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Offline the dictatorTopic starter

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Re: [1.32] False Gods Stats Thread https://elementscommunity.org/forum/index.php?topic=53573.msg1123817#msg1123817
« Reply #12 on: January 29, 2014, 05:23:59 pm »
(snip)
Values for 'skips' - If the above idea of not allowing skips in test data is implemented, it becomes a non-issue for public-overall-FGei.
(snip)

Just saying, no it isn't a non-issue, because it the efficiency of skipping gods heavily depends on how long a skip takes (the shorter the skip, the more gods can be skipped with profit). Once I get the rest of the calculations up and running I think I will take a look for both quarter of a turn, half a turn and a full turn, to see what seems most accurate.

(snip)
*If you did a drop-down menu for skips it'd be nice. I mean, after calculating the FGei for every God and average it, where the FGei for a single God is written there should be a drop-down menu with two options: one shows the FGei, the other one proposes, instead, the skip result (which should be something like 4*Cost*TPH and, with TPH=333). A player should, then, try each God's skip and see if the FGei rises or not. If it does, keep that God skipped, if it doesn't, put it back in the To-Be-Played list. Rinse and repeat 'till the optimal FGei.
(snip)

Regarding your different TPH values, I think I will just go with 333/hour when making the thread, people that play faster (or slower, I use a netbook, and I do very close to 250/hour), can easily compensate for that. (The difference between 333 and 250 is simply a factor 0.75 on the end result.) Having all studies use the same numbers means the results are easily comparable.
For your skip algorithm, while that would be the best way to do it, there would be 2^29 combinations, and I don't really feel like checking them all when doing the numbers for each deck. (brute force always works, but isn't always the most efficient method.)

Aside from this, I pretty much agree with you guys (and with CG, we had some discussion in chat, today and earlier), and I think I'm going with:
  • Turns instead of time.
  • Disallowing Skips
  • Excluding Turns to Lose/Turns to Finish. While it is nice and more accurate than using turns to win, I'm afraid it's too subjective.
  • Regarding droprate per god, I think I'm going to run a few million tries in xenosim and use those to get numbers for Spin Profit PER god, I will record the data as I get it in the 4th post of the thread.

This means the only thing still up for debate is deciding on how to turn the skipless data into an FGei with skip numbers. For now I'm considering the following (a simplification/variation of Leodips brute force):
Calculate the individual FGei for each god, these weighted by average turn to win per god should give an accurate normalized FGei without skips.
Sort them from lowest to highest FGei per god, and replace start skipping those gods one by one (lowest individual FGei first, until you find the break point where skipping is no longer raises the FGei). This should come up with accurate numbers, without having to try all 2^29 combinations.
After that we need to decide on a certain skip tolerance, in my VDB example, there are a bunch of gods (using the old FGei formulae), that raise the FGei by less than 50 per god when skipping them (on a total FGei of 10k+). A slight variation in the winrates for those gods (10 fights against each god means a total of 290 games, but only 10% accuracy on the individual winrates), makes a big difference here, which is why I would like to exclude them from the recommended skiplist, despite the fact that skipping them based on those numbers would slightly raise the FGei. (compared to an increase to the FGei of 200 up to 600 for clear skips like destiny and seism).
« Last Edit: January 29, 2014, 05:42:06 pm by the dictator »
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Offline CuCN

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Re: [1.32] False Gods Stats Thread https://elementscommunity.org/forum/index.php?topic=53573.msg1123818#msg1123818
« Reply #13 on: January 29, 2014, 05:27:46 pm »
For your skip algorithm, while that would be the best way to do it, there would be 2^29 combinations, and I don't really feel like checking them all when doing the numbers for each deck. (brute force always works, but isn't always the most efficient method.)

I think that Leodip's algorithm is O(n^2) at most.

Offline the dictatorTopic starter

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Re: [1.32] False Gods Stats Thread https://elementscommunity.org/forum/index.php?topic=53573.msg1123822#msg1123822
« Reply #14 on: January 29, 2014, 05:44:26 pm »
For your skip algorithm, while that would be the best way to do it, there would be 2^29 combinations, and I don't really feel like checking them all when doing the numbers for each deck. (brute force always works, but isn't always the most efficient method.)

