Walkthrough for deckstats and FGei calculationsCAUTION:
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Thus, Chicos case is a little outdated, however still shows the way to calculate it by Hand.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 deckChico 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 + ... / 24There 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/hChico 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/hAs 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 + WombatmanWhenever 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, PacoEven 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."
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.
