NotaNumber (div by zero) just ruin everything! they're contagious and infect everything they contact.
Oh my, how did those got in the database! Eligius must have been sending out some crazy stats if they managed to get through all the layers of sanity checks. Cleaned up the database and slapped another sanity check, just to be sure. Besides that and btcmine glitches, the database has held up rather well over the past week.
The reason for my

is that I'd thought that is what "Efficiency" already represents. Eg: atm if you solo 877000 shares/blocks, or do the same at a proportional pool at "luck" multiplier = 1.0, you expect 50 coins. You can check for yourself that efficiency is calculated as (received coins/expected coins), which means it would also be (utilised shares/accepted shares). But efficiency!=utility/shares - again, you can check this with a few of your own.
I prolly have this the wrong way around, and it'd be handy for stats purposes if it relates to eg. the total shares in that block. Then (I hope to) relate results to Raulo's original paper on hopping and not just calculate hopping efficiency but predict best hopping algos for each pool.
As I see it, utility is related to what the multipool algorithm expects the shares to be worth ahead of time, while efficiency is related to what their real worth turns out to be after the fact, once multipool knows how many coins it will actually collect for them. Confusingly the two are not expressed in the same way, one is expected total worth, while the other is real worth per share (both in relation to the average worth of one share at the current difficulty).
That's what I suggested should be changed, so that you'd have "expected worth per share" and "real worth per share" instead, allowing for a direct comparison. If the algorithm is correct, these numbers should more or less converge over time.
TeaRex is exactly correct in the explanation. The reason I didn't display utility as "expected per share" to begin with, is that each share has unique utility. The database keeps count of the number of shares submitted by each user to each pool in each round, and also of the sum of the shares' utilities in that round. When a round is rewarded, each user receives a proportion of the round's reward equal to the proportion of the user's total utility against the total utility of all users in that round. To me it is easier to think of expected utility in these terms. Couldn't someone write a greasemonkey script if there really is demand for displaying utility as per share, rather than total?
So what's the deal with eligius? Eligius-us is back up, serving stats and getworks, and accepting shares, but it is "down"? I guess I'll keep it out of rotation while it decides its existential problem.