Unified Efficiency Index - How to compare apples to oranges

[Silux]

i managed to get a pretty precise estimation of how much turns last in milliseconds and i'm testing differences between a pc old 8years and a brand new machine.
I tested also with different network speeds, but it doesn't matter, as long as you aren't playing the arena.

In the arena the delay you have to wait to deck to load is just the ping time +10ms.
Ping time is around 200ms with my network.It's significant in long runs, but no deck could even shorten this time.

I found AI takes an average of 500ms more on the old pc, but the interface is responds with nearly the same time whether you are playing with an old or a new pc(300ms is the threesold which faster clicks are ignored).

I tried to find exactly haw much time the ai takes to pass the turn, but it seems to take a constant time to play the cards, plus some time to let the player to see the effects.Each effect last at roughly 500ms.

So if you want to know how much a turn takes in ms (avg_number_of_clicks*300)+5000+500*(is_a_really_old_pc)
avg_number_of_click=(7,5+TTW+number_of_clicks_for_abilities)/TTW
is_a_really_old_pc=1 if your pc usually lags, 0 otherwise

[Leodip]

Uhh, where should I start from? I think that calculating in ms SHOULDN'T be done. I'll be freely using some mathematic terms cause I think you know them well enough. Let's start:
1.The basic formula uses a whole lot of approximations, this itself defies the purpose of using more precise calculations in the least interesting matters of the formula itself, but let's just ditch this because you could simply answer that this is in order to make the formula itself more precise;
2.Let's say that we're using your formula, the time of the animations will greatly vary when you're using a deck with 6 hourglasses, 6 precognition, 6 golden nymphs, 12 time pillars, 6 silence, mark of aether (simple example) because the animation for the draw is crazily long and a simple immorush, and even the opponent matters, if it is a 30-pillar deck or the aforementioned time deck;
3.You're calculating the particulars too much, but you aren't calculating the time from one game and another, while you're calculating the time for the software to load the opponent's deck.

TL;DR, this isn't worth it, and maybe is too advanced for something like this. I appreciate your hard work, though, because it is good material for additional studies.

[Silux]

i agree that there are too details, but since the time is deterministic, it can be calculated.
Anyway with knowledge about how much time an ability require, you can compare complex control decks to mindless rushes.

I just used the web debugger to get these info, so no sweat:)

[Leodip]

Hmm, I was wondering, for Arena, would accounting the multipliers for the top10 be relevant for the outcome? I don't know the exact multipliers (the only ones I found aren't accurate apparently), but probably it would modify the value per win by just the 3%. Still, I don't know exactly the result, if it's worth it, and if it will show in the long run. Still, it'd just be a change to the set value, it's not that hard to modify. If I can find the values for the multipliers, I'll post them here.

[Silux]

there is bonus gain for beating a deck in the top 10 of the arena?

[Leodip]

Yeah, never seen decks who EM'd a deck in the arena in plat and gettin' 3000 or so electrums?

[CuCN]

You would have to consider that the chance to win against a top 10 deck is different from the chance for other decks.

[ColorlessGreen]

For what it's worth, my opinion on the subject of top-ten arena decks is the same as my opinion on the subject of arena decks that are non-biting rare/nymph farms and my opinion on the subject of arena decks that are at 1 hp:

Nice boost if you get it, far too inconsistent to factor in.


Considering that top ten decks are 2% of games, and as noted by CuCN, these decks are presumably in the top ten because they have a much higher chance of winning (so that even though they provide a boost when you win, you don't necessarily have a much greater expected profit at the start of the match), and considering that there's no way you can plan ahead for "top ten decks" by building a deck specifically designed to target them, I would just consider this to have the effect of yet another rounding error.

All that being said, anyone who can come up with a convincing argument on how to account for them will definitely have my attention.

[Leodip]

Most of the times in the top there are 1 HP decks because the day before they were about 65 or less, yesterday I happened to meet two of them while testing a deck in gold (lucky ^^), both at really low HPs, and won against both, that's why I wanted to account that. What's more, it's not like they're decks built by superhumans, simply they had a giant MU against the main decks used to farm, that's why using an unused deck I could kill them, it wasn't expected.The best way, probably, to account them is to make an average of the rewards, something like: [average electrums per win of first deck+average electrums per win of second deck+...+average electrums per win of tenth deck (IIRC, though, the tenth deck doesn't have multipliers on it, but let's just say it has till we can get our hands on the real values of the multipliers)+(average reward of regular wins*490)]/500.
The problem is that it'll increase, even if by only a little, your electrums per hour, but if you get two of them like I did, it'd be awesomely off. Oh well, that's the problem of calculating the UEI of the Arena in general, it has too many random factors.

[Silux]

arena decks change day to day.
A way to account for all this randomness is considering also standard deviation when considering stats of a deck in the arena.
While AI3 grinders usually have a s.d. of 1.5 turns on TTW, arena decks have often a s.d. of 5.5 or more, because hp aren't the same for all decks.
UEI will be something like 4500 ± 1500  / hour and both if you score 3000 or 6000 you are in the predicted UEI range.

[ColorlessGreen]

Note that pretty much everything I'm saying in the first part of post is a worst case scenario and any actual effects are probably significantly less.

If you take pdials in gold, which is the most exaggerated place where arena reward matters (and includes extra max hp from pdials and such) and you multiply the stated reward value by 1.06 (which is the average of the reward of all ranks of arena according to an estimated table by RootRanger I found somewhere (which I have no idea if it is actually accurate or not, but still)), it modifies the UEI from 8626.19 to 8845.84, or a 2.5% increase. Chaos Wyrms in gold changes from 6809.24 to 6952.35, a 2.1% increase (which is probably a more typical result, as few decks other than pdials are built for high maxHP EMs).

Note that the 1.06 factor when applied to the stated reward is less than the variation in the stated reward itself, so this change instantly becomes useless if you aren't updating the stated reward every day. When using the approximate value of 120 that I personally use as a rough average of gold, accounting for top ranked decks changes that value of 120 to 127.2.

If you factor in the presumption of a lower win rate against higher ranked decks (which IMO is a pretty safe assumption), those seven extra electrum shrink down even further.


I do not want to add extra reward from arena into the formula unless we can account for the win rate change, as I firmly do not believe that just averaging the reward from all 500 slots is representative of the actual rewards which come from arena, and we need to weight the average in some way that accounts for the lower odds of winning against the top tier decks. The end result of such a study is going to be a very minor change in arena stats as shown above.

With all that being said, I am willing to bet that some weighting could be done through surveying the win rates of the arena decks on the arena leaderboards screens and comparing the win rates of top ten decks with other decks of the same age in the same arena at the same time. Not 100% sure where we'd go from there, but my current instinct is something like taking the bonus reward and dividing by the amount better than an average non-top-ten deck the top-ten deck's win rate is. I don't think I'm going to be doing that particular bit of data mining at the moment due to my time being limited and my considering the change to be so minimal that it's going to effectively be lost in the noise, but anyone else who wants to do so is welcome to it, and if we come to a satisfactory conclusion, I'll put it in the Stated Value section of the OP. This would not involve changing the actual UEI formula in any way - it can be accounted for by multiplying the SV for a given arena league by X (with X being the factor we get to through the study mentioned above, or X being 1.06 if you don't account for win rates).

[rob77dp]

Necro!!  (I see you, big red warning box... and I continue on!)

I used the Xeno Slot Simulator to calculate 'TSP' for AI2 decks as posted by majofa in All AI2 Decks (new) an old-ish but seemingly still accurate post.
Note:  150,000 simulations per deck were completed.

I realize AI2 TSP may not be too valuable, but for minimal (30 minutes, approx) effort we can now have even better stats (UEI) for the AI2 stats thread some are collaborating on here.

TSP_AI2=13.325833 extra from slots per win (this is supposedly inclusive of the +5 bump for 2-match occurrences)

-snip-

So, here's the bare bones of the formula from above all in one place:
*code tage removed to allow pink-bold font*
Turns Per Hour ("TPH") = 333
Win Rate ("WR") = Wins/(Wins + Losses)
Loss Rate ("LR") = 1 - WR
Turns Per Win ("TPW") = Turns To Win ("TTW") / WR
EM Rate ("EMR") = EMs / Wins
Win Value ("WV") = ((SV * 0.7833 * (1 + (EMR * 2.55)))
Loss Value ("LV") = 15 <arena> || (0.5 * SV) <AI3/AI4>
Extra HP Factor ("XHP") = subjective. I like adding 1/3 of (potential max hp - 100).
Total Spin Profit Per Win ("TSP") = 25.60 <AI3/arena> || 104.77 <AI4>
Games Per Spin = ((WR^-1) + (WR^-1)^2 + (WR^-1)^3 + (WR^-1)^4 + (WR^-1)^5), truncated appropriately.
Special Spins Per Hour ("SSPH") = TPH / (TTW * Games/Spin)
Special Spin Value Per Win  ("SSV") = 153 <unupped> || SSPH * 1290 <upped>
Wins Per Hour ("WPH") = TPH/TTW*WR
Losses Per Hour ("LPH") = TPH/TTW*LR
*code tag removed*

-snip-

I think there is an error at the pink-bold item in the quote above but I cannot quite place my finger on it.  Is SSV supposed to be a "per hour" value?  Or should unupped also be "* SSPH"?  Or should upped be GPS insetad of SSPH?  Am I way off here?!?