I think that Leodip's algorithm is O(n^2) at most.

Is it? I count 29 gods, each with 2 options (skip or no skip), making 2^29 possible combinations. But even if you come up with a an algorithm that works in O(n^2), I think mine (sort by individual FGei first, skip in order) is O(n), so I like that even better :)

Edit: Serprex pointed out in chat that my algorithm is o(n*log(n)) since it requires sorting first :)
But, I'm not really concerned with the complexity of the sorting, since whatever spreadsheet I use can easily do that for me, thus it is mostly the number of skip/no skip selector tries I'm worried about.
« Last Edit: January 29, 2014, 05:52:37 pm by the dictator »
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Offline Leodip

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Re: [1.32] False Gods Stats Thread https://elementscommunity.org/forum/index.php?topic=53573.msg1123850#msg1123850
« Reply #15 on: January 29, 2014, 08:12:07 pm »
-snip-
Calculate the individual FGei for each god, these weighted by average turn to win per god should give an accurate normalized FGei without skips.
Sort them from lowest to highest FGei per god, and replace start skipping those gods one by one (lowest individual FGei first, until you find the break point where skipping is no longer raises the FGei). This should come up with accurate numbers, without having to try all 2^29 combinations.
-snip-
This idea is pretty good, but if you want the spreadsheet to order them following their personal FGei, it'll require more coding (unless you're gonna make the player do so, but if it is like that, keep reading).
I probably created a misunderstanding, but what I said requires a lot less than 2^29 combinations. It's simply what you did, but letting the player do that. He simply sets the god with the lowest FGei to "skip". If skipping raises his FGei, he gets the second last, and so on until it drops instead of rising.
So, yeah, at most the player will have to click 28 times (if only one god is playable and the other 28 aren't playable he simply has to check the other 28 to "skip").

And, before other misunderstandings are generated, I'd want to fix a phrase I said before:
I mean, after calculating the FGei for every God and average it, where the FGei for a single God is written there should be a drop-down menu with two options: one shows the FGei, the other one proposes, instead, the skip result (which should be something like 4*Cost*TPH and, with TPH=333)
I'm sure you would have noticed that by yourself, but I didn't want to cause more troubles: when I said to change the options to get the Skipped FGei what you have to change is the TTF, and not the FGei itself (otherwise it'd average considering, eg, 18 turns of TTW, but really have half a turn played).

It was obvious, but probably worth saying.

Offline the dictatorTopic starter

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Re: [1.32] False Gods Stats Thread https://elementscommunity.org/forum/index.php?topic=53573.msg1123852#msg1123852
« Reply #16 on: January 29, 2014, 08:23:16 pm »
I'm afraid I will have to do all that myself (or automate it somehow), as least for the numbers I'm going to post in the OP (see the arena study), because if I let the different testers decide on the skips, there is bias between the different testers again.

Basically, I would need lots of people to play lots of games, record the data and post it here, which I will then use to manage to opening posts to report the numbers, that means I will be the one making the final decision on the skips.
This thread is not so much about finding your own personal FGei with deck X, but about getting numbers that are fairly (or rather, as fair as possible) comparable for the different decks, to be able to figure out which are the best for farming electrum and as a bonus, preferably comparable to the other (UEI) studies in this subforum as well (AI3, AI4 and Arena).
In the end it the thread should be comparable to the arena study and the halfblood study.

Therefore the spreadsheet I usually refer to will be mostly a personal tool, that I will use to collect the data from the different testers and that combines them into neat output to put into the opening post.
That said, I will probably make some kind of tool for FG statgathering, like the arena statsheet I created (for arena, but it can handle AI2, AI3 and AI4 as well), if nobody else beats me to it. (Jangoo's Old Statmasta tool already does it quite well, except it would need an update to use new standards (no skips, using turns instead of time, etc).
« Last Edit: January 29, 2014, 08:31:30 pm by the dictator »
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Re: [1.32] False Gods Stats Thread https://elementscommunity.org/forum/index.php?topic=53573.msg1124092#msg1124092
« Reply #17 on: January 31, 2014, 02:57:07 am »
I didn't think auto calculating skips would be that hard.
You get the efficiency of each of the gods without skips.
You get the efficiency of the average.
Starting with the lowest efficiency score, replace is a -30 Electrum and 1 Turn cost * test runs and average that into the other gods
If the efficiency is higher with the skip, mark as skip and continue moving up the list until you have one that is worse off with the skip. 
Done

