Unified Efficiency Index - How to compare apples to oranges

[ColorlessGreen]

I indeed posted it as a reference for more fixes and to get some feedback (that's why it is a beta). Thanks, though.
BTW, I was thinking of adding a "Reward" slot, this way you can put the exact value of the League, if you want to.

Yeah, on the spreadsheet I use at home, I have all of the various constants set up in the formula as cell references rather than just numbers so I can play around with them as needed. Arena's stated value fluctuates a whole lot, and while I don't personally feel the need to update it for 1-2 electrum swings, it's worth doing for bigger swings, particularly if you're trying to determine whether today you should play platinum or gold.

Turns per hour is the other thing that IMO is most useful to be able to easily change. While I currently don't have anything science-based to work from here, my gut feeling is that eventually someone will come up with a good way to handle this which will result in there being a different turns-per-hour assumption for gold/platinum/FG than for ai3/ai4/bronze/silver (or possibly if we're really lucky, different assumptions for each league).

[ColorlessGreen]

edit: Forum-bork-related double post.

[Leodip]

In the spreadsheet I said that, if the user felt like it, he could measure his TPH, otherwise, he could simply imagine how much his TPH would be like. I did some studies myself. Approximatively, I reach the 310 TPH, if I don't distract myself with anything and I consider the time from shifting from one game to another, 250 if I do my usual tab shifting, 400 (a little more, actually, near 410, but I lost some data on the way) if I don't distract myself during games, try to play faster than possible without hurting WR and TTW and don't consider the time to shift from one game to another. I simply averaged those and it is, more or less, 325, and then I'm keeping 333.

[Jyiber]

First I'd like to congratulate you for making this, I asked a question when I first came to the forums about something along these lines and I was greeted with bickering and speculation between older players. I then realized the amount of work it would take to do it myself and gave up. I'm one of those people who's head will explode after a certain amount of time crunching numbers.

Second, I agree with your switching the time variable to number of turns instead of units of time. The variability of the latter is subject to many factors you mentioned. Though, I'd like to add that I think the speed of the player is also affected by the type of deck. Some decks have more open strategies and create more circumstances where the players has to stop to make decisions.

I prefer these decks because I don't think I could stand automatically clicking without thought for long periods of time.

[Leodip]

First I'd like to congratulate you for making this, I asked a question when I first came to the forums about something along these lines and I was greeted with bickering and speculation between older players. I then realized the amount of work it would take to do it myself and gave up. I'm one of those people who's head will explode after a certain amount of time crunching numbers.

Second, I agree with your switching the time variable to number of turns instead of units of time. The variability of the latter is subject to many factors you mentioned. Though, I'd like to add that I think the speed of the player is also affected by the type of deck. Some decks have more open strategies and create more circumstances where the players has to stop to make decisions.

I prefer these decks because I don't think I could stand automatically clicking without thought for long periods of time.

I'm not sure I understood your reasoning: you said that you'd prefer using turns as unit of time instead of seconds because there are many things that can distract you while playing and augment your playing time, right?

Well, if that's it, my answer is:
Indeed, following your reasoning, it would be better to keep seconds (or TPH, to be more precise) as unit.
The entire reasoning behind the UEI is to calculate how efficient a deck would be for you and calculate the amount of money you can obtain from a specific amount of time of play (in this case, one hour is the standard). Of course if you don't calculate the time "wasted" doing other stuff, you could calculate that you'll obtain (for example) 5000 per hour but effectively obtain 3000 or 2000 .

Though what you said isn't impossible. We could setup the spreadsheet so that it calculates elec per turn (or per game, or per a given number of turns) so that it gives a, pretty much, standard result that's about the same for everyone and then, for the personal part, add the number of turns per hour to see how much time it'll take to gain that much money considering personal speed.

[ColorlessGreen]

Right now, it actually basically does give output in terms of electrum per turn (or, as written, electrum per 333 turns). The only reason I bother with attempting to convert turns to hours is for easy comparison to FGEI. IMO, tracking data in terms of turns is the most transferrable between people, since there is a huge variation in the way individual players play as everyone has noted. Number of turns, however, should (mostly) be relatively constant between players, at least aside from fundamental shifts in the way the deck is played such as withholding a killing blow in hopes of drawing a card you need for an EM instead of going for quicker kills without regard to EM.

The formula as written uses 333 turns for the reasons I've mentioned in the OP and elsewhere, because this seems to be the closest thing to a sweet spot based on the preliminary surveys I've done of average time per turn in studies that record both TTW and average game time, but I do hope to get a better system for it as the discussion (and studies) move forward.

Right now, for individual use purposes, I *absolutely* recommend that if you feel you play a specific deck much slower than other decks, that you either replace the 333 with another number (250, 300, 200, whatever) or that you multiply the UEI number by 0.9 or 0.8 or 1.1 or whatever you feel represents how much slower it is used. This will give you personal information that will be more suited to your personal play styles and is a good idea when choosing a deck. If you don't feel comfortable guessing at it, play ~5 games with a deck and figure out your average seconds/game, divide by TTW for seconds/turn, and then calculate turns/hour from your personal seconds/turn.

I believe that for now, though, using a standard turns/hour to discuss overall performance (not tied to a specific player) of a deck is the most objective way to handle it, as you then do not have to attempt to account for the timing play style of the person(s) who did the testing. You still have to account for their skill and their general play style and such, but you have to do that either way, and speaking in terms of turns just eliminates one factor you need to account for.

Thank all of you who are participating in this discussion. The more input we have, the better the final result will be.

[Leodip]

Right now, it actually basically does give output in terms of electrum per turn (or, as written, electrum per 333 turns). The only reason I bother with attempting to convert turns to hours is for easy comparison to FGEI. IMO, tracking data in terms of turns is the most transferrable between people, since there is a huge variation in the way individual players play as everyone has noted. Number of turns, however, should (mostly) be relatively constant between players, at least aside from fundamental shifts in the way the deck is played such as withholding a killing blow in hopes of drawing a card you need for an EM instead of going for quicker kills without regard to EM.

The formula as written uses 333 turns for the reasons I've mentioned in the OP and elsewhere, because this seems to be the closest thing to a sweet spot based on the preliminary surveys I've done of average time per turn in studies that record both TTW and average game time, but I do hope to get a better system for it as the discussion (and studies) move forward.

Right now, for individual use purposes, I *absolutely* recommend that if you feel you play a specific deck much slower than other decks, that you either replace the 333 with another number (250, 300, 200, whatever) or that you multiply the UEI number by 0.9 or 0.8 or 1.1 or whatever you feel represents how much slower it is used. This will give you personal information that will be more suited to your personal play styles and is a good idea when choosing a deck. If you don't feel comfortable guessing at it, play ~5 games with a deck and figure out your average seconds/game, divide by TTW for seconds/turn, and then calculate turns/hour from your personal seconds/turn.

I believe that for now, though, using a standard turns/hour to discuss overall performance (not tied to a specific player) of a deck is the most objective way to handle it, as you then do not have to attempt to account for the timing play style of the person(s) who did the testing. You still have to account for their skill and their general play style and such, but you have to do that either way, and speaking in terms of turns just eliminates one factor you need to account for.

Thank all of you who are participating in this discussion. The more input we have, the better the final result will be.

Easy way: the output is electrums/hour. 1 hour=333 turns (by standard). The output could be defined as electrums/333 turns.
Result: take the last number, divide it by 333 and you'll obtain electrums/turn.

[Jyiber]

I'm not sure I understood your reasoning: you said that you'd prefer using turns as unit of time instead of seconds because there are many things that can distract you while playing and augment your playing time, right?

Well, if that's it, my answer is:
Indeed, following your reasoning, it would be better to keep seconds (or TPH, to be more precise) as unit.
The entire reasoning behind the UEI is to calculate how efficient a deck would be for you and calculate the amount of money you can obtain from a specific amount of time of play (in this case, one hour is the standard). Of course if you don't calculate the time "wasted" doing other stuff, you could calculate that you'll obtain (for example) 5000 per hour but effectively obtain 3000 or 2000 .

Though what you said isn't impossible. We could setup the spreadsheet so that it calculates elec per turn (or per game, or per a given number of turns) so that it gives a, pretty much, standard result that's about the same for everyone and then, for the personal part, add the number of turns per hour to see how much time it'll take to gain that much money considering personal speed.

That was part of what I was getting at, but I was also reiterating the fact that different players and decks will have different speeds. Another factor is what your playing (AI3, AI4, FG, PvP1, PvP2). Other factors: computer, ISP, and network conditions. End result is that any per/hour table produced will be an approximation.

Not entirely sure if this has been brought up, but perhaps different tables for things that have the greatest effects on play speed. Or at least predetermined modifications you can add or take from the base formula on a case by case basis, so people can make their own. Which all leads to someone collecting more data...

The way to finding which table is applicable to you is taking sample data of your deck to track turns and/or time to win x number of games and calculating an average to use as a key.

Sorry if I'm not making sense or I'm being redundant, I'm mostly talking to myself as I go through how to use this 
By all means correct me if needed. I hate it when I'm wrong an nobody tells me...

Oh, and if you've never heard of this try putting formulas in here:
http://www.wolframalpha.com/
EDIT: I had to modify your formula to single letters to make it work on that.

[Keeps]

There are two problems with TTW as a scalar value though.
1.) Is skips, is quicker than a turn, doing an automatic 5 seconds (coin spin, mouse movement, and 5 clicks) is easier to measure and more precision than a turn (although you could just call it a percentage of a turn.
2.) Is as the game progress or there are more creatures on the board, the more the actual game slows down, in processing, rule checking, attacks, targetting and such.  So a deck like pdials takes about the same amount of time per turn consistently, where a deck like malignant balls starts out just as fast as pdials, but slows down as you get near the end, and a CCYB with Mutations is even longer...

[Leodip]

@Jyiber, that's why you should use TPH, it's just as I said. You should calculate all of the distractions and troubles with your PC or internet connection and stuff because it'll interfere with your gains, that's why you should keep them. As I said, TPH is fully personal.

@Keeps, eventually, we could add a skip function, but will it really be needed? Remember that we're not playing against FGs, those are the only who are to be consistently skipped. Plat and Gold could get near to it in terms of skips, but we have still fewer skips. Remember, too, that the UEI uses a whole lot of approximations (necessary ones), it'll need to be a big one in order to interfere in the calculations.

[ColorlessGreen]

Skips are easy to accurately include in the formula. They are currently considered in FGEI (though I can't speak to whether or not they're handled accurately in this version of FGEI. They were handled accurately in the previous version of FGEI). They are not included in UEI because UEI is not intended to replace FGEI for FGs, and no other target (besides AI3) has predictable enough decks to have autoskips be a factor.

There is discussion a page or two back of how exactly to factor autoskips into UEI. If there winds up being more interest, I'll write down the actual skip-including formula, but the TL;DR is to basically change win rate into non-skip win rate, then factor in the costs for the skips (in both time and money) later on.

[Leodip]

Little update on the StatKeeper