[1.32] False Gods Stats Thread

[the dictator]

This thread is a continuation/improvement of the study started by Pella, meant to both revive the study, and to update the underlying formulae to use the new information available.

Table of Contents

• Results
• Unupgraded Decks
• Upgraded Decks
• How to Participate
• Testers Instructions
• Tools, Tips and Tricks
• Mathematical Explanation
• Assumptions and Set Values
• Initial Calculations
• Skips
• Skip Reliability Checks
• Skiplists
• Other
• Thanks and Sources
• Changelog
• Original Opening Post

Stats acronym glossary:

Spoiler for Glossary:

TTW: Turns To Win
TTL: Turns to Lose
EM: Elemental Mastery (winning with 100% of your max hp's)
UEI: Unified Efficiency Index (approximate electrum/hour assuming all spun cards are sold)

For more details on the formulae used for UEI, see the UEI thread, and the third post in this thread.

Results
Results are sorted by Optimal UEI. Results as reported on top are the expected results when skipping all gods on the optimal skiplist. Winrate and EMrate are averages of the per god numbers. For each deck there are two skiplists, the first is the optimal one (skipping these gods gets you the Winrate, EMrate and UEI listed, but its a very strict procedure, overly strict at times). Therefore all decks also list a sure skiplist, which excludes questionable gods (see Mathematical Explanation for the procedure). Similar decks are grouped together, open the spoilers to see the (results of) the different modifications.

Unupgraded decks
Unupgraded decks are allowed up to 9 upgrades. Within groups, modifications are sorted by number of upgrades, then number of rares, than Optimal UEI, with the highest ranking deck used as representative deck.

RoL/Hope Unupped, By Krathos, Modified by Zawadx, Tested by Zawadx, 116 matches played.
Opt. WR: 54,17%   Opt. TTW: 11,93   Opt. EMR: 5,93%   Opt. UEI(333): 6711   Opt. UEI(250): 5039   Recommended Skiplist: 15 Gods

Spoiler for Additional Info and (Best) Deck:

My RoL/Hope (mostly) unupped (More Upgrades, Yay! Mod)

Hover over cards for details, click for permalink

Deck import code : [Select]

5la 5la 5lk 5lk 5lk 5lk 61o 61o 61o 61o 61o 61o 61u 61u 622 622 622 622 63a 63a 63a 63a 63a 63a 7jp 7jp 7jp 7jp 7jp 7jp 80e 80i 8pu

	Winrate (Played)	TTW	EMrate	UEI(333)	UEI(250)	Skips
Optimal	16,81% (54,17%)	11,93	5,93%	6711	5039	20 Gods
Secure	22,27% (46,13%)	12,35	3,81%	6306	4734	15 Gods
Skipless	26,44%	12,39	2,81%	3896	2925

Spoiler for Graph and Table:

Upgraded decks
Within groups, modifications are sorted by UEI, with the best deck used as representative deck.

Voodoo Bravery, By eaglgenes101, Modified by The dictator, Tested by The dictator, 863 matches played.
Opt. WR: 60,84%   Opt. TTW: 8,16   Opt. EMR: 0,41%   Opt. UEI(333): 13510   Opt. UEI(250): 10143   Recommended Skiplist: 6 Gods

Spoiler for Additional Info and (Best) Deck:

Voodoo Bravery 1.2

Hover over cards for details, click for permalink

Deck import code : [Select]

6u3 6u3 6u3 6u3 6u3 6ve 6ve 6ve 6ve 6ve 74d 74d 77l 77l 77l 77l 77l 77l 7ee 7ee 7ee 7ee 7ee 7tg 7tg 7tg 80b 80b 80b 80b 8pu

	Winrate (Played)	TTW	EMrate	UEI(333)	UEI(250)	Skips
Optimal	39,86% (60,84%)	8,16	0,41%	13510	10143	10 Gods
Secure	46,20% (58,25%)	8,15	0,65%	13363	10032	6 Gods
Skipless	48,97%	7,91	0,51%	11966	8984

Spoiler for Graph and Table:

Pdials, By Sevs, Modified by neuroleptics, Tested by Keolino and Unknown, 524 matches played.
Opt. WR: 83,85%   Opt. TTW: 15,06   Opt. EMR: 65,95%   Opt. UEI(333): 11058   Opt. UEI(250): 8302   Recommended Skiplist: 12 Gods

Spoiler for Additional Info and (Best) Deck:

Pdials (34 cards)

Hover over cards for details, click for permalink

Deck import code : [Select]

710 710 710 710 710 710 718 718 718 718 718 718 71a 71a 71a 71u 71u 71u 71u 71u 71u 72i 72i 72i 7km 7km 7km 7km 7q9 7q9 7q9 7q9 7q9 7q9 8pq

	Winrate (Played)	TTW	EMrate	UEI(333)	UEI(250)	Skips
Optimal	40,48% (83,85%)	15,06	65,95%	11058	8302	15 Gods
Secure	47,06% (80,27%)	15,10	64,76%	10911	8191	12 Gods
Skipless	53,01%	14,69	61,45%	7780	5841

Spoiler for Graph and Table:

Spoiler for Individual Modifications:

Pdials (34 cards), By Sevs, Modified by neuroleptics, Tested by Keolino, 200 Games Played
Opt. WR: 86,47%   Opt. TTW: 14,82   Opt. EMR: 67,18%   Opt. UEI(333): 11333   Opt. UEI(250): 8508   Recommended Skiplist: 15 Gods

Spoiler for Deck:

Pdials (34 cards)

Hover over cards for details, click for permalink

Deck import code : [Select]

710 710 710 710 710 710 718 718 718 718 718 718 71a 71a 71a 71u 71u 71u 71u 71u 71u 72i 72i 72i 7km 7km 7km 7km 7q9 7q9 7q9 7q9 7q9 7q9 8pq

[the dictator]

How to participate

Of course, to get lots of decks listed here with accurate data, we are going to need lots of tests, with lots of decks, and I'm sure YOU want to help out.

Testers Instructions

Here's what you need to do:

• Select the deck you are going to test (duh)
• Note down deckname, deckcode and forumthread. If the deck doesn't have a thread, encourage the creator of the deck to make one, or ask permission to make one yourself.

For the data to be eligible, I want at least 100 games per set, smaller samples are unlikely to be included.
Skipping during the testing is allowed, and counts towards those 100 games, but skipped games won't be considered in the calculations (a record of 1 win, 1 loss, 50 skips counts as 50% winrate). This specific rule allows for minimal imbalance, while allowing lots of freedom on the part of the tester: if you decide there aren't enough games with deck X against god Y, you can skip all other gods, and mark them as such to increase the speed of the data collecting, without affecting the rest of data. You can also use the trainer for this, but we can't be sure that uses the same AI as the actual AI, especially with version 1.4 coming up.
Because of this, I want at least 3 games against each god per deck. I will accept data that does not fit this requirement, because I do count them towards the deckgroup (if there are other similar decks in the study already), but the individual deck won't show up with it's own stats (in the modifications), until it fits the requirement.

Because skips are completely excluded from the data, I have to be strict: a skip is only a skip for the purpose of this study if it's based solely on the name of the opposing god. Quitting because of a misplay or a bad starting hand counts as a loss.

Now, note down per god:

• Number of Wins
• Number of Losses
• Number of EM's (not required, but I will assume 0 if not listed)
• Number of Skips
• Total turns to Win, yes, that is TURNS to WIN, Not Losses, Not Finish, not time.

That's all that is needed. That said, more data is never a bad thing, maybe some other study can use it. Especially Time to Win would be nice in this case, to get a better idea of the general playing speed of the community.
Using import function from the trainer is not allowed, though completing the testdata by skipping all but a few gods using the normal fight FG button in the trainer to get the last few results is fine. This is because the specific FGs can have slight differences in their personal AI that the import function doesn't load in (since that one uses the general AI).