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Re: [1.32] False Gods Stats Thread https://elementscommunity.org/forum/index.php?topic=53573.msg1124118#msg1124118
« Reply #18 on: January 31, 2014, 09:49:58 am »
Thats an interesting change to make with turn-to-win instead of time-to-win.

I would be against a full elimination of time for a few reasons.

-Computers are not going to be vastly different in speeds unless you are still running windows 95.

- If you allow a ton of time for each turn you are not getting a true idea of how fast it is to play realistically.
       a) decks like life rush vs something like CCYB (examples) are going to have turns that are 5x different. especially something rather mindless like poison dials vs something          that might take more careful thought possibly voodoo bravery for more current decks
       b) extra time to think resulting higher than expected winrates.

- I think the whole idea of using time also gave a true estimate/ example of how fast/slow it should be played and the actual results rather than guessing how long a turn on average takes. I want to see how I compare to an optimal fgei

I believe most of the previous studies also included turn to win in the data. I would be interested in seeing how turn vs time would affect the old studies.

The whole skip thing actually isnt that hard if you need some help programming the spreadsheet just ask.
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Re: [1.32] False Gods Stats Thread https://elementscommunity.org/forum/index.php?topic=53573.msg1124145#msg1124145
« Reply #19 on: January 31, 2014, 04:10:44 pm »
"-Computers are not going to be vastly different in speeds unless you are still running windows 95. "
At first you think so, but observed otherwise. Also low quality for life

"- If you allow a ton of time for each turn you are not getting a true idea of how fast it is to play realistically."
Colorless has observed that time per turn between people is much greater than time per turn between decks. Observation trumps theory wrt reality

Applying your own (read: personal, and thus not easily useful to others) time related data to turns ends up involving applying constant coefficients to the listed UEI

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Re: [1.32] False Gods Stats Thread https://elementscommunity.org/forum/index.php?topic=53573.msg1124146#msg1124146
« Reply #20 on: January 31, 2014, 04:11:40 pm »
Thats an interesting change to make with turn-to-win instead of time-to-win.

I would be against a full elimination of time for a few reasons.

-Computers are not going to be vastly different in speeds unless you are still running windows 95. I have a Pentium 4 desktop PC at home on XP with 2GB RAM.  On lowest settings with only the game windwo, balb chat, and GDocs (stat and record keeping from EtG) open it takes noticeably longer for AI turns and the animation-effects (the few still "on" with these settings) to happen.  It is not insignificant nor would I consider this PC as so outdated as to be an extreme outlier for all EtG players.

- If you allow a ton of time for each turn you are not getting a true idea of how fast it is to play realistically.
       a) decks like life rush vs something like CCYB (examples) are going to have turns that are 5x different. especially something rather mindless like poison dials vs something          that might take more careful thought possibly voodoo bravery for more current decks  In my experience, this _vast difference_ is only evident at the first few times using a 'new' deck.  Also, it is never a 5x difference in my grinding experience and after a good number of times using any deck I can play it within a second or so of the same speed regardless of tactics.  *Note:  Something like Firecell which requires lots of animation effects AND card clicking may be noticeable.  Hence the adjustable TPH value. /*
       b) extra time to think resulting higher than expected winrates.  The average players should not have to do much REAL thinking time after using a given deck for more than about 30 games.

- I think the whole idea of using time also gave a true estimate/ example of how fast/slow it should be played and the actual results rather than guessing how long a turn on average takes  The 10.8 seconds/turn (which gives the 333 TPH value) is not a random-plucked-from-thin-air guess.  Per CG, it came from review of prior testing stats where time WAS the base of the stats.. I want to see how I compare to an optimal fgei

I believe most of the previous studies also included turn to win in the data. I would be interested in seeing how turn vs time would affect the old studies It would vary based on how you set the TPH - UEI utilizes a TPH to relate time and turns.  This step allows the 'removal' of time as a factor.  Time is still considered via the adjustable TPH value..

