*Author

Offline JangooTopic starter

  • Sr. Member
  • ****
  • Posts: 877
  • Reputation Power: 0
  • Jangoo hides under a Cloak.
  • New to You
The FalseGod(deck)-efficiency-index (FGei) https://elementscommunity.org/forum/index.php?topic=14626.msg185669#msg185669
« on: October 27, 2010, 12:26:06 am »

CONTENT OF THREAD

POST1:   Introduction

POST2:   Walkthrough/Example for calculating FGeis manually

POST3:   STATMASTA™realtec (http://elementscommunity.org/forum/index.php/topic,21654.0.html)  Calculating stats automatically









INTRODUCTION


The Elements-community loves crafting decks and to statistically evaluate them:

What is the fastest Rush-deck? How many turns till kill on average? How high is the chance to draw a certain
card in your opening hand? How is the quanta-distribution and consumption? What's your per turn dmg by turn 5? ...

When it comes to FalseGod-decks it is usually all about the win-percentage:
A FG-deck is generally judged by how many games it statistically wins.
If it reaches the magical 40%, it is considered pretty good or even "as good as it gets".

Now of course the fun-factor plays a big role when farming FGs but most people do it to grind electrum for
their card-collection, it's called "farming" for a reason right?  ;)
While properly calculating win-percentages has already become a science, interestingly enough
the actual time it takes you to kill a FG with a certain deck is mostly expressed by rough guesstimates:
"It's pretty fast", "You don't have to click as much with this", "Stall-rainbow is too slow I find" ...

Here, I would like to introduce a second set of "stats" that will be very easy to keep track of and that will
lead to a reliable evaluation of a FG-decks actual farming-performance in the form of an index:


The FalseGod-efficiency-index (FGei)

The following stats are required to create an FGei for your deck:

Number of games
Number of games won, lost, EMed
Time played
Cards won*
god-by-god wins/losses**

All of these are very easy to keep track of and even the time has become easy since Zanz added the matchtimer
to the game. (It shows in the upper right corner of the slot-maschine screen if you won. If you lost,
you will have to click "details" to see your time in seconds.)
Personally, if weren't using the STATMASTA™ (see post3), I would just mark down the times per game in seconds in my notepad and add them all up when I am ready to calculate.
Any significant disturbances, like your grandma calling you about that cake for your birthday,
lead must not be taken down of course. Be wary though, not to consider every little
bit as "irregular disturbance": E.g., if you usually smoke while FG-farming, lighting up is part of your game-time.
Especially ingame-happenings are ALWAYS just what they are, so if you have to take e.g. 2min to calculate that
damage to see if you can still win this match ... so be it! 


With the above stats an FGei is very easy to calculate:

won game: +47 elec
lost game:  -30 elec
EM:             +120 elec
card won:   +1160 elec


-> Add and substract everything to create a net-profit-value.
-> Translate your game-time into hours. Caution! An hour has 60mins, so 30mins are not 0.3 hours but 0.5 hours, for example!
-> Divide your net-profit by your game-time in hours and you got yourself an

FGei(e) = net-profit/hour



-------------------------------------------------------------------------------------


FGei(e)  FGei(c)  FGei(n)  FGei-XXXⁿ


FGei(e)
The above example shows how you calculate your personal (e)mpirical FGei for a certain deck.
That of course includes a variety of very personal and situational factors, for example how many
"minor disturbances you had" that increased your game-time, if you maybe had a bad day and played
especially slow, if you only hit the damn Hermes for 20 games straight, but most important of all:
How lucky you got with the card-spins this time.
Therefore, the FGei(e) alone is not yet a very good index for evaluating a decks performance.


*FGei(c)
This is the "card-spin-normalized" FGei. It is still a personal-, that means one-player, index!
Zanzarino can see in his databank how big the card-spin rate against FGs is. That includes every game
played against FGs by everyone! I don't know if he can also see the spin-rate for a certain time-frame, but if
he does that would be awesome since it probably changed significantly with the introduction of short-decked
FGs. The last time I asked him, he said that the card-spin against FGs is 33%. (erm, late summer 2009 maybe?)
Currently, 35% is used since the card-win-rate seems to have gone up.

Now, card-spin-normalizing your FGei(e) to create an FGei(c) is very easy too:
You simply forget about the actual cards you won during your matches and assume, for example, the 35%
which the entire elements-community is supposedly statistically spinning.
Naturally, the through (c)-normalization mathematically assumed number of won cards will most likely be a fraction.
Needless to say that an FGei(c) is really saying something about a decks efficiency already.


