IOTA tip selection mechanism is based on a weighted random walk. A parameter α>0 dictates how important a transaction’s cumulative weight is. The transition probability P is proportional to , where is the difference between the cumulative weights of the site and the tip. If the tip is a lazy tip, will be big and P will be small. Thus, it is less probable that a lazy tip will be selected (which is an important characteristic of a good tip selection mechanism).
If α is very small, it is an unweighted walk which does not punish lazy tips. If α is very big, it is a super-weighted walk, where too many transactions will be left behind and need to be reattached, which leads to decreased confirmation rate.
So, the parameter α is a major dictator of confirmation rate. Unfortunately, how we can improve it and what an ideal confirmation rate is are still speculative questions as of today. We are still unsure, and further research needs to be done before we can reach a conclusion.