# Eastlake Club 2013 Payoff Matrices

by Matthew Kidd
May 8, 2014

I introduced the Payoff Matrix concept last October and showed results for six years of the La Jolla unit game based on the output generated by the Payoff Matrix software. Here I present similar results for the 2013 calendar year for the Eastlake Club in San Diego. As usual, the data shown in the visual matrices is limited to regular partnerships who play in enough sessions to generate decent statistics but full data is presented in the tab delimited text files which are available as a download at the end of this page.

The Eastlake Club runs several sessions per week, both open and limited games. The following table shows the average field strength for each session in order of decreasing strength. The 2013 La Jolla unit and San Diego unit open games are also included for comparison.

Field strength for each session
Session Mean (MP) Geomean (MP)
San Diego Unit open pairs 2874 1787
La Jolla Unit open pairs 2711 1567
Eastlake Wed Eve pairs 420 166
Eastlake Wed Mor pairs 400 152
Eastlake Thu Aft pairs 258 75

Both the mean and geometric mean is shown. I have argued previously that the geometric mean is a better indicator of field strength than the mean. In a geometric mean, the mean is taken in a logