The analysis is interesting. However I'm not sure it has much practical value due to transpositions. For example, as white I play 1.Nf3 and if black plays d5 I play d4 and we have a d4 opening. If black plays c5 I play c4 and depending on what black does it will transpose into either an English opening (1. c4) or a maroczy sicilian (1. e4) or an indian defence (1. d4).
So basically, my opening move would be classed as 'other' but really it is one of 1.d4, 1.e4, 1.c4 in terms of the classifications of this post.
If any of the alternative paths were common enough, they would show up in the charts as well. I didn't limit the analysis to a particular set of moves; I simply counted all of the paths present in the data set and showed the most common ones. This is why two variations of the Indian Defence show up in the "White's second move" chart.
I think it'd be interesting to try to combine all possible paths for an opening into a single count, but that would probably be complicated if multiple openings can be reached through the same path. (e.g., which opening would the shared path be assigned to?)
The traditional way to handle this is by classifying a game according to the last cataloged position that occurs in it. This is how ECO classification works; you can see its catalog of positions at http://www.chessgames.com/chessecohelp.html.
For example, just after White plays 1.Nf3, the game is classified as A04, but after 1...d5 2.d4, it's now officially a D02, over in the Queen's Pawn category, just as it would have been if the game had started 1.d4 d5 2.Nf3.
Databases usually keep track of chess openings played by ECO code rather than by specific moves, exactly so that these transpositions are handled smoothly.
It is quite complicated. The examples I gave are quite simple, but in a lot of cases the transpositions can happen many moves into the game. The maroczy sicilian example I referred to is one of these cases, where I might not actually play e4 until say move 8-10, but in a general sense it probably should be classified as an e4 opening.
As an overall guide I think what you have done is fine, but I suspect something in the order of 10-20% of games might be subject to transpositions where the opening move isn't an accurate categorization.
for some openings, the 'paths' do not really matter. You might have 25 transpositions leading up to the same position after 10 moves. A well known example is the classic isolated d4 pawn position that might come from:
- Nimzo Indian
- Caro-Kann Panov
- QGD
- Slav
- c3 Sicilian
- Alekhine's defence
and others.
Popularity has not a lot to do with the openings themselves but with other things like a good book being published, or a popular match (like WC).
Another thing you have is that some variations are really popular, and have good results, but are at one point refuted by a single game. As a result of this, the variation dies. but remains to have very good statistics.
So basically, my opening move would be classed as 'other' but really it is one of 1.d4, 1.e4, 1.c4 in terms of the classifications of this post.