I think this is the right section to post. Anyway, a new discovery on GameFAQ's (Don't laugh, I'm serious) has lead to evidence that equipping a Lucky Egg to the father results in a similar average of IV's. Read about it here:
http://boards.gamefaqs.com/gfaqs/genmessage.php?board=925601&topic=36627808
PsychoDragon from GameFAQS said:
In trying to make myself a Ninjask, I bred eight generations of Nincadas. Based on the rumor that Lucky Eggs are beneficial, I made the Father hold one each time. The mother was holding an Everstone, to pass on the Jolly nature that I wanted).
Because of the limitations in making a non-ugly graph for all 53 Nincadas, I'll just post the results of each generation here.
I had my original Ninjask and Ditto. The average of Ninjask's IVs is 11.25, and Ditto's IVs average to 14.97. The average of these two numbers is 13.11. They beget the Number Generation, for I named the Nincadas 1, 2, 3, and so on until 7.
The average IVs for 1 through 7 are 13.25, 16, 4.75, 10.33, 10, 18.75, and 17.42. The average for this entire generation is 12.93.
Do you see that? The average IVs for the parents was 13.11, and 12.93 for the children- a difference of 0.18!
First of all, the size of the sample used is only 7, which is clearly not enough to warrant such claims. Secondly, a little mathematics should convince people that this is nothing but what probability would give you anyway.
Since the average of the parent's IVs is 11.25 and that of Ditto is 14.97, the total average would be 13.11, as the guy here says. In 8 out of 9 cases (according to our guide), you get 2 or 3 IVs passed. So, in 8/9 of cases, you get either:
1) 2 IVs from Ninjask: average of 11.25.
2) 2 IVs from Ditto: average of 14.97.
3) 1 IV from Ditto and 1 from Ninjask: average of 13.11.
whose average is 13.11 (this happens 32.98% of the time), or
4) 3 IVs from Ninjask: average of 11.25.
5) 3 IVs from Ditto: average of 14.97.
6) 2 IVs from Ditto and 1 IV from Ninjask: average of 13.73.
7) 2 IVs from Ninjask and 1 IV from Ditto: average of 12.49.
whose average is 13.11 (this happens 54.49% of the time).
So you either have 2 IVs with an average of 13.11 and 4 random IVs, or 3 IVs with an average of 13.11 and 3 random IVs, in 8/9 of cases. (I'm not going to calculate the other cases since they won't alter these numbers much.)
In the case of 2 IVs, the other 4 random IVs' average is 15.5, and so the average for the six generated IVs is (13.11*2 + 15.5*4)/6 = 14.70. Since this happens 32.98% of the time, this average rounds down to 14.70 * (32.98 / 100) * (100 / (32.98+54.49)) = 5.543.
In the case of 3 IVs, the other 3 random IVs' average is 15.5, and so the average for the six generated IVs is (13.11*3 + 15.5*3)/6 = 14.31. Since this happens 54.49% of the time, this average rounds down to 14.31 * (54.49 / 100) * (100 / (32.98+54.49)) = 8.915.
Hence, the average IVs if you transfer 2 or 3 IVs are 5.543 + 8.915 =
14.458.
This means that, by using the hypothetical 'Lucky Egg' averaging out boost, you actually tend to get a worse IV average (12.93) than without. This means that the influence of Lucky Egg to IV breeding is not statistically significant.