so last night, voltan was asking this question and i thought maybe i can use my database of leaderboard values to figure this out
sure, you can graph someone's rank and just "eyeball" it but i was looking for a way that actually involves some calculation
enter linear regression. so up till now, i actually had no idea what "linear regression" meant but after googling around a little, i'm learning that i can probably use this as a rough estimate to predict how soon someone's rank might go up.
still not knowing what i'm doing, i got a hold of some fragment of code that allows me to run a function called "least squares fit" on a set of numbers (like rank values over a period of time) and get an output of ($q, $m, $r, and $rms) where:
$q and $m
satisfy the equation C($y = $m*$x + $q).
$r
is the Pearson linear correlation cofficient.
$rms
is the root-mean-square error.
so the only thing that looks familiar to me so far is this y=mx+q (line equation) which i'm hoping i can use to extrapolate future rank values and figure out the original question: "how long will it take for my rank to increase?"
my question: is my method completely way off? can you steer me in the right direction to use my database to answer the "original question"? maybe some terms i can google for...
thanks in advance
estimating the next time rank will increase
Last edited by fwiffo on Sat Aug 22, 2009 11:19 pm, edited 1 time in total.
A Spathi's Axiom for Survival: "The only brave Spathi is a dead Spathi. RUN YOU FOOLS!"
well right now you have simple (one variable) linear least squares regression. you can add more terms and you can add terms that are not, uh, "line linear". it all still has to be linear, ie f(x + y) = f(x) + f(y), but not every term has to be a line.
for example, you could model both a sigma and a mu term. but i wouldn't make sigma a simple term here.
that looks pretty logarithmic to me so try to fit a line through that scatter is never going to work that well. in fact, i'm pretty sure that curve they have there is least squares, or at least close. you probably already have the formula available for sigma if you can find who made the graph.
you can have pretty much any group of independent variables you want but the restriction is that they have to all be linearly independent. ie if you recreate them in matrix form they don't create a singularity as regression is all done using linear algebra.
for example, you could model both a sigma and a mu term. but i wouldn't make sigma a simple term here.
that looks pretty logarithmic to me so try to fit a line through that scatter is never going to work that well. in fact, i'm pretty sure that curve they have there is least squares, or at least close. you probably already have the formula available for sigma if you can find who made the graph.
you can have pretty much any group of independent variables you want but the restriction is that they have to all be linearly independent. ie if you recreate them in matrix form they don't create a singularity as regression is all done using linear algebra.
cool thanks.. i see.. so the general idea is plot a bunch of points first and see what kind of a graph we're dealing with, then pick a model according to the type of graph.
rank is a function of mu and sigma. sigma is definitely looks logarithmic so im prolly not using the right type of regression to predict rank... need something that models the curve closer..
thanks!
rank is a function of mu and sigma. sigma is definitely looks logarithmic so im prolly not using the right type of regression to predict rank... need something that models the curve closer..
thanks!
A Spathi's Axiom for Survival: "The only brave Spathi is a dead Spathi. RUN YOU FOOLS!"
more issue. sigma seems pretty consistent across players but mu is going to vary wildly b/t players. you might be able to get away with a line but i don't think it'll work for everyone.
second, the stack rating of the game affects the final mu adjustment, but i can think of no way to accurately control this. it may not even be neccesary but my instincts tell me you're gonna end up with pretty high variance on mu.
third, delta_mu is dependent upon sigma. this presents problems as now you have to start combining terms and stuff to really model it correctly. and i'm pretty much at the limit of my regression knowledge. it's very commonly used among the soft sciences like economics, sociology, finance, etc. if you know anyone who does research in these fields they can probably help.
second, the stack rating of the game affects the final mu adjustment, but i can think of no way to accurately control this. it may not even be neccesary but my instincts tell me you're gonna end up with pretty high variance on mu.
third, delta_mu is dependent upon sigma. this presents problems as now you have to start combining terms and stuff to really model it correctly. and i'm pretty much at the limit of my regression knowledge. it's very commonly used among the soft sciences like economics, sociology, finance, etc. if you know anyone who does research in these fields they can probably help.
Helpful hint understand what Mu and Sigma represent, throw out any notion of time played coorsponding to sigma, the stacker rating is not coupled to anything and Im unsure if it has even been vetted yet. I really want you not to do this Fwiffo since you don't know what you are doing, don't understand AllegSkills, your results will not be valid, and will only cause confusion. The leaderboard does not hold enough info to compute Mu and Sigma btw.
Thanks
MrChaos <--- on the origional AllegSkill team
Thanks
MrChaos <--- on the origional AllegSkill team
Last edited by MrChaos on Sun Aug 23, 2009 12:47 am, edited 1 time in total.
