A lot of new advertisers take a good deal of time trying to outline some acceptable tactics for identifying and alleviating their own Quality Score symptoms and it seems that many times Quality Score is the real issue when it comes to the usual minimum CPC bid complaints made by them. Historical Quality Score for the search terms themselves, however, might prove to be a real nightmare for savvy professionals as well. Just imagine, you have not even had a chance to accrue a single impression as yet, not to mention a clickthrough, but your keyword term is already carrying a certain historical Quality Score. It is called a historical Quality Score, but the adjective "historical" does not tell you all the story. Because actually it does refer to the history of the keywords and their performance as used in the past in other Google AdWords accounts held by other advertisers.
If you happen to inherit poor historical Quality Score for a search term of yours it means you inherit the poor results associated with terrible targeting, unlikely bids and bad account management of people who have used your search term in the past. That is the most probable reason for which you can often see extremely high minimum CPC bid requirements within your account. Even when you do not have any competition for a particular keyword you might be doomed to suffer the consequences of a poor historical Quality Score. To be straightforward, you get your punishment for sins committed by others you don't even know.
To be honest there might be a few instances when it seems that the system has decided to give you some grace period upfront. It might seem to you that you are given the opportunity to prove you are different from the historical average. However, as soon as the system realizes that you are just the same your minimum CPC bid requirement can start sky-rocketing right away. It is a most frustrating experience for highly trained pros too. Even though they know pretty well that when competition is very little for a potentially popular search term, poor historical Quality Score is the underlying reason in 99% of cases. That is what makes the minimum CPC bid requirements too high for reasonable bidders.
Is there anything you can do to cure this problem? Not much. Of course, you are free to move your keyword labeled with poor historical Quality Score to a different ad group, to a different campaign, and even to a different Google AdWords account. However, no matter what you do, the historical information will always follow your search term everywhere. Still there is a vague chance of a remedy. What you can try to do is to change your matching option because as a rule your keyword will not carry the historical information across different matching types. Therefore if e.g. the broad match keyword equipment goes inactive for search due to a sudden increase in your minimum CPC bid requirement there is still a chance that the phrase match "equipment" or the exact match [equipment] will not be labeled with a bad historical rating.