OK. Position is determined by your rank number compared to your competitor's rank number. Rank number is defined as the keyword's Maximum CPC multiplied by the keyword's CTR. For example a keyword with a Max. CPC of $0.40 and a CTR of 1.8 has a rank number of .40 multiplied by 1.8, or .72
Note: the higher the ad's rank number, the higher the ad's position.
CPC pricing is adjusted so that one pays the minimum amount required to have a rank number just slightly above your nearest competitor. To calculate, we take the rank number of the nearest competitor (lower than you), and increase it by a tiny fraction. Then, using that 'new' rank number and your existing CTR, we calculate your CPC.
To simplify, essentially your CPC = 'new' rank number divided by your CTR.
In Advertiser 123's example, rank number and position look like this:
A sets maximum Bid at $1.00 CTR 3% - Rank number = 3, and Position = 1
B sets his maximum Bid at $0.70 CTR 2% - Rank number = 1.4, and Position = 2
C sets his maximum Bid at $0.50 CTR 1% - Rank number = 0.5, and Position = 3
D last bidder maximum Bid at $0.10 CTR 1% - Rank number = 0.1, and Position = 4
In terms of each advertiser's CPC in the above example, it looks like this:
A sets maximum Bid at $1.00 CTR 3% - CPC paid = 47 cents
B sets his maximum Bid at $0.70 CTR 2% - CPC paid = 26 cents
C sets his maximum Bid at $0.50 CTR 1% - CPC paid = 11 cents
D last bidder maximum Bid at $0.10 CTR 1% - CPC paid = 05 cents (minimum CPC)
With all that said, I feel that the above information is of limited practical value, beyond simply understanding how it works. I say this because:
* positioning is variable, and literally changes from one moment to the next. So calculating it gives one information that is outdated long before you've even finished the calculation.
* the calculation also requires that you know your competitor's CTR, in order to figure our their rank number. However, this information is the confidential 'property' of your competitor.
When all is said and done, it boils down to focusing on creating well targeted ads & keywords that get great clickthrough rates, then using a competitive Maximum CPC.
I hope that this info will prove useful, and I do regret that it was so long in coming.