The Double Dummy Opening Lead Accuracy Rate (DDOLAR) measues the accuracy of the opening lead compared to double dummy.
There are some DDOLAR facts:
This data includes both cheating players and honest players.
If I ran a tournament of 1,000 boards, with 1,000 top experts, I would expect a DDOLAR of just under 81%.
If I ran a tournament with the same 1,000 boards, but randomly selected 1,000 ACBL BBO tournament players, I would expect a DDOLAR of just under 80%.
If I ran a tournament with the same 1,000 boards, but randomly selected 1,000 VACB BBO tournament players, I would expect a DDOLAR of just under 79%.
I choose a different group of players. Let's call this group, PLAYERS_1. If I ran a tournament with the same 1,000 boards, but randomly selected 1,000 players from PLAYERS_1, I would expect a DDOLAR of about 83%. Or, put another way, I could take any of the groups above and give them simple instructions to increase their DDOLAR to 83+%. I would expect the same percentage of cheating players in my group as the others; I would not expect them to cheat any more, or any less, if they were in PLAYER_1.
How can this be? This is the DDOLAR paradox.
The following is a continuation of the same paradox:
I can look at the overall data for a pair what has played a large number of boards, let say 5,000 boards, and they have a DDOLAR of 84% and say they are likely not cheating. But I could look at the same overall data for a pair that has played the same number of boards and have a DDOLAR of 83% and say they are likely cheating. How can this be? This is the same DDOLAR paradox.
If you do not understand this and cannot explain the DDOLAR paradox, you probably should not be using DDOLAR in any cheating discussions.
This is all part of understanding the data behind the data.