• Ad rank is the position of your ad in search results.
• CPC is cost per click (sometimes referred to as MCPC when dealing with AdWords, meaning Maximum Cost Per Click).
• CTR is your click through rate.
• Bid rank is determined by max cpc x ctr.

Ad rank is determined by max cpc x ctr.

Actual paid cpc is determined by what cpc you need to pay to have a 1pt higher bid rank than the competitor below you.

Example:
bidder 1: 10% ctr, $1 max cpc, rank=10
bidder 2: 5% ctr, $3 max cpc, rank=15
bidder 3: 7% ctr, $2 max cpc, rank=14

Bidder 2 will be in position 1. However, bidder 2 will only pay $2.81 (5% ctr x $2.81 cpc= 14.05 rank) for the click, not their max cpc of $3.

Bidder 3 will be in 2nd place for their bid. They will need to pay $1.43 for their bid ($1.43 x 7 = 10.01 which is 0.01 higher than the bidder 1).

If there is no 4th bidder, the clear winner here, even though the ad is in 3rd place, is Bidder 1. Their CPC is the minimum $0.05, and they have the highest CTR rate.

Because bidder 1 has the highest ctr rate, they have a lot of control. If they adjust their max cpc to $2, everything changes.

The new bid ranks would be:
bidder 1: 10% ctr, $2 max cpc, rank=20
bidder 2: 5% ctr, $3 max cpc, rank=15
bidder 3: 7% ctr, $2 max cpc, rank=14

Bidder 1 is now in the top position. However, their paid cpc jumps to $1.51 (still $0.50 less than bidder 2 was paying for the top position because of their excellent click through rate).

Lets look at the last scenario, a bid rank tie.

If bidder 2 did not like being in 2nd place, and wanted to raise the stakes, they could raise their bid to $4. However, this does not guarantee them first place, this guarantees them a bid rank tie.

Ties are broken by actual paid CPC.

In the above example, bidder 2 is willing to pay $4 a click, which is twice as high as bidder 1, so they will win this tie and be in first place. The rest of the bids will fall accordingly.

Because they are paying over double what bidder 1 is paying for first place, bidder 2 must maintain a very high conversion rate on their website to be able to afford this highly increased bid rate. If bidder 1 and 2 both make the same amount per conversion, and have similar conversion rates. bidder 1 is maintaining a higher ROI on their investment.

It looks like bidder 2 is banking on the fact that the top position can raise their ctr, and thus get more visitors.

If you can maintain more visitors and conversion per day than your competitors, your ROI might be less, but your total profit could be the same. Mass sales at low profits can make the same as small sales at high profits.

This type of bidding strategy will depend on how your business model works.