The whole skip thing actually isnt that hard if you need some help programming the spreadsheet just ask I believe the 'issue' at-hand regarding skips is not knowing how to program Excel or GDOcs, but rather what METHOD should be programmed to do skips.  When Pella and I put in effort on the interim-FGei (now being replaced with a UEI sort of value), the skips were done along the lines of Keeps suggestion.  Incremental is likely the way to do it.  However, I would suggest not going ALL THE way on drawing the line.  What I mean is if skipping a certain FG increases UEI by 1.2% (or some agreed upon level of tolerance) does not mean AUTO-SKIP.  Rather, divide into 3 categories:  GO; CAUTION; and SKIP with a user adjustable value of 'tolerance' for setting how tight or loose they want the skips calculated.  Or at least something along those lines. :D.
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Re: [1.32] False Gods Stats Thread https://elementscommunity.org/forum/index.php?topic=53573.msg1124147#msg1124147
« Reply #21 on: January 31, 2014, 04:14:03 pm »
As an additional point regarding time vs turns, it is trivial for someone to figure their personal time/turn with a given deck and convert stats reported based on turns into being based on personal time. It is not trivial to go in the other direction.

Offline the dictatorTopic starter

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Re: [1.32] False Gods Stats Thread https://elementscommunity.org/forum/index.php?topic=53573.msg1124153#msg1124153
« Reply #22 on: January 31, 2014, 04:45:26 pm »
Serprex, Rob and CG made most of my points for me, so I won't bother repeating their answers in replying to Sevs, though I will announce that I am planning to play a few 100 games PDials at some point to compare (I already have a 1000 games of VDB logged, though those 1000 games are split into 3 sets of data, where only the last set of 500 games has logged both time to win and turns to win).

I am working on a reply for to Keeps question, though that is going to take a bit of typing, so I decided to post half a post first.

I didn't think auto calculating skips would be that hard.
You get the efficiency of each of the gods without skips.
You get the efficiency of the average.
Starting with the lowest efficiency score, replace is a -30 Electrum and 1 Turn cost * test runs and average that into the other gods
If the efficiency is higher with the skip, mark as skip and continue moving up the list until you have one that is worse off with the skip. 
Done

This is pretty much the idea yes (define an order, and add skips 1 by 1 on top of each other according to the order in that list).
Bolded the important part, where the issue comes up. Yes, you can calculate the UEI[FG] for each individual god using CG's formulae (I'm using these to get results more easily comparable with arena and AI4 data), and yes, the average of those numbers is exactly the UEI for the overal without skips. Sadly, that order isn't always the same as the order in which you should skip: a FG with a very high TTW should be skipped before one with slightly worse numbers, but a better TTW (and no, this doesn't happen inherently, I think it's best explained as: your aren't looking for the gods that make you the least profit, you are looking for the gods that result in the largest increase of profit if you were to skip them, which isn't always the same thing).
Once you include skips, you introduce a new factor: skipped games are of an entirely different duration. Including skips alters your average turns/game, because you are replacing TTW numbers per god with skip durations (currently set at 1 turn per skip, but that is up for debate, and easily changed/personalized). Either way, you need a more advanced way to rank them. Here is where CuCN had a stroke of genius (CG and me had been at it in chat for a few hours, when he showed up, joined the discussion and eventually managed to figure it out):

Quote from: CuCN
[2014-01-30 02:08:40] CuCN: I think the profits and ttws should be added separately
[2014-01-30 02:08:47] CuCN: and then the sums divided by each other
[2014-01-30 02:10:53] CuCN: overall UEI should be calculated as (sum of profit from one game against each god)/(sum of turns for one game against each god)
[2014-01-30 02:13:04] CuCN: I think to determine what to skip, it should be sorted by (profit/game-profit/skip)/(turns/game-turns/skip)
[2014-01-30 02:13:50] the_dictator: we are using 1 turn per skip for now CuCN
[2014-01-30 02:14:17] CuCN: so the FGs should be sorted by (profit/game+30)/(turns/game-1)
[2014-01-30 02:15:38] CuCN: then, when calculating the overall UEI, have a column with profit/game if not skipping, or -30 if skipping
[2014-01-30 02:15:48] CuCN: and a column with turns/game if not skipping, or 1 if skipping
[2014-01-30 02:16:00] CuCN: sum the columns, divide the sums and multiply by 333

