game. Can't be sure about that... and hh.. still the issue of TV... so... two rookie teams... perfect.
Posted by Wreckage on 2014-10-23 15:49:17
Somewhat strange, Chaos vs Woodies was the best I could find.
But look at this.
https://fumbbl.com/p/match?op=view&id=3613295
Proxarm plays his first game, so his CR is alterated by 2.83.
Tefrais rating on the other hand is altered by precisely 1. (Previous match: https://fumbbl.com/p/match?op=view&id=3613271)
That is not at all what I had assessed based on the formular.
But Christer said he kinda excelled the speed at which he altered the speed at which rookie players get CR.
I figured a way to do that would be to modify the K value for the first couple of games. Whatever you do, it quantifies the effect. But how do you end up with a strange number like 2.83 when the other guys CR changes by precisely 1?
Is the rookie k value precisely 2.83 of other peoples k value? mmmm
Or is the formular maybe altered if you play AGAINST a rookie coach?
Hhhh, I didn't even want to think about this. Back to the basic questions. Lets see if i can find a better matchup.
But look at this.
https://fumbbl.com/p/match?op=view&id=3613295
Proxarm plays his first game, so his CR is alterated by 2.83.
Tefrais rating on the other hand is altered by precisely 1. (Previous match: https://fumbbl.com/p/match?op=view&id=3613271)
That is not at all what I had assessed based on the formular.
But Christer said he kinda excelled the speed at which he altered the speed at which rookie players get CR.
I figured a way to do that would be to modify the K value for the first couple of games. Whatever you do, it quantifies the effect. But how do you end up with a strange number like 2.83 when the other guys CR changes by precisely 1?
Is the rookie k value precisely 2.83 of other peoples k value? mmmm
Or is the formular maybe altered if you play AGAINST a rookie coach?
Hhhh, I didn't even want to think about this. Back to the basic questions. Lets see if i can find a better matchup.
Posted by Wreckage on 2014-10-23 16:14:38
After checking a number of rookie games I can say that not a single one produced the same amount of CR for one side as the other side lost.