**FGei(n)
This is the "FG-encounter-normalized" FGei. This is also still a personal-, that means one-player, index!
Now I am not very good at statistics but you know how even after 100 games with a deck you still see clearly
that you played ChaosLord and Hermes like 8 times whereas you played Neptune only once?

In order to create an FGei(n) you will have to normalize your FG encounters: Spread them out more "fairly" that is.

Since this is in itself already very surgical, the FGei(n) will most likely be paired with (c) to create an FGei(cn) right
away. Why keep the actual (e) card-spin rate after this? It's nice for knowing how insanely much cash you "would
have" won if it hadn't been for dumbass DreamCatcher who bashed you like 20 times, but other than that the pure FGei(n) is pretty useless here. ;)
The (n)-normalization will likely lead to fractions as assumed win-, loss- and EM-numbers.

When calculating stats by hand, normalizing the FG-encounters as such is the only option you got.

Note, that the STATMASTArealtec will also normalize your game-time. This means that the assumed evened number
of games against each FG also implies that especially lengthy/short games against certain gods get toned
down (or up) in your total game-time, if you have played this god more (or less) than average.



* **FGei(cn)
A sample of FG-games is card-spin-, and FG-encounter-normalized (see above) to create an FGei(cn).
Although this is still a personal index, because it includes only your win-rate, game-time and all the habits
that affect these, it has otherwise been statistically purified to a degree that it makes for an awesome
performance-index.


FGeiXXXⁿ(cn) = FGei
The ultimate performance-index!
You will have to merge your stats with as many other (clean) player-stats as possible to create a larger sample
that represents a diverse player-experience with a certain deck.
-> XXX        stands for the total number of games played to create this FGei
-> ⁿ             stands for the total number of players that have contributed to this FGei
-> c and n    may be added to the description if EVERY single contributing sample was indeed normalized correctly.
            Otherwise this FGei remains strictly (e)mpirical, which is really not bad if the total number of games and players is high.

-> An FGeiXXXⁿ that has more than 300 (?) games, 3 players (?) and has been c+n-normalized is so awesome that it
can be simply put as "FGei" whenever there is talk about this decks performance.
Just make sure the math behind it can somewhere in this forum be found,
in case someone is wondering if that FGei is really all that good ...  ;)


----------------------------------

Now I know all this may sound really complicated but it's actually not.
It just takes a while to explicitly write it down in a post like this, thats all.  ;)






Offline JangooTopic starter

  • Sr. Member
  • ****
  • Posts: 877
  • Reputation Power: 0
  • Jangoo hides under a Cloak.
  • New to You
Re: The FalseGod(deck)-efficiency-index (FGei) https://elementscommunity.org/forum/index.php?topic=14626.msg185680#msg185680
« Reply #1 on: October 27, 2010, 12:39:03 am »
Walkthrough for deckstats and FGei calculations

CAUTION:
Individual card-spin rates for each god (after winning a match), 47 electrum per win (default, you can also enter exact numbers), and 1160 electrum per card won
is being used to calculate FGeis in the recent STATMASTA™realtec (http://elementscommunity.org/forum/index.php/topic,21654.0.html).
This reflects ingame-reality by 99,9%.
The overall card-spin-rate against ALL GODS is on average 47%. Use this number if you really have to do the math by hand.
Thus, Chicos case is a little outdated, however still shows the way to calculate it by Hand.  ;)




The player Chico has created an awesome deck: His very own adaption of the RoL/Hope-deck!

What makes it so special is, that is has only 2 Electrocutors, five SoGs and an additional Archangel!
Chico names his deck "Chico-RoL/Hope-deck" and creates a thread for it so that everybody can profit from
this innovation and comment on it.
Soon, people start commenting and while the feedback is mostly positive, some players seem doubtful:
Does that Archangel really make any sense? Is the win-percentage as high as unionrulers deck gets? Won't
all the SoGs only slow down the matches? ...


1. Chico figures out the basic stats of his deck

Chico decides to take some stats on the deck and opens his word-pad while he plays it.
He carefully notes the time he has needed for each game, all the wins, losses, EMs and he marks
the wins and losses for each god seperately. He also bumps his "card-counter" by one every time he
spins a card. (YAAAY!)
After one week of playing the deck for a couple hours or so each day he counts his matches and decides that
90 matches are enough to calculate some meaningful statistics for the Chico-RoL/Hope-deck.

Here is what he has got:

90 games
35 wins (25 EMs)
55 losses
God by God-breakdown for wins/losses
10.5 hours played
14 cards won

These stats yield Chico the following statistical factsheet for his deck:

35wins/90games = 38.9% win-rate
25EMs/35wins     = 71.4% EM-rate
10.5h x 60min/90games = 7min/match (interesting side-stat)

"Nice winrate", he thinks and "Awesome! 71% EM-rate!" but then he wonders how that proves anything to those
people who were claiming his SoGs would slow down the deck waaay too much. Sure his EM-rate rocks but he also
remembers that some games were taking forever to finally win them.
He thinks to himself that those numbers really don't go very deep, at least not when he wants to convince people
that his deck is suited for effective electrum-grinding against the FGs.


2. Chico calculates an FGei(e) for his deck.

So he proceeds to calculate an FGei for his deck by starting with his profits:

25 EMs = 25 x 120 electrum won = +3000 elec
10 wins = 10 x 45 electrum won = +450 elec
55 losses = 55 x 30 electrum lost = -1650 elec
14 cards won =    14 x 1150         = +16100 elec
In Sum                                          = 17900 electrum net-profit !

He knows he has played for 10.5 hours over several days, so he divides his profit by this number:

17900elec/10.5h = 1704 elec/h = FGei(e)

Because this is really only Chicos personal experience and FG-encounters and card-spin-rate have not been
normalized yet, he only has an empirical FGei(e) for now, an FGei that reflects his particular series.


3. Chico wants to know his decks FGei(c)

Chico knows that the statistical card-spin-rate for everybody is 33%, Zanz said so.
(EDIT: Yes, in 2010 perhaps. As of now, this number is: 47%. Once again: Better use the Statmasta anyways ;) )
So he decides to calculate a more meaningful FGei: the FGei(c).

When he calculates his own card-spin-rate ... 14cards/35wins = 0.4 = 40% ... he discovers that he was
actually pretty lucky during his 90 games. Who would have guessed that? Seemed like he was constantly
not getting the upped cards he deserved!

With an assumed spin-rate of 33%, Chico would have only won 0.33 x  35 won games = 11.55 cards.
So his profit calculation would look like this:

25 EMs = 25 x 120 electrum won = +3000 elec
10 wins = 10 x 45 electrum won = +450 elec
55 losses = 55 x 30 electrum lost = -1650 elec
11.55 cards won = 11.55 x 1150  = +13280 elec
In Sum                                          = 15080 electrum net-profit !

Which then turns out to be Chicos FGei(c) as follows:

15080elec/10.5h = 1436 elec/h = FGei(c)

Although he is a little bit dissappointed about the drop in value now, Chico is happy that he now has an
index with which he can actually advertise his deck and tell those people in his thread, that his SoG-deck
is not so slow after all. 1436 electrum per hour is a fine profit indeed!


4. Chico finds out about his decks FGei(n) and FGei(cn)

By now Chico has gotten the hang of the whole deck-statistic thing ... When he was playing his 90 games,
he was bashing Divine Glory 10 times and lost horribly to Hermes ... 8 times! Damn Graviton and Rainbow
also scored a pretty high number of victories against him.
Chico knows that this is not very representative for his decks general performance and hence wants to
normalize his encounters against the FGs to create an FGei(n) first, then even an FGei(cn)!

To normalize your win-rate, you basically calculate 24 win-rates (for each individual god) first.
Then you add those 24 win-rates and divide them by 24 again:

norm-win-rate = win-rate1 + win-rate2 + ... / 24

There are also an awesome couple posts that show how to do it ... right after the next post, here in this thread.
It turns out that while Chico certainly profited way too much from Glorys (and some other gods) presence, Hermes,
Graviton and Rainbow brought down his win-rate much more than they would have, if he had met them
a normal amount of matches and not like 8 times each!

Chicos FGei(n) is therefore calculated with an assumed higher number of wins than his 35: 40wins! (hypothetical)
Now this changes Chicos profit-calculation completely since more wins would also mean more electrum through
wins, EMs and of course cards!


40wins x 0.714 EM-rate = 28.56 EMs                 = +3427elec
40 - 28.56                      = 11.44 wins (regular) =  +515 elec
90 - 40                           = 50 losses                  =  -1500 elec
40 x 0.4 (card-spin)       = 16 cards won          = 18400 elec
                                       In Sum:                       = 20842 net-profit!

Chicos FGei(n) is therefore a roaring 20842/10.5 = 1985 elec/h = FGei(n)

Marked in red, this index is still assuming, Chico would have kept up his 40% card-spin rate.
At this point (after having normalized the complete battle-lineup) it is totally pointless to hold on to this thought
of actually winning more than one normally would. Chico accepts that the pure FGei(n) is merely a mathematical
steppingstone and is smiling about "what would have been if".
He then proceeds to recalculate his FGei(c) with the new (n)ormalized number of wins and losses,
hence finally finding out about his FGei(cn):

28.56 EM income (n)
+ 11.44 wins income (n)
- 50 losses deficit (n)
+ 40wins x 0.33 (norm.cardspin) x 1150elec (c) 
= 17622elec net-profit

-> 17622/10.5h = FGei(cn) = 1678 elec/h

Chico is more than happy now: Not only is his number back up again, it is finally also a number that really and
absolutely quantifies his decks performance as played by him in those 90 games.
Of course he could play even more games to stabilize this FGei-value but apart from that, there is nothing
Chico could further do on the statistics side to create a more reliable index.


5. FGeiXXXⁿ: Other players ask Chico to integrate their stats on his deck into his index.
 
Some weeks pass and after wondering what the hell those weird FGei-numbers Chico has posted with his deck
 were, some other players finally found out about it: "Awesome, an index that actually tells you how effective a deck is! ... "
Two of those players grew extremely curious about Chicos deck because after flipping some numbers in their
head ~1700 FGei(cn) seemed awfully high to them: "Hell, that must be a pretty damn good grinding-deck!" 
So they went ahead, bought the deck and started grinding with it. Naturally curious if they would actually meet
that so-called "reliable index" themselves, they started taking stats themselves.

One of them, Paco1987, only hit a very low FGei(e) although having about the same win-rate as Chico
and the other, Wombatman, got a much higher FGei(e) while having a lower win-rate.
They got a little mad and accused Chico of cheating.
Chico explained to them that these indizes are more likely to express something else:
Paco1987 was most likely playing slower than Chico and got a bit unlucky with the slots.
And Wombatman certainly had some luck with the slots and/or just speed-busted through the FGs.

Either way, they decide to take no risks and start their calculation from scratch:

Chico (cn-Status): 90 games, 40 won (28.56 EM), 50 lost, 13.2 cards won, 10.5h played, Godbreakdown
Paco1987 (c-Status): 140 games, 55 won (10 EM), 85 lost, ?? cards won, 25h played, no Godbreakdown
Wombatman ("cn-Status"): 50 games, 16 won (0 EM), 34 lost, 7 cards won, 3.75h played, Godbreakdown


Now the problem arises that Chico and Wombatman have everything it would take to recalculate everything
for a joint FGeiXXXⁿ(cn), Paco however forgot how many cards he won and didn't put down his god-by-god breakdown.
The cards-stats are not crucial (Paco just can't really get his FGei(e), however he calculated it before ... noob)
but for getting an FGei(n), the missing god-stats are indeed crucial.
They still decide to take Pacos stats into the index, simply because he brings a whuppin 140 games to the table,
which will make the whole index much more reliable even if it will have to be (c)-status.
After all: The best way to "normalize" your FG-encounters is really by actually playing many more games, not by
recalculating how many times you "should" have fought/won/lost against each god.

Chico and Wombat will still bring their (cn)-stats into the index by first throwing all their raw, unnormalized (e) stats together and then normalizing the FG-encounters as well as card-spins for their whole joint-segment (90+50 games).
Their combined win, loss, EM values will then most likely be fractions again (as they are already in the example
for Chico). 

After the three are done with integrating all the stats, they wind up with:

280 games played
39.25h played
114.3 won                     -> +3424elec (76.1 regular wins)
(38.2 EM)                       =  +4584 elec
165.7 lost                      =   -4971elec
37.7 cards won              =  +43377elec
In Sum:                          =  46414 net-profit

Win-rate:    40,82%
EM-rate:      33,42%
cardwin:      [33%]
min/game:   8,42

FGei280³(c) = 1182 elec/h


As of now, there is a small variety of indizes available to evaluate Chicos deck:

- FGei280³(c)
No doubt this index has been influenced by just about anything you could imagine:
-> a noob who couldn't have possibly played slower
-> a progamer who carelessly ripped through the timeframe while jeopardizing win- and EM-rate
-> a deck-creator who probably made the best of it
-> a 140 games with "unnormal" god-encounters possibly unaccounted for
-> a 140 games that have been carefully normalized
Sure, it's still not the most pure and untainted index possible but it beats a totally relative "my deck has a
60% win-rate" -> "how many games have you played?" -> "dunno, maybe like 30" ... doesn't it?

- FGei(cn): Chico + Wombatman
Whenever the next best "60%"-guy thinks that an FGei of ~1200 is too low, Chico can always provide his
personal FGei(cn) of 1680 to show what he, the deck creator, can do with the deck.
While the FGei280 serves as a realistic orientation what this deck "generally" can do, peak performance
remains with the most skilled of course. Wombats FGei(cn) is also somewhere out there and should probably
be posted in the deck thread to see what a seasoned player like him makes of the deck.

- FGei(e): Chico + Wombat |  FGei(c): Chico, Wombat, Paco
Even though the indizes above are much better, it is still nice to see what really, actually happened during
the matches. These indizes were ridiculously easy to calculate and still say a ton more than just win-percentages.
They might also be required by a certain trait of people: "You can't just do your math-witchcraft and then claim
that the deck is good." Chico: "Aah no? Well, then just take my plain and simple electrum/hour-index as it actually happened."  :P
Unfortunately, since Paco failed to take stats for the individual FGs and to count his cards, his FGei(c) is the
only personal FGei he has got. It can still be of great use to other players:
E.g., a new player may not expect to play Chicos deck as good as Chico himself plays it ...
expecting those 1680 electrum to roll in every hour would probably just lead to frustration.
Now Paco, being a new and veeeery slow player, has got an FGei(c) of 753. He is definitely the reason why the
FGei280 turned out to be so low but hey: He was playing the deck for 140 games, he gave his best ... end of story.
Looking at those two numbers 753 - 1680 clarifies the range this deck has, depending on personal player
performance. The said new player looking for a good FG-deck will be happy to have those numbers as an
orientation.  ;)



Offline JangooTopic starter

  • Sr. Member
  • ****
  • Posts: 877
  • Reputation Power: 0
  • Jangoo hides under a Cloak.
  • New to You
Re: The FalseGod(deck)-efficiency-index (FGei) https://elementscommunity.org/forum/index.php?topic=14626.msg185682#msg185682
« Reply #2 on: October 27, 2010, 12:39:30 am »

STATMASTA™realtec (http://elementscommunity.org/forum/index.php/topic,21654.0.html)

Calculating stats automatically



The STATMASTA™realtec is an OpenOffice-file which will ease the pains of taking
comprehensive stats when playing against FalseGods with a specific FG-deck.

The good news:

It will calculate tons of stats, including all FGeis and score/h, for you!
It does include the more complicated background-calculations like normalizing game-time
when calculating an FGei(cn) or tracing your electrum-gain back to average HPs left in regular wins.

All you have to do is enter your individual games, the time needed to play them and
(only if you feel like being scientific) your electrum won in regular wins.



Check out the STATMASTA™realtec - thread (http://elementscommunity.org/forum/index.php/topic,21654.0.html) to read more and for the download.










Krahhl

  • Guest
Re: The FalseGod(deck)-efficiency-index (FGei) https://elementscommunity.org/forum/index.php?topic=14626.msg185759#msg185759
« Reply #3 on: October 27, 2010, 02:01:43 am »
FGei(n)
This is the "FG-encounter-normalized" FGei. This is also still a personal-, that means one-player, index!
Now I am not very good at statistics but you know how even after 100 games with a deck you still see clearly
that you played ChaosLord and Hermes like 8 times whereas you played Neptune only once?
In order to create an FGei(n) you will have to normalize your FG encounters.
(Can somebody please post how this would be done properly?)
Basically, you should meet each of the 24 gods once in 24 games. However, due to probability, this is not the case. So instead, you normalize the statistics.

Take your average win rate for each god and add them all together, then divide by 24. This sets your numbers as if you had met every god an equal number of times.

Ex. You face Osiris 10 times with 9 wins and Ferox twice with one win. Your total win percentage would be 10/12, or about 83%. Broken down, you have a 90% win rate against Osiris and a 50% win rate against Ferox. Your normalized win rate would be 70%. Of course, this requires at least one game against every god to work.

However, it works much better with larger samples. If you only face Paradox once in 100 games and lose, then your normalized stats assume that you will lose every single game against Paradox. It's good to get at least 10 games against each god for a more accurate percentage.

Offline JangooTopic starter

  • Sr. Member
  • ****
  • Posts: 877
  • Reputation Power: 0
  • Jangoo hides under a Cloak.
  • New to You
Re: The FalseGod(deck)-efficiency-index (FGei) https://elementscommunity.org/forum/index.php?topic=14626.msg185934#msg185934
« Reply #4 on: October 27, 2010, 07:25:32 am »

Lol ok. Thats really just how I imagined it to be ... one way to do it at least. (see below)

In your example of 10/12 (83%) games won, I would have my stats normalized to

4.2 won/6 VS Osiris
4.2 won/6 VS Ferox
----
8,4/12 won = 70%, which happens to be the middleground between 90% and 50%, awesome.



Example2 (from the Walkthrough):
you meet ~75% the gods your deck ain't made for and only ~25% the ones that rock for you:

10 won DivineGlory -> 100%
8 lost Hermes        ->0%
7 lost Rainbow       ->0%
7 lost Graviton       ->0%
----
10/32 won             = 31.25 win%,
normalized win-rate  :25%, right? 


So we got ourselves:

2/8 won DG
2/8         Herm
2/8         Rainb.
2/8         Grav.
----
8/32 won = 25%       --> the three stooges drag the glory-case down and simulate that loosing more often
                                       is the case: 2 games less in your favour!


Example 2b
two other average gods are in the mix

10/0 DG
0/8 Herm
0/7 Rain
0/7 Grav
2/0 Miracle
2/2 Gayoslord
--------
14/38 won     = 36,8%
normalized:     42%


So:

2.66/6.33 won DG
2.66/6.33 Herm
.
.
.
.
------
16/38 won    =42%           --> slight increase cause non-heavy weight Miracle simulates 100% rates



Is that how it's supposed to work? Distributing everyones games AND winrates equally?
Are there yet other methods of normalizing? How about something like mulligan:
Any matches that are too far from the known average will just be canceled out?
That way a 2:1 of e.g. bad-FGS wouldn't drag down the rest of the stats and vice versa.


Krahhl

  • Guest
Re: The FalseGod(deck)-efficiency-index (FGei) https://elementscommunity.org/forum/index.php?topic=14626.msg185950#msg185950
« Reply #5 on: October 27, 2010, 08:50:44 am »
You aren't distributing wins evenly among all the gods. You are equalizing the weight of each average.

From your example, you have a total of 32 games. Since 10 of them are against Divine Glory, his games carry 10/32 of the weight. In other words, they make up a larger portion of your unnormalized percentage. However, Graviton games only count for 7/32 of your percentage.

To normalize it, you take all games against the same god and make it a single stat, so you have four stats, each of which weighs for 1/4 of your percentage. So 10/32, 0/32, 0/32, 0/32 gives you 31.25%, which you change to (10/10=)100%, (0/8=)0%, (0/7=)0%, (0/7=)0%, for a normalized win rate of 25%. It doesn't mean you won 25% of the time against each god; it means you won 100% of the time against one god and 0% of the time against the other three.

For example 2b, you simply add Miracle (2/2=100%) and Chaos Lord (2/4=50%) to get 100%, 0%, 0%, 0%, 100%, 50%, which averages to around 42%.

As for nullifying outliers, that's just not a good idea. Taking the example from my previous post, that you play one game against Paradox in 100 FG games and lose, your win rate is 0%. Weighted, this would only be 1/100 of your total percent, which isn't a big deal. But normalized, it's 1/24 of your percent, much larger. However, if you pretend you didn't play that game, you basically don't have any statistics to work with for Paradox. That's the same as never facing him. That isn't the case though. The best way to get the most accurate sample is just to take a large one: play lots of games.

Offline JangooTopic starter

  • Sr. Member
  • ****
  • Posts: 877
  • Reputation Power: 0
  • Jangoo hides under a Cloak.
  • New to You
Re: The FalseGod(deck)-efficiency-index (FGei) https://elementscommunity.org/forum/index.php?topic=14626.msg185985#msg185985
« Reply #6 on: October 27, 2010, 10:16:06 am »


Allright then. I understood the following:

1. I have made the calculations in examples 2 and 2b correctly ... that is how you would calculate it.
2. There is no other way to "normalize" stats like this, because that is what it per definition is ...
3. "Normalizing" isn't exactly suited for small sample-sizes.

Correct?


So here are some more questions:

1. Is there maybe another process of tuning the stats to represent more "reality"/larger sample sizes? ...
maybe it's called "equalizing", "parameter-curve-fitting" or whatever ...?

2. Of course a larger sample-size "would be nice" ... but in most elements-cases that is just not going to happen:
Playing 100 games while strictly keeping stats with a deck can already be quite a drain, getting other people to
do it (properly) is almost impossible. So being able to deal with around 100 matches is just about a requirement here because nobody is going to play 240games just to (still not) get those 10 matches per god.
I assume flawed "normalization" gets less and less the larger the sample size gets ... a sample the size of
[close to infinity] would be so evenly distributed that a normalization wouldn't even make any difference at all.

Question:
Is there a range/sample size which mathematics would typically require to even start with normalizing in a case like
this? Now I am not talking about your college professor who would probably normalize his dogs paws just
because he can... I am picturing rather more practical people, say, market-researchers.

In the above, rather extreme, examples the shift through normalization is 2 matches out of 32/38 in both cases ...
in either direction.
-> Extrapolating this for my example with Chico in the 2nd OP, that would imply a possible one-directional shift of
up to 6 matches out of 90 Chico has played. (So my assumed 5 weren't all that bad a guess it seems.)
-> With a normalized cardspin-rate of 33%, this would mean winning 2 more/or less cards during those 90 games.
-> Which finally amounts to roughly 2 x 1150 = 2300 electrum, which then again amounts to a
shift of about 220elec/h for the FGei(cn)-value in this particular example with Chico.

220 is quite a lot ... Chicos FGei-values have been shifting back and forth between 1400 and 1900 during the process due to various variables being taken into account, or not.
But when considering that these 220 are only maybe illfated and one-directional (due to a very odd series
of FG-encounters that screwed up the normalization) but most likely won't even happen because a shift in
one direction gets canceled out by another one in the other direction ... well then it doesnt seem all that bad and
normalization is definitely an option for samples of about 100 games.

Question:
Am I missing something in this reasoning? something like: "no, no, no ... take for example ... you would have a
shift of 15! matches out of 100 just like that."
Is there any way to generally express an "expected" shift for normalizations of such small sample-sizes? (100)




Krahhl

  • Guest
Re: The FalseGod(deck)-efficiency-index (FGei) https://elementscommunity.org/forum/index.php?topic=14626.msg186043#msg186043
« Reply #7 on: October 27, 2010, 12:52:32 pm »
Allright then. I understood the following:

1. I have made the calculations in examples 2 and 2b correctly ... that is how you would calculate it.
2. There is no other way to "normalize" stats like this, because that is what it per definition is ...
3. "Normalizing" isn't exactly suited for small sample-sizes.

Correct?
1. I'm not sure exactly how you did your calculations, but we came to the same numbers, so it is correct.
2. Yes. The definition of normalization as we use it with statistics is basically to put them on a common scale. In this case, the win rate against each god is written as a percent, all of which are averaged to get a total percent.
3. Correct.

1. Is there maybe another process of tuning the stats to represent more "reality"/larger sample sizes? ...
maybe it's called "equalizing", "parameter-curve-fitting" or whatever ...?
Perhaps there are other methods, but normalization is what I'm familiar with as far as Elements decks are concerned. A small sample just only gives so much data; there will be oddities no matter how you use it to represent a larger sample.

If you are 0/1 against Paradox, your win rate is 0%. There just isn't any other number to go by. If you were to guess how many games you would win in the next 10 against Paradox, the only number the data allows you to guess is 0. Personal experience may say otherwise, but the solid data doesn't give anything else.

2. Of course a larger sample-size "would be nice" ... but in most elements-cases that is just not going to happen:
Playing 100 games while strictly keeping stats with a deck can already be quite a drain, getting other people to
do it (properly) is almost impossible. So being able to deal with around 100 matches is just about a requirement here because nobody is going to play 240games just to (still not) get those 10 matches per god.
I assume flawed "normalization" gets less and less the larger the sample size gets ... a sample the size of
[close to infinity] would be so evenly distributed that a normalization wouldn't even make any difference at all.
Of course while a larger sample size is more reliable, it is not practical to take. But if you use that deck as your FG deck and take stats while grinding, you may end up with more numbers than you expect. Other people can test as well. Your assumption about a near infinite size sample is correct.

Question:
Is there a range/sample size which mathematics would typically require to even start with normalizing in a case like
this? Now I am not talking about your college professor who would probably normalize his dogs paws just
because he can... I am picturing rather more practical people, say, market-researchers.
I'm not sure about a mathematically accurate yet practical sample size, but three matches per god is probably enough to give a reasonable estimate, assuming no extreme luck factors. In a 100 match sample, you should average a bit over four matches per god, so it's not extremely difficult.

In the above, rather extreme, examples the shift through normalization is 2 matches out of 32/38 in both cases ...
in either direction.
-> Extrapolating this for my example with Chico in the 2nd OP, that would imply a possible one-directional shift of
up to 6 matches out of 90 Chico has played. (So my assumed 5 weren't all that bad a guess it seems.)
-> With a normalized cardspin-rate of 33%, this would mean winning 2 more/or less cards during those 90 games.
-> Which finally amounts to roughly 2 x 1150 = 2300 electrum, which then again amounts to a
shift of about 220elec/h for the FGei(cn)-value in this particular example with Chico.

220 is quite a lot ... Chicos FGei-values have been shifting back and forth between 1400 and 1900 during the process due to various variables being taken into account, or not.
But when considering that these 220 are only maybe illfated and one-directional (due to a very odd series
of FG-encounters that screwed up the normalization) but most likely won't even happen because a shift in
one direction gets canceled out by another one in the other direction ... well then it doesnt seem all that bad and
normalization is definitely an option for samples of about 100 games.
Yes.

Question:
Am I missing something in this reasoning? something like: "no, no, no ... take for example ... you would have a
shift of 15! matches out of 100 just like that."
Is there any way to generally express an "expected" shift for normalizations of such small sample-sizes? (100)
Well it really depends on your luck. If you play 10 games against some gods and 0 against others, your normalized stat will obviously have a much larger shifting range than if you had played 4 or 5 games against every god.

Offline JangooTopic starter

  • Sr. Member
  • ****
  • Posts: 877
  • Reputation Power: 0
  • Jangoo hides under a Cloak.
  • New to You
Re: The FalseGod(deck)-efficiency-index (FGei) https://elementscommunity.org/forum/index.php?topic=14626.msg191197#msg191197
« Reply #8 on: November 02, 2010, 11:26:02 am »


Oh ... you clandestinely just edited your post. :))

Thanks for your help Krahhl.

Now that we seem to have all the normalization-math problems sorted out I'd have one last question for you:

How do you like the idea as such?


Krahhl

  • Guest
Re: The FalseGod(deck)-efficiency-index (FGei) https://elementscommunity.org/forum/index.php?topic=14626.msg191299#msg191299
« Reply #9 on: November 02, 2010, 03:14:05 pm »
Ah sorry, I failed to remember that you wouldn't have any way of knowing I had edited without actually looking at the thread.

I think this is a great way to figure out the electrum gain of decks for those who don't care about score. Taking time into account makes for a much more accurate calculation of efficiency, rather than just pure win rate.

Offline nerd1

  • Hero Member
  • *****
  • Posts: 1137
  • Country: us
  • Reputation Power: 15
  • nerd1 is a Blue Crawler starting to think about his first run.nerd1 is a Blue Crawler starting to think about his first run.nerd1 is a Blue Crawler starting to think about his first run.
  • kind of active
Re: The FalseGod(deck)-efficiency-index (FGei) https://elementscommunity.org/forum/index.php?topic=14626.msg215275#msg215275
« Reply #10 on: December 02, 2010, 11:42:23 pm »
this is the single most in-depth study on how to decide how good your fg grinder deck really is gratz.
+karma
The laziest elements player this side of one thousand posts.

kirchj33

  • Guest
Re: The FalseGod(deck)-efficiency-index (FGei) https://elementscommunity.org/forum/index.php?topic=14626.msg268225#msg268225
« Reply #11 on: February 10, 2011, 06:27:14 pm »
This is a really great post and I have a few questions:

It seems to have been awhile since this was posted on or used, but I'm in the midst of a Shakar's study and would like to add to the data already posted for that deck and would like to move onto a FG farming study afterwards, which will utilize FGei as well.

1.  Does the FGei differentiate between both rare and regular upped cards won in terms of electrum (I have been documenting both)?

2.  Did the original FGei account for bonus 5 electrum spins or was this around when it was posted (I have not been documenting this)?

3.  Is the spin rate for cards won vs. false gods still considered to be 33% (I saw some data using 35%)?

Anyone that could help answer these questions would be helpful.  I appreciate it!

 

blarg: