I do look at past games, but not h2h, because head to head doesn't give good outcome if you ask me, I look at recent games, like how the teams played in the last 5-10 games, if you look at that then you are going to see how the team is doing and I am pretty sure that we are going to end up with a good result without a doubt. I am not entirely sure how this could end up being different all that much, but we need to be considering how things could change without a doubt.
If people could put their analysis on just how the teams are doing right now, that would be better, instead of focusing on head to head. Think about it, these teams meet maybe twice or three times a year, so if you look at last five games, you are looking into not just last season, but also season before that, makes no sense.
I will not reject your process by only look at the recent games, because it is not true all the time match out come will only depends on the head to head result. Because there was of the some factors like the best player can be injured and also it is not all the time a player or a team do the same performance.
However, I think we cannot ignore the fact, that head to head stats provide many important facts, that is to say, it can initially provide some insights into a match which can be useful for later analysis.
In my case I to check the head to head stats first and then check the recent performance of the both team and them make any bet on that match to be honest it is help me to execute the possible result of a match.