# Can the "bishop pair advantage" be supported by statistics?

I heard a lot about the advantage of having a bishop pair and I am interested in the statistics about this. More specifically, if we collect a huge number of games (master games only, or games including non-titled players) for which at any point of the game, one side has exactly two bishops as his/her only minor pieces and his/her opponent has exactly two knights (or N+B) as his/her only minor pieces, what is the winning percentage?

I will be interested in the winning percentage of:

1. BB vs NB
2. BB vs NN
3. NB vs NN.

Edit I know this is extremely rare; but what will happen to the winning percentage for BB vs NB and BB vs NN if the two bishops are of the same colour? (Here is a related question.)

• An important element with statistical investigations is that samples need to be random and independent, and you need sufficient many to give the result the required degree of confidence. I doubt that you can get independent samples, as the bishop pair advantage is taught to just about everyone, and you may/might have players who believe it to the point where they go for a draw if their opponent get one. So ... to get answers by statistics is going to be tricky. Jan 21 at 18:49
• IM Watson did a data study and found that the winning advantage of BB, QN, and other "advantageous" piece combinations could be explained by the rating difference between the players. He also posed the question if the higher rated player sought this advantage due to learned bias. Jan 22 at 21:58

• Download all games from top players. Around 341k games excluding the duplicates.
• Use pgn-extract to get BBvNB, BBvNN and BNvNN games.
• Run bayeselo to get the stats.

## Results

##### Table 1
``````Rank Name:   Elo    +    - games score oppo. draws   win  loss  draw
1 BB  :    29    2    3 67811   55%     0   37% 24402 18049 25360
2 NB  :     0    3    2 67811   45%    29   37% 18049 24402 25360
``````
##### Table 2
``````Rank Name:   Elo    +    - games score oppo. draws   win  loss  draw
1 BB  :    37    3    4  9896   56%     0   31%  3990  2873  3033
2 NN  :     0    4    3  9896   44%    37   31%  2873  3990  3033
``````
##### Table 3
``````Rank Name:   Elo    +    -  games  score oppo.  draws   win  loss  draw
1 NN  :     3    4    4  31993  50.4%     0  35.7% 10421 10160 11412
2 NB  :     0    4    4  31993  49.6%     3  35.7% 10160 10421 11412
``````

The elo leads are significant for table 1 and 2. For table 3 the elo advantage is still within the error margins.

• Please could you explain the numbers in the columns Elo, +, -? Jan 22 at 13:17
• Margins of error at 95% confidence level. In table 3, NN has an interval of [3-4, 3+4] or [-1, 7], while NB has [0-4, 0+4] or [-4, 4]. Though NN leads by 3, it cannot fully claim superiority because it has a minimum of -1 while NB has a maximum of 4. In table 2, BB has [33, 40] while NN has [-3, 4], the minimum of BB which is 33 is more than the maximum of NN which is 4 so the lead of 37 is significant, BB is really superior. Jan 22 at 15:28
• What do Elo and oppo. mean in this table? How much of an elo advantage and disadvantage the piece combinations give the players? Jan 22 at 15:54
• It would be interesting to split the data with regards to who has the material advantage. Jan 22 at 17:40
• Number of pawns on the board may be a factor (source). Jan 23 at 2:06