Every single great advancement is chess engines has been due to a reduction in branching factor. While it is obviously a mistake to prune away good stuff let's take a quick look at the list:Uri Blass wrote:I think that better search does not mean lower branching factorDann Corbit wrote:If an engine scales better, it is most likely search that is better (lower branching factor).
The second most likely thing would be the SMP implementation.
The evaluation will not affect scaling much, except for improvement in the move ordering.
It is easy to get lower branching factor by dubious pruning.
I think that evaluation is important and I expect top engines not to scale well if you change their evaluation to simple piece square table evaluation.
1) Alpha-Beta : Enormous improvement over mini-max
2) Null move reduction: Enormous improvement over plain alpha-beta
3) PVS search: Modest improvement over null move reduction due to zero window searches
4) History Reductions: (As pioneered by Fruit) - huge improvent over plain PVS search
5) Smooth scaling reductions in null move pruning (As, for instance, Stockfish) - significant improvement over ordinary null move
6) Razoring (like Rybka and Strelka): Enormous improvement over plain pvs search
7) Late Move Reductions: (with Tord taking the lead in both effectiveness and publication) -- a huge improvement over not having LMR.
There are, of course, many others that I did not mention here.
It is not a coincidence that the top ten engines all have branching factors of about 2, and it is not a coincidence that most weak engines have a large branching factor.
Now, your point in well taken with individual cases. For instance, ExChess had the best branching factor of all engines at one point. But it was not the strongest engine by far. So poorly tuned reductions are not nearly so beneficial as properly tuned reductions.
But almost every big advancement comes from a reduction in branching factor and the next revolution will come from a reduction in branching factor.
There are, of course, some exceptions. The material imbalance table in Rybka was another revolution, and almost entirely due to evaluation improvement in that case (as a 'for instance'). We can thank Larry Kaufman for that, I think.