Serprex, Rob and CG made most of my points for me, so I won't bother repeating their answers in replying to Sevs, though I will announce that I am planning to play a few 100 games PDials at some point to compare (I already have a 1000 games of VDB logged, though those 1000 games are split into 3 sets of data, where only the last set of 500 games has logged both time to win and turns to win).
I am working on a reply for to Keeps question, though that is going to take a bit of typing, so I decided to post half a post first.
I didn't think auto calculating skips would be that hard.
You get the efficiency of each of the gods without skips.
You get the efficiency of the average.
Starting with the lowest efficiency score, replace is a -30 Electrum and 1 Turn cost * test runs and average that into the other gods
If the efficiency is higher with the skip, mark as skip and continue moving up the list until you have one that is worse off with the skip.
Done
This is pretty much the idea yes (define an order, and add skips 1 by 1 on top of each other according to the order in that list).
Bolded the important part, where the issue comes up. Yes, you can calculate the UEI[FG] for each individual god using CG's formulae (I'm using these to get results more easily comparable with arena and AI4 data), and yes, the average of those numbers is exactly the UEI for the overal without skips. Sadly, that order isn't always the same as the order in which you should skip: a FG with a very high TTW should be skipped before one with slightly worse numbers, but a better TTW (and no, this doesn't happen inherently, I think it's best explained as: your aren't looking for the gods that make you the least profit, you are looking for the gods that result in the largest increase of profit if you were to skip them, which isn't always the same thing).
Once you include skips, you introduce a new factor: skipped games are of an entirely different duration. Including skips alters your average turns/game, because you are replacing TTW numbers per god with skip durations (currently set at 1 turn per skip, but that is up for debate, and easily changed/personalized). Either way, you need a more advanced way to rank them. Here is where CuCN had a stroke of genius (CG and me had been at it in chat for a few hours, when he showed up, joined the discussion and eventually managed to figure it out):
[2014-01-30 02:08:40] CuCN: I think the profits and ttws should be added separately
[2014-01-30 02:08:47] CuCN: and then the sums divided by each other
[2014-01-30 02:10:53] CuCN: overall UEI should be calculated as (sum of profit from one game against each god)/(sum of turns for one game against each god)
[2014-01-30 02:13:04] CuCN: I think to determine what to skip, it should be sorted by (profit/game-profit/skip)/(turns/game-turns/skip)
[2014-01-30 02:13:50] the_dictator: we are using 1 turn per skip for now CuCN
[2014-01-30 02:14:17] CuCN: so the FGs should be sorted by (profit/game+30)/(turns/game-1)
[2014-01-30 02:15:38] CuCN: then, when calculating the overall UEI, have a column with profit/game if not skipping, or -30 if skipping
[2014-01-30 02:15:48] CuCN: and a column with turns/game if not skipping, or 1 if skipping
[2014-01-30 02:16:00] CuCN: sum the columns, divide the sums and multiply by 333
And this is exactly what we ended up using. Calculate the profit/game (so not per turns, or per second, or per hour, per GAME) for each god, and calculate the average TTW for each god. Calculate '(profit/game+30)/(turns/game-1)' for each god, and sort based on that value (I doesn't have any easily defined meaning, sadly, we ended up simply calling it skip index). It works because it follows the
mediant inequality, I will elaborate one I make a write-up of the full math in the OPs somewhere.
After that is simply maximizes the UEI[FG] using that order, which comes up with very nice (but believable) values, though usually with a high number of recommended skips (not very strange, considering it is currently trying to squeeze out every last electrum per hour). While this does give the highest possible UEI[FG], it does make for long skip lists (I think the calculations based on 200 games of PDials from the old study currently recommends skipping 16 out of 29 gods) AND it's rather sensitive to small number bias (if you have a 100% winrate or lossrate, based on a sample of 1 game, it will likely come up as one of the last gods to skip (or first)). Because of this I plan to add 2 filtering methods: the first one, already in place, reruns all the data, answering the question: if this data were exactly one fight larger, what would that do to the skip recommendations. (it checks for each game outcome (win or lose), and for each possible god, I leaving all other gods, and EMrate/TTW exactly as they were). The second filtering method, which I'm working on right now, is going to do what rob suggested: look at the increase in UEI[FG] resulting from skipping that god, and comparing that to a certain threshold.
Currently I'm mostly focusing on getting myself a tool that I personally can use to calculate the numbers that should be put in the opening post, along with skip recommendations and such, however I will likely end up making a public version for use by individuals to use when testing their data, and I plan to let that one also include options to change certain personal settings (like turns per hour, and skip durations), and ideally, even an option to take the official list as maintained on the forum to be recalculated based on those personal settings, though that, especially the last part, is something on my to do list later.
That said, CG and I agreed to show the numbers for all studies for both 333 turns per hour and 250 turns per hour, to give people some more options, and to some more options when comparing between different opponents (for example, when someone looking at the different studies personally knows their turns take a lot longer against false gods than platinum arena, though I would advice people to actually note down numbers for a few games instead of just doing it based on a feeling).
I believe the 'issue' at-hand regarding skips is not knowing how to program Excel or GDOcs, but rather what METHOD should be programmed to do skips. When Pella and I put in effort on the interim-FGei (now being replaced with a UEI sort of value), the skips were done along the lines of Keeps suggestion. Incremental is likely the way to do it. However, I would suggest not going ALL THE way on drawing the line. What I mean is if skipping a certain FG increases UEI by 1.2% (or some agreed upon level of tolerance) does not mean AUTO-SKIP. Rather, divide into 3 categories: GO; CAUTION; and SKIP with a user adjustable value of 'tolerance' for setting how tight or loose they want the skips calculated. Or at least something along those lines. .
You are right yes, spreadsheet coding isn't really a problem (though I did learn some new functions along the way, Google was sufficient so far).
I will leave the skip strategy implementation open for discussion for now (it will be covered in my reply to Keeps), though anyone who wants to take a look, we have a WIP version of the formulae
*here* the result of work/discussion by CG, CuCN and me (pieces of the discussion about it should be in chat history of the past 2-3 days)