I later wrote some reports for Mr. Bertens, the latest was dated November 2, 2020. It lists his statistics and compared his data with other top players from face-to-face (FTF) Bridge. You cannot use any comparisons to the recent top level online Bridge because so many players were cheating in those events.
I was contacted by USBF in early November, after I had written the November 2 report, and asked to prepare a report for USBF for the hearing. My deadline was very short. I think it may only have been 1-2 days as USBF were coming up with the deadline for submitting information for the pre-trial discovery documents. I wrote a report, dated November 9, 2020.
At this time, I do not plan on releasing either report.
I was asked to appear as a witness to the USBF hearing.
During the hearing I was asked by the prosecution about my correspondences with Mr. Bertens. My answer was that I considered any emails/conversations to be private and I would not discuss them. I have had lots of discussions with many players over the last 12 months and I consider these to be private with no reason to discuss them. In this particular case, Mr. Bertens later gave permission for me to release the contents of our emails to the hearing and I provided a copy of our original emails.
H_BERTENS (HB) played 1,303 total boards with NARENG (NG) in 2020. Three of them were passouts. I will focus on two main statistics for HB through this data set: DECWER and DEFWER. They are explained in the terminology section of this web site. I will also mention DDOLAR though this was not used (by me) for this case.
I then compare this with all US players that had 1,300 total boards played in top level FTF competition. The hearing was by USBF, they were interested in comparisons with known US players, so the comparison data is with US players.
The chart shows the declarer weighted error rate (DECWER) on the horizontal (X axis) and the defensive weighter error rate (DEFWER) on the vertical (Y axis). As the declarer play improves, the dots will move more to the right. As the defensive play improves, the dots will move lower. Perfection is the bottom right corner. There are no US players with this number of boards that have a DECWER less than 1.50% or a DEFWER less than 1.00%.
The top left red dot is Mr. Bertens performance with Mr. Bakkeren. This is from 1,413 boards of top level FTF play. The top red dot is Mr. Bertens performance with Mr. Cheek from top level FTF play. There are only 603 total boards, therefore this dot should not really be a comparison to players with 1,300+ total boards.
The lower right red dot is HB performance with NG from 2020 on-line play.
However, these 1,303 boards include practise matches and what might be considered to be non-serious events. It is only fair to compare against "real" events. This is HB/NG data from "real" events.
|Alt III||04/20 - 04/24||7||120||0.91%||77.78%||0.88%|
|1st OCBL Open Teams||05/07 - 05/10||5||76||0.62%||85.00%||0.43%|
|Alt Mixed Plate||05/22||1||20||1.52%||0%||1.20%|
|Alt V||05/25 - 05/29||6||120||1.19%||85.29%||0.68%|
|USBF Invitational||05/30 - 06/03||20||253||1.33%||89.23%||0.45%|
|Alt VI||06/08 - 06/10||3||72||1.91%||88.24%||0.74%|
|1st OCBL Cup||06/16 - 06/17||4||40||0.60%||90.00%||0.52%|
|Major Alt I||06/22 - 06/26||9||116||1.48%||83.33%||1.25%|
|2nd OCBL Cup||07/06 - 07/08||7||70||2.64%||84.62%||1.34%|
|All before 06/04||- 06/04||39||589||1.14%||85.03%||0.60%|
|All after 06/04||06/04 -||23||298||1.81%||85.71%||1.04%|
The Alt Mixed Plate was a third/fourth place playoff. Special rules were allowed so that there had to be two male and two female per team, however each pair could be single sex. HB only made one lead in this event. It was not a good lead (per double dummy).
There is disagreement about when Mr. Bertens was first informed that he was under suspicion. One data point suggested by the defense was all data before the USBF event and all data after, hence the cut-off date of June 4, 2020.
My November 9 report only included the USBF event and one of the Alt events as this was the request from USBF.
The following chart shows top US players with 550+ total boards in top level FTF competition. I have removed nine sponsors from the list, all of these sponsors had a DECWER above 2.4%. The purpose of the graph is comparison to Mr. Bertens' peers.
The data includes all of the top US pairs. The lone blue dot just below the 1.00% DEFWER horizontal line is Mr. Hamman playing with Mr. Bramley.
The various red dots show Mr. Bertens individual performance using different data sets above. The only fair comparison should be with dots with 550+ total boards.
The dots by themselves are not necessarily indicative of cheating. They point out that Mr. Bertens was playing at a level above and beyond any US player that had played more than 550 boards in top level competition. To statistically determine the likelihood of this being random, or at least to approximate it, requires knowing the expected variance of the data. This information is not provided here, but was provided, by request, at the hearing.
An argument is that this was against weaker players. For the hearing, comparison data was provided with top US players as specified by the panel showing that these players' performance had remained mostly unchanged (within statistical limits) from both FTF play and on-line play.
I was not paid for any of this work, either by Mr. Bertens or the USBF, nor at any time did I ask for any payment from anyone. Given I have just spent over three weeks in a hearing for this one case, I may have to start charging for my time and work in the future.