After you are done, post your data in this thread.


tl;dr: Deckname, Deckcode, Forumthread, Author and creator of the specific modification. Per god Wins, Losses, EMs and total Turns to Win.

Tools, Tips and Tricks

As of now, I haven't created a handy tool yet for taking the stats, I might do so in the future, in the meantime I will point you to Pella's old GDocs Sheet and StatMasta. Both use outdated formulae, and StatMasta doesn't even allow tracking of Turns to Win (but you can toss them into the time to win column just fine), but they have a handy table with the list of gods, and headers for the required stats. Of course, pen and paper also works, as well as making your own quick sheet.

If you are using a spreadsheet, you can easily track totals (like Total Turns to Win), by turning it into a formula. Before the first number type a '='. After you have done that, you can use the f2 key to go to the end of the formula in that cell (after selecting the cell, of course), and add '+'new number for every new entry.

[the dictator]

Mathematical Explanation

Warning, lots of math ahead (duh).

Spoiler for Glossary:

W = Wins
L = Losses
EM = Elemental Masteries
TPH = Turns Per Hour
TPS = Turns Per Skip
TTW = Turns to Win
TTL = Turns to Lose
TTF = Turns to Finish
UEI = Unified Efficiency Index
XHP = Average number of additional hit points at the end of each match, to be set by whoever is doing the calculations. (assumed 0 if not set)

Assumptions and Set Values

During the complete calculation for the purpose of this thread, the following numbers are assumed:
Expected HP remaining on a non EM win: 50% of max HP (same as UEI)
Turns per Skip: 1 (yes, that might be on the high side, but it's plenty profitable that way already, I don't really want to lower it, to stop the skiplists from becoming even longer).
Turns per Hour: 333 and 250 (results given for both values)
The following values are used for spinprofits (I ran the simulations in xenosim, just to have 'something' for now. It is can easily be changed if someone comes up with better (more accurate) numbers):

Spoiler for Xenosim simulation numbers (200000 simulations per god):

God	Extra won	Extra per game
Akebono	125032819	625.164095
Chaos Lord	90548400	452.742000
Dark Matter	96430561	482.152805
Decay	144238096	721.190480
Destiny	105440040	527.200200
Divine Glory	166270630	831.353150
Dream Catcher	88154879	440.774395
Elidnis	87814092	439.070460
Eternal Phoenix	130711542	653.557710
Ferox	104511820	522.5559100
Fire Queen	120121402	600.607010
Gemini	116466436	582.332180
Graviton	110247357	551.236785
Hecate	128189945	640.949725
Hermes	91454251	457.271255
Incarnate	113644302	568.221510
Jezebel	139587344	697.936720
Lionheart	112147941	560.739705
Miracle	91208340	456.041700
Morte	89199889	443.999445
Neptune	113289586	566.447930
Obliterator	112587375	562.936875
Octane	144100200	720.501000
Osiris	129062000	645.310000
Paradox	114020018	570.100090
Rainbow	85640181	428.200905
Scorpio	86554103	432.770515
Seism	98122061	490.610305
Serket	113748823	568.744115

The following are also assumed:
Turns to Lose is 75% of Turns to Win per god. This (arbitrary) number I based  on the ratios  of TTW and TLL from older tests (it was 74,44%).
The TTW for a god without games won (and thus without a Turns to Win entry) is assumed to be the average of the other TTWs.

Initial Calculations

First it calculates Turns to win per god (Total turns to win/Wins), or for gods without any wins, it uses the average of the other gods. Then it calculates the assumed turns to lose for that god (TTL = 0.75 * TTW). Based on those two is calculates the TTF for each god as a weighted average: TTF = (TTW * Wins + TTL *Losses)/(Wins+Losses)

Profit per Game and UEI[FG]
Next, the profit per game per god is calculated based on the wins, losses, EM's and spin profit. This follows the general UEI calculations, with a few changes:
First, since we are calculating profit per game, instead of per hour, we don't have have to use TTF or TPH yet. Aside from that, some changes had to be made to the formula, because of the differences between FG's and the other opponents.

