I have researched closing cards in depth and have some considerable experience in closing cards in the last couple of years since in 2009 almost all the banks I had cards with went completely nuts and every time I opened my mail box there was some kind of letter saying they were taking some kind of adverse action against me in reward for many years of perfect account history.

There are two main issues in closing cards. Average account age and utilization.

Closed accounts DO apparently still count towards average account age up until they drop off in 10 years. This means there will be no immediate impact at all on average account age. Only in 10 years when it falls off will you take a hit on average account age and by that time any effect should presumably be muted by age on additional accounts acquired in the mean time or other existing accounts which you have maintained open. Opening new accounts may have a big impact on average account age. Especially for people with a short credit history. But closing accounts has little impact.

On the issue of utilization. IF the creditor is reporting the credit limit, it is lowering your utilization by showing you have more available credit in relation to any outstanding balances. If you close these cards it will immediately raise your utilization and if you have high outstanding revolving debt in relation to your remaining credit limits it could have a profound impact on your credit score. However if you have plenty of other cards with good credit limits and low outstanding revolving debt it will probably have no impact. Furthermore, most "World" cards, "Signature" cards, and Amex cards do not report the credit limit at all and therefore do not impact your utilization either positively or negatively so for those cards it is usually a non-issue.

In my case, in the last year or two I have closed about 8 cards. Many with 10 plus year histories. I also opened about 6 new cards. It knocked my FICO score from ~760 down to ~720. I believe the point loss was almost entirely due to the increase in my utilization because many of the cards I closed had very high limits and I do have significant outstanding debt. I was closely monitoring my FICO score and when a card with a high limit reported as closed it always resulted in an immediate drop in my credit score. However when my "World" cards and "Signature" cards reported as closed there was zero impact on my credit score.

In summation, it depends on the person. People with solid long established credit histories and low revolving debt will have little if any impact from closing cards. People with short credit histories or high outstanding debt may see a much greater impact. Closing "World", "Signature" or Amex cards that do not report the credit limit should have little impact on almost anyone.