Ssssh
more issue. sigma seems pretty consistent across players
nope
but mu is going to vary wildly b/t players.
actually between 0 and 50
you might be able to get away with a line but i don't think it'll work for everyone.
since rank is a range of values in reality your kind of right but if your going to use LINEAR REGRESSION it will be a line
second, the stack rating of the game affects the final mu adjustment
wrong it has no effect on it at all
it may not even be neccesary but my instincts tell me you're gonna end up with pretty high variance on mu.
variance is sigma^2 and mu is a single value... every player in the game has a mu and sigma with the highest being 8.33
third, delta_mu is dependent upon sigma.
wrong
it's very commonly used among the soft sciences like economics, sociology, finance, etc.
ah it is used by the hard sciencies too in my case for DOE and the like in engineering testing
if you know anyone who does research in these fields they can probably help.
me
this is not a valid application and while Im sure well meaning your way off base
nope
but mu is going to vary wildly b/t players.
actually between 0 and 50
you might be able to get away with a line but i don't think it'll work for everyone.
since rank is a range of values in reality your kind of right but if your going to use LINEAR REGRESSION it will be a line
second, the stack rating of the game affects the final mu adjustment
wrong it has no effect on it at all
it may not even be neccesary but my instincts tell me you're gonna end up with pretty high variance on mu.
variance is sigma^2 and mu is a single value... every player in the game has a mu and sigma with the highest being 8.33
third, delta_mu is dependent upon sigma.
wrong
it's very commonly used among the soft sciences like economics, sociology, finance, etc.
ah it is used by the hard sciencies too in my case for DOE and the like in engineering testing
if you know anyone who does research in these fields they can probably help.
me
this is not a valid application and while Im sure well meaning your way off base
Last edited by MrChaos on Sun Aug 23, 2009 12:45 am, edited 1 time in total.
Ssssh
sigma changes pretty consistently across time. see also: above scatter plot.
i'm pretty sure delta_mu is dependent upon sigma. as i understand it, as sigma goes down adjustments to mu also go down.
QUOTE Stacked games
Q. Do I lose points if I win a horribly stacked game and I was on the stacked team?
A. No. The higher the imbalance, the less surprising the game outcome is in this case, and thus the less Mu and Sigma change. For very stacked games the changes in ratings, for both winners and losers in this scenario, are negligible compared with those resulting from well-balanced game. Your stack rating will be affected, though.
Q. Do I lose points if I lose a horribly stacked game whilst I was on the stacked team then?
A. Yes, lots. Since this outcome is considered highly surprising by AllegSkill, the losing (stacked) team is assessed as being much less skilled than had been initially assumed. The opposite is true of the anti-stacked team. In this case, the winners would receive a large increase to their skill rating, and the losers a large decrease.[/quote]
the stack rating of the game certainly does affect delta_mu.
QUOTE The leaderboard does not hold enough info to compute Mu and Sigma btw.[/quote]
...it tells you the values.
i'm pretty sure delta_mu is dependent upon sigma. as i understand it, as sigma goes down adjustments to mu also go down.
QUOTE Stacked games
Q. Do I lose points if I win a horribly stacked game and I was on the stacked team?
A. No. The higher the imbalance, the less surprising the game outcome is in this case, and thus the less Mu and Sigma change. For very stacked games the changes in ratings, for both winners and losers in this scenario, are negligible compared with those resulting from well-balanced game. Your stack rating will be affected, though.
Q. Do I lose points if I lose a horribly stacked game whilst I was on the stacked team then?
A. Yes, lots. Since this outcome is considered highly surprising by AllegSkill, the losing (stacked) team is assessed as being much less skilled than had been initially assumed. The opposite is true of the anti-stacked team. In this case, the winners would receive a large increase to their skill rating, and the losers a large decrease.[/quote]
the stack rating of the game certainly does affect delta_mu.
QUOTE The leaderboard does not hold enough info to compute Mu and Sigma btw.[/quote]
...it tells you the values.
Civlde Im irritated with something else and am going to refrain from posting anymore since Im going to take it out on you (I kind of already have sorry) but please be aware Im one of the people who worked on the ranking system with Baker being the other. Im speaking from knowledge, and the time graph is exactly what got in the mess with artifically inflating newb ranks. Sigma is not time dependent trust me. There may be a correlation but you have to prove it, and using a graph is not the way to do it.civilde wrote:QUOTE (civilde @ Aug 22 2009, 07:55 PM) sigma changes pretty consistently across time. see also: above scatter plot.
i'm pretty sure delta_mu is dependent upon sigma. as i understand it, as sigma goes down adjustments to mu also go down.
the stack rating of the game certainly does affect delta_mu.
...it tells you the values.
You really got to read what I write
Ok one final comment: I thought you meant the stacker rating on the leaderboard since the only info Fwiffo has is on the leaderboard. The fact that your Mu and Sigma is effected by those you play with and against is a given. If that is what you meant then your right... Fwiffo can't compute these values since he has only the leaderboard to work with in his graphs.
Again sorry for leaking all over you Im quite peeved atm
fwiw logrithmic and line go hand in hand, something that is logrithmic is linear.
Last edited by MrChaos on Sun Aug 23, 2009 1:22 am, edited 1 time in total.
Ssssh