Code: [Select]

PPG = Profit per game (per god) = (W*60*19/24*(1+EM/W*(48/19-1))*(1+XHP/200)-30*L+W*SP)/(W+L)
This is calculated for each god separately (using the numbers of that god).
The average profit per game per god, divided by the average duration of a game (in turns), gives the average profit per turn. Multiplying this by TPH gives profit per hour. Because there are averages on both sides of the division, it's possible to use sums instead, which simplifies the later calculations.

Code: [Select]

Sum of PPG / Sum of TTF * TPH = UEI

Skips
Essentially, factoring in skips is very simply: you set the profit per game for each skipped god to -30, and the TTF for that god equal to the turns per skip (TPS, assumed 1), and recalculate the UEI using the above formula.

Recall, so far we are using:

Code: [Select]

Sum of PPG/Sum of TTF * TPH = UEI
We are interested in knowing for which god a skip is profitable, and for which it isn't. Turns per hour isn't relevant, if it's more profitable per turn, it will also be more profitable per hour, so that part is omitted from the formulae for now. (once we find the optimal profit per turn, we can simply multiply by turns per hour).

Code: [Select]

Sum of PPG/Sum of TTF < (Sum(without god X) of PPG – 30)/(Sum(without god X) of TTF +TPS)
For now we are only interested in the sign in the middle: is it a less than or a greater than sign. This is where CuCN came in, and introduced the mediant inequality.

Code: [Select]

Sum(Without god X) of PPG – 30 = Sum of PPG – 30 – PPG(god X)
Sum(Without god X) of TTF + TPS = Sum of TTF +TPS – TTF(god X)
Looking at this, it seems like we should be able to use the mediant property to do something useful, and that turned out to be right, using the following 2 fractions a original fractions:

Code: [Select]

(Sum of PPG – 30 – PPG(god X))/(Sum of TTF + TPS – TTF(god X))
Skip Index = (PPG(god X) +  30)/(TTF(god X)-TPS)
The mediant of the two is

Code: [Select]

([Sum of PPG – 30 - PPG(god X)] + [PPG(god X) +  30])/([Sum of TTF + TPS – TTF(god X)] + [TTF(god X) – TPS]) = Sum of PPG/Sum of TTF
Because of the mediant inequality we know that the mediant is always in the middle of the two, in other words. If and only if:

Code: [Select]

(PPG(god X)+30)/(TTF(god X)-TPS) < Sum of PPG/Sum of TTF
then

Code: [Select]

Sum of PPG/Sum of TTF < (Sum(skipping god X) of PPG -  30) / (Sum(without god X) of TTF + TPS)
Or, in other words if the skip index is smaller than the average profit per turn, it's profitable to skip that god.
Therefore, we are going to sort by skip index, and cumulatively skip in that order, adding one additional god to the gods already skipped, starting with the god with the lowest skip index.

Skip reliability checks
The above procedure is accurate (or well, as accurate as it gets under the assumptions made), but that doesn't mean it's optimal. After all, we are dealing with a set of statistical data, so there is going to be a certain margin of error. In most of the studies in this board that isn't a problem, because you win one more game against one opponent, and then lose that game against another, big deal. In this case it can affect the ratings significantly, because that 1 lost game might push that god over the edge, so that he now ends up on the skip list, which might be a bit of an overreaction all because of 1 game. For this reason, I built in some additional checks. These two checks don't alter the UEI reported (since that is the optimal one), but they do determine the secure version of the skiplist.
The first check is actually 58 checks in 1. I asked myself the question: what if you played 1 more game with this deck, how could that affect the current ratings?
Hence 58 checks in 1: there is 58 possible outcomes to that additional game, win or loss against 29 different gods. So, it calculates the altered ratings if that additional one game would have been a loss or win against each god, and concludes per god if he should be skipped or played with that one additional game taken into account. If a different conclusion is returned for losing compared to winning, the god is marked as ‘fluctuating’ (too close too the breaking point to tell, a single game can swing the rating from skip to play or play to skip, likely because of a small number of games played (remember, skips are excluded from the stats): if you only have 2 games against a god, there is only 3 possible winrates: 0%, 50% or 100%. It’s clear that this isn't going to give very accurate winrates, thus not very accurate skip recommendations, which then likely results in an ‘fluctuating’ rating).

The second check checks something different: even if it is theoretically profitable to skip all games against a certain god, I probably won't do if it only gets me a very small increase in UEI. Thus, it checks if the UEI after not skipping that god (and all gods above this god in the listing), is within 2% of the optimum, if it is, the god is marked as ‘Marginal’, changing the behavior against these gods (still cumulative along the ordered list), from skip to play, changes the UEI by so little its not relevant, therefore I’m not giving a strict recommendation on these gods. Yes, unlike the ‘fluctuating’ marker, this one is only applied to gods listed as skip. (Nobody is going to skip MORE gods because it only lowers their income by 2%), and if a god is both ‘fluctuating’ AND ‘marginal’, ‘fluctuating’ takes precedence.

Skip Lists
All gods skipped to reach the optimal UEI are included in the optimal skiplist. All gods still marked skip after factoring in both the fluctuating and marginal check are included in the secure skiplist.

[the dictator]

Other

Thanks and Sources

Spoiler for Thanks to:

ColorlessGreen, CuCN for helping out with the formulae, and for their input/opinions whenever I another set of eyes (or brains).
Pella, ColorlessGreen (yes, again), for the earlier studies that I could base my methods and formatting on.

Spoiler for Sources used:

UEI - The Unified Efficiency Index
The Return of FGei
Arena Study
AI4/Halfblood Study

Changelog
Nothing Yet.


To-do List

• Decide on the output format
• Look through the data in the old study to make the first few entries
• Expand personal spreadsheet to automate more stuff, like autocreating forum code output
• Create a (simplified) public version that people can use to collect their data while getting real time number updates
• I likely forgot something
• ???
• Profit!

Original opening post

Spoiler for Archived for completeness, and so people can make sense of the first pages of discussion:

A few weeks ago, CG asked me if I was interested in taking over the FGei study, I then replied I would think about it, but only after my exams. Since my exams are almost done now, I decided to make this post, so that people can give their input before I have done all the work

Besides managing the study, I was planning to first improve the fomulae/procedure, which is why I would like some input.

Things I plan to do:

• Making the FGei use turns to win instead of time to win.
• Updating the droprate to use the droprates for the individual gods.
• Disallowing skips during testing, using the data to figure out the gods that should be skipped.

Things I'm not sure about:

• Using an updated version of this, which uses not only the droprates per god, but also the droprates and values of the individual cards.
• Including turn to turns to lose numbers in the FGei stats.

Any objections or other critics, or any suggestions for improvements I forgot about are welcome.

Also, some discussion might be needed on the strategy used to determine what gods to skip after all the data are in.

Spoiler for Xenosim simulation numbers (200000 simulations per god):

God	Extra won	Extra per game
Akebono	125032819	625.16
Chaos Lord	90548400	452.74
Dark Matter	96430561	482.15
Decay	144238096	721.19
Destiny	105440040	527.2
Divine Glory	166270630	831.35
Dream Catcher	88154879	440.77
Elidnis	87814092	439.07
Eternal Phoenix	130711542	653.56
Ferox	104511820	522.56
Fire Queen	120121402	600.61
Gemini	116466436	582.33
Graviton	110247357	551.24
Hecate	128189945	640.95
Hermes	91454251	457.27
Incarnate	113644302	568.22
Jezebel	139587344	697.94
Lionheart	112147941	560.74
Miracle	91208340	456.04
Morte	89199889	446.00
Neptune	113289586	566.45
Obliterator	112587375	562.94
Octane	144100200	720.50
Osiris	129062000	645.31
Paradox	114020018	570.10
Rainbow	85640181	428.20
Scorpio	86554103	432.77
Seism	98122061	490.61
Serket	113748823	568.74

[ColorlessGreen]

As TD said, this is now the current official FGEI thread, under TD's management, and is the place for any current FGEI discussion/tests. The previous FGEI thread has been locked.

[Leodip]

Will your spreadsheet be also calculating skips agains FGs not worth it for the droprate? (take a look at the brave malignant ball that could topic to get my idea)

[Chapuz]

Skipped FGs can be calculated as a 1-turn lose. That's the most precise way to make it.
Also, the forum output can still be the average results (turns and FGEI) and a spoiler with the deck and the details for each FG.
I don't think the formula needs to be changed unless it's proved there's a more precise one or there's something new that the old one didn't consider.

[Leodip]

Skipped FGs can be calculated as a 1-turn lose. That's the most precise way to make it.
Also, the forum output can still be the average results (turns and FGEI) and a spoiler with the deck and the details for each FG.
I don't think the formula needs to be changed unless it's proved there's a more precise one or there's something new that the old one didn't consider.

I'm personally accounting for 2 seconds per skip, but only after getting the stats (I wouldn't want to alter the raw data from the tests, so I don't skip at all while testing).

BTW, posting this here in order to not forget. Link.

[the dictator]

Skipped FGs can be calculated as a 1-turn lose. That's the most precise way to make it.
Also, the forum output can still be the average results (turns and FGEI) and a spoiler with the deck and the details for each FG.
I don't think the formula needs to be changed unless it's proved there's a more precise one or there's something new that the old one didn't consider.

I will clarify the earlier post a bit more:

Things I plan to do:
Making the FGei use turns to win instead of time to win.
Currently (and historically), time to win (and lose), have been used to mark the speed of a deck in the FGei studies, and while accurate, this is very dependant on the tester (and the computer of the tester). Explanation by CG
Updating the droprate to use the droprates for the individual gods.
The different gods have vastly different droprates, because the the differences in their decks. Divine Glory has a deck with only a few cards, and lots of copies, while Rainbow has lots of different cards with relatively few copies, and as a result of that, Divine Glory drops nearly twice as many cards as Rainbow. Because of that, decks that win against DG while losing against rainbow will make more money than an equally fast deck that loses against DG and wins again Rainbow. The current study uses an (arbitrary) average number of 45% droprate for all gods.
Disallowing skips during testing, using the data to figure out the gods that should be skipped.
While skips are nice when you are farming, because of the speed at which you lose, it isn't accurate to do so when taking the data, therefore I would like to disallow skips during testing. That does however mean we need to come up with a procedure that uses the skipless testnumbers to calculate which gods should be skipped to maximize the FGei. Which is harder than it sounds btw: I played just over 500 skipless games with VDB, and while I can manually select gods to skip, and see if that improves the FGei, it comes pretty close to the testing randomness, one more win over 15 games can make the difference between skip or not skip in the final results. Of course there are some obvious skips (Chaos Lord, Dark Matter, Destiny, Lionheart, Osiris, Seism) that improve the FGei with over 200 each when skipped instead of played, there are also a few that improve the FGei by only 20. Which is where the subjectivity comes in: should Ferox, Graviton, Hecate, Octane .... be skipped because it improved the FGei (a bit), or should they be left out of the skip list, because RNG didn't favor them, as a result of which they got a slightly too low winrate, pushing them just over the tipping point. On top of THAT, the more gods you skip (and thus the higher you raise the TTW), the more profitable it becomes to skip more gods, especially if the time per skip is set very low.

Things I'm not sure about:
Using an updated version of this, which uses not only the droprates per god, but also the droprates and values of the individual cards.
This (outdated) calculation by kev and dark weaver, used the droprates per individual card, coupled with the individual sell values to come up spin income numbers even more accurate for each god. (Ex: Divine Glory gets another boost, because of the high spinrates of the rare cards in his deck).
Including turn to turns to lose numbers in the FGei stats.
Currently, the old study uses the time to lose as well as the time to win, which is fine, and accurate, though I'm not sure if I will continue that after switching from time to turns. The current UEI formulae (which is what the FGei should be, and likely will be, compared against), don't include turn to lose numbers, because CG wanted to remove as much human play style as possible: some people play a lost game until they are actually killed, while others quit as soon as it is clear they aren't going to win this match. Because of this, turns to lose (and the old time to lose), is much more subjective than turns to win, which means the person doing the testing gets to influence the FGei (aside from the obvious misplaying the deck).

I would like some input on these things, preferably before I have updated all the formulae

As a sidenote, since the new unit for 'time' will be 'turns', we would need to discuss how much turns a skip would take. I was thinking half a turn (5.4 seconds when using 333 turns/hour), which is what the old study used, but that does sound a bit high, considering that number was for use for actual skipped games for varying reasons, instead of theoretical skips based solely on the name of the FG you encountered. (It was also used for skips up to 1 minute in the game because of bad draws and stuff, at least, that is what Pella assumed when coming up with said numbers). Therefore, I think I'm going with a quarter of a turn, or 2.7 seconds (at 333 turns/hour, 3.6 seconds at 250/hour), on the other side, if we set a low time/turns per skip, it means skipping is quickly profitable, meaning lots of gods will be selected to be skipped.


Another option: instead of altering the formulae, would be to remake the whole formula from scratch, probably based on the UEI formula.
I was thinking: calculate the UEI for each individual god, weigh that by average TTW for that god, and average those results. The ones with the lowest individual FGei's should be the ones to skip (first), which means you could replace them with numbers resulting from skipping all matches.

[ColorlessGreen]

Disallowing skips during testing, using the data to figure out the gods that should be skipped.
While skips are nice when you are farming, because of the speed at which you lose, it isn't accurate to do so when taking the data, therefore I would like to disallow skips during testing. That does however mean we need to come up with a procedure that uses the skipless testnumbers to calculate which gods should be skipped to maximize the FGei. Which is harder than it sounds btw: I played just over 500 skipless games with VDB, and while I can manually select gods to skip, and see if that improves the FGei, it comes pretty close to the testing randomness, one more win over 15 games can make the difference between skip or not skip in the final results. Of course there are some obvious skips (Chaos Lord, Dark Matter, Destiny, Lionheart, Osiris, Seism) that improve the FGei with over 200 each when skipped instead of played, there are also a few that improve the FGei by only 20. Which is where the subjectivity comes in: should Ferox, Graviton, Hecate, Octane .... be skipped because it improved the FGei (a bit), or should they be left out of the skip list, because RNG didn't favor them, as a result of which they got a slightly too low winrate, pushing them just over the tipping point. On top of THAT, the more gods you skip (and thus the higher you raise the TTW), the more profitable it becomes to skip more gods, especially if the time per skip is set very low.

With regards to method for autocalcing ideal skips, we could add a column to the spreadsheet that, for each individual god, assumed the results for that god were skipped and recalc'd FGEI based on skipping that god and none of the others. The 1-skip FGEI could then be compared to the skip-nothing FGEI, and if it was higher, that god could be flagged as skip. Then a final with-skips FGEI could be calculated by skipping all FGs flagged skip by the algorithm.

I am obligated to mention the fact that I am very, very early in my morning cup of coffee, so I am very very possibly missing something huge in this algorithm, so please think about it in detail before assuming it'll work.

[Leodip]

If I may, this is my opinion on what should be done:
1.Consider single Gods' droprate, as I said in the link (even though it wasn't meant to help in this discussion) indeed says that farming Divine Glory would be much better than farming Rainbow;
2.Do not put a column in which to account for skips, this should be done manually, IMHO (more on this later)*;
3.Use turns instead of seconds, I thought this much was obvious;
4.Use both a default TPH and a personal TPH (more on this later)**;
5.Uniform TTW and TTL, I always was against the TTW-TTL stuff, simply average them and it should be fine (as long as you weight it) (and, if I may, I think that calling it TTF would be good to explain the change);
6.I'm okay with a quarter/fifth a turn for skips.

I kind of disliked the old FGei because of Time to lose and Time in general, but I feel I may like this one. And, well, I need money, so I could even do some tests when this'll be ready.
However, I've got a couple of things which shouldn't be hard to implement into the spreadsheed once it's ready but I think it'd be better to say now, if you think it is nice enough to be included:
*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.
**Another drop-down menu should offer two possibilities for TPH: the standard 333 and a personal one based on the TTW and TimeToWin (it simply is TTW*3600/TimeToWin). I know I said I wanted to drop TimeToWin, but in order to get a personal FGei it may be needed. This drop-down menu should offer the possibility to both calculate the official FGei to be posted online and a personal FGei to know, effectively, how much you can gain in an hour of playing.


Hope I was of help.

[rob77dp]

T(urns)TW instead of T(ime)TW - I agree here.  After some days reviewing/implementing UEI in my personal stat-sheets I think that approach is very good with a simple cell modify-able by the end-user for custom values (i.e. - you have a fast comp and use a non-trackpad mouse?  Set an override value to 400 TPH instead of the 'standard' 333).
TL;DR I agree that TURN based is superior for our 'ei' purposes.

Updating drop rates - I concur that drop rates per FG should be used.

Disallowing skips during testing - Until very recently, I used to be on the side of 'allow skips during testing because large sample sizes hopefully reduce this impact and it lowers inhibition of a tester not wanting to slog through skip-able FG matches'.  Now, I am firmly on the side agreeing with your stance not allowing test results into the study which had skips.  Non-testing, which is when users are grinding or in non-stat-taking-mode, obviously should allow each user to decide if they like using skips (this plays in to later comments I'll have in this post).
TL;DR I agree - do not include test data-runs that have skips in FGei calculation(s).

Updating drop rates per FG - Xenocidious' slot spin simulator is best for this.  Last I knew, results from that matched darkweaver's calculated values.  However, a couple hours spent now to input each FG deck and sim a TON (150,000 or more each FG) to prove or improve the current accepted drop rates is a good idea.
TL;DR Update drop rates.

Inclusion or exclusion of T(urns/ime)TL - Again, here I used to be certain that all time(turns) should be included.  However, further consideration has changed my opinion to exclusion of turns from losses.  The reasoning generally follows what you stated, td, about many players having varying "losing styles".  If there was developed a smooth and accurate way of a player indicating "loss type" in stat recording to implement into the FGei, then perhaps I may support inclusion.  That being stated, I would tend to be opposed to any method not considerably adding to accuracy that also puts up more roadblocks (read:  EFFORT by the tester ) to getting more testing completed by the community.
TL;DR Do not include TTL for calculations.

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.  I could see it being a factor still when a player wants to track their own efficiency where one is not 'restricted' from skipping.  For a long time now, my own methods have used 5 seconds for skips (until now I did time-based efficiencies (sp?)).  This relates to half-a-turn, and since it is being re-done with 'turn' base instead of 'time' there is no need to think about "how much time would this be if we still did time-based?".  Also, 'skipping' is basically taking your turn ignoring the coin toss and using it to "not have a turn".  This seems very fair to call 1/2 a turn.
TL;DR Use 0.5 turns for skips.