And this is exactly what we ended up using. Calculate the profit/game (so not per turns, or per second, or per hour, per GAME) for each god, and calculate the average TTW for each god. Calculate '(profit/game+30)/(turns/game-1)' for each god, and sort based on that value (I doesn't have any easily defined meaning, sadly, we ended up simply calling it skip index). It works because it follows the mediant inequality, I will elaborate one I make a write-up of the full math in the OPs somewhere.
After that is simply maximizes the UEI[FG] using that order, which comes up with very nice (but believable) values, though usually with a high number of recommended skips (not very strange, considering it is currently trying to squeeze out every last electrum per hour). While this does give the highest possible UEI[FG], it does make for long skip lists (I think the calculations based on 200 games of PDials from the old study currently recommends skipping 16 out of 29 gods) AND it's rather sensitive to small number bias (if you have a 100% winrate or lossrate, based on a sample of 1 game, it will likely come up as one of the last gods to skip (or first)). Because of this I plan to add 2 filtering methods: the first one, already in place, reruns all the data, answering the question: if this data were exactly one fight larger, what would that do to the skip recommendations. (it checks for each game outcome (win or lose), and for each possible god, I leaving all other gods, and EMrate/TTW exactly as they were). The second filtering method, which I'm working on right now, is going to do what rob suggested: look at the increase in UEI[FG] resulting from skipping that god, and comparing that to a certain threshold.
Currently I'm mostly focusing on getting myself a tool that I personally can use to calculate the numbers that should be put in the opening post, along with skip recommendations and such, however I will likely end up making a public version for use by individuals to use when testing their data, and I plan to let that one also include options to change certain personal settings (like turns per hour, and skip durations), and ideally, even an option to take the official list as maintained on the forum to be recalculated based on those personal settings, though that, especially the last part, is something on my to do list later.

That said, CG and I agreed to show the numbers for all studies for both 333 turns per hour and 250 turns per hour, to give people some more options, and to some more options when comparing between different opponents (for example, when someone looking at the different studies personally knows their turns take a lot longer against false gods than platinum arena, though I would advice people to actually note down numbers for a few games instead of just doing it based on a feeling).

I believe the 'issue' at-hand regarding skips is not knowing how to program Excel or GDOcs, but rather what METHOD should be programmed to do skips.  When Pella and I put in effort on the interim-FGei (now being replaced with a UEI sort of value), the skips were done along the lines of Keeps suggestion.  Incremental is likely the way to do it.  However, I would suggest not going ALL THE way on drawing the line.  What I mean is if skipping a certain FG increases UEI by 1.2% (or some agreed upon level of tolerance) does not mean AUTO-SKIP.  Rather, divide into 3 categories:  GO; CAUTION; and SKIP with a user adjustable value of 'tolerance' for setting how tight or loose they want the skips calculated.  Or at least something along those lines. :D.

You are right yes, spreadsheet coding isn't really a problem (though I did learn some new functions along the way, Google was sufficient so far).
I will leave the skip strategy implementation open for discussion for now (it will be covered in my reply to Keeps), though anyone who wants to take a look, we have a WIP version of the formulae *here* the result of work/discussion by CG, CuCN and me (pieces of the discussion about it should be in chat history of the past 2-3 days)
« Last Edit: January 31, 2014, 08:09:59 pm by the dictator »
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Offline Sevs

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Re: [1.32] False Gods Stats Thread https://elementscommunity.org/forum/index.php?topic=53573.msg1124210#msg1124210
« Reply #23 on: February 01, 2014, 12:17:44 am »
I guess my point didn't get across

I would be against a full elimination of time for a few reasons.

Just keep it a stat you still record just like turns were recorded when time was the main factor. I am honestly interested in seeing how this affects stats
"Elements is the greatest game ever made" - Abraham Lincoln

 

anything
blarg: