Actually, paying off an installment loan for FICO purposes can significantly drop your scores. If you have been showing responsible payment history for years on an auto loan for example and all of a sudden you paid it off, now all those years of payments are gone from the equation. The reason the FICO scores drop is because now its a Closed account and is no longer helping your scores. This is why many people are encouraged to keep long standing accounts open as long as possible and not start closing accounts right away because it WILL lower your scores.
It will only lower your scores if it is your only open installment loan. That's important to understand.
Also, I'm not sure what you mean by all those years of payments are gone from the equation. Upon a manual review, any potential lender will be able to see the payment history on that account, as it would remain on one's credit report for 10 years.
Number of on time payments don't matter. Certain "fluff" software such as the charts/tables that Credit Karma provides may suggest otherwise, showing that a certain percentage of on-time payments equates to a different score category/range. The same fluff software may suggest that total on time payments are divided by total payments, thus suggesting that more on time payments would increase the percentage.
When it comes to payment history and on time payments, there are only two categories really. 100% on time payments and everything else, with the only exception being a lone low severity (say, 30 days) late payment that wasn't recent. Actual number of on time payments isn't relevant to FICO score. What matters is number of missed payments; If that number is > 0, scores suffer.