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From a couple of pennies
Example 1. Yours Max. CPC = $0.10, CTR=1% position = 2
Your competitor Max. CPC= $0.10 CTR =1.1% position =1
Your ad-position = 0.10x1=0.1
Your competitor's ad-position = 0.1x1.1=0.11
You should raise your ad position to 0.11+0.01=0.12 and this costs you only 0.12/1=$0.12/click or 2 cents more to take over the top position.
To over $100
The same example above but your competitor sets Max. CPC=$25.0 and CTR=3% (Note that his Max. CPC and CTR are unknowns to everyone except Google.)
Now his ad-position is =25*3=75
and you have to pay 75.01/1=$75.01 to move to #1.
If you keep the same Max. CPC of $0.1, a ten cent is the only thing he need to be #1.
He uses Max. CPC of $25 to keep the number 1 position for himself. However, he can pay dearly for this practic. For example, you work on your ads and your CTR increases to 3% and the same time you increase your Max. CPR to $20. Now your ad-position is 20*3=60. Your competitor is still at #1 but he has to pay 60.01/4=$15.01 and you pay only 10 cents for second position.
Example 2. Yours Max. CPC = $10, CTR=1% position = 2
Your competitor Max. CPC= $50 CTR =4% position =1
Your ad-position = 10x1=10
Your competitor's ad-position = 50x4=200
To move to position #1, your ad position must be at least 200+0.01=200.01 and this costs you 200.01/1=$200.01/click or $190.01 more per click. $200.01/click is over limit of ($100?) and it prevents you to move to the top position even you have that kind of money to spend. The only way to move up is to improve ads to raise your CTR. In this example, although your competitor has a Max. CPC of $50 but he pays only 10.01/4=$2.51 (not $50).
These examples are to illustrate the complication of ad-position in Adwords. If you do not understand how it works and play the bidding war game, it may cost you more than you expected and get nothing in return.
If this post is above your head, and you want to learn more about what is being explained, message 11 in this thread: [webmasterworld.com...] has a nice BidRank explanation by AWA.
Particularly for a new keyword where there are very few impressions or clicks. Initially CTR is clearly undefined ( 0 divided by 0 ). Also, it must be given some kind of boost until a decent number of impressions have occurred.
Google must have some kind of heuristic for this, I'd guess something like assuming an initial history of (say) 500 impressions with 5 clicks ( 1% CTR ), and then update from there.
They might also take into account the average CTR from the account / campaign / group, and info about the keyword.
Does anyone know precisely how CTR used in the ad-position calculation is determined?
These two threads should answer your question:
It is the average of ctr of all the advertisers for that particular keyword, at the time you enter the keyword.
In terms of positioning, it is the CTR of the keyword in the moment it is searched on that matters - but this is a reflection of its entire history.
The most recent 1000 impressions are weighted (slightly) more heavily, though the entire past history is considered as well. Part of the reason for considering the entire past history it to protect a keyword that has worked well for a long time from being disabled if it has a truly miserable 'most recent' 1000 impressions.