*The following is a response to simc, a full time miner at slush's pool:*

https://bitcointalk.org/index.php?topic=1976.msg728345#msg728345

It started to get long (especially with chartage) so I decided to put it here instead. Look a few posts up from the one I linked to if you want context.Thank you for the data, simc. As for the number of shares from the score, integrate the score formula and make shares the subject. Wolframalpha can help if you're not sure how to.

The first chart shows a clear peak in pool hashrate for rounds about 274000 shares total, after which there is a gradual decline in average hashrate. The trend is fairly clear even with this very limited dataset. This is interesting since that's about the current hop point, which can be calculated as follows:

Hop point =0.0164293+1.14254/(1.8747*D/(hashrate*c)+2.71828)

and making D=1300000, hashrate=1600 and c=300, we get an estimated hop point of 0.16*D which rises to 0.18*D at 1900Ghps. This is close to the 0.21*D that 274000 represents, so this gradual increase is probably due to hoppers - many will miss the start, and other proportional pools may be available instead, but the decline afterward and the ramp before are, to me at least, very likely accurate or at least close. The ramp and decline are also gradual because we are dealing with the average hashrate for the round, not the hashrate at the time.

The other two graphs show your earnings per round against pool hashrate and total round shares. There do seem to be some trends there, however.

ANOVA of the linear model:

lm(formula = BTC.reward ~ log(totalRoundShares))

with coefficients:

(Intercept) log(totalRoundShares)

-0.0022730 0.0008777

gives p<0.0001, so it seems possible that (for your data set) the your reward will increase with increasing round length:

simc's round reward = 0.0008777*log(totalRoundShares) -0.0022730

Similar analysis of

lm(formula = BTC.reward ~ hashrate)

and

lm(formula = BTC.reward ~ log(hashrate))

resulted in p>0.05 so with this limited dataset I'm not willing to accept either of these relationships as probable.

In summary, simc's data shows:

1. A probable hopper effect of about 36% increase in round average hashrate by about 0.21*D

2. A probable positive relationship between reward and round length, meaning that for the rounds under 3 600 000 shares on this particular day, total shorter rounds tend to reward less.

3. No relationship of significance between simc's reward and total pool hashrate. This is a bit odd since an increase in pool hashrate implies shorter rounds and less reward per round. Since slush uses a score method for payment and it's late here, I'm not going to work out the p value for that relationship with this data.

Keep in mind all this is based on minimal data, and I estimate I'd need a few weeks worth of a single miners data to have results worth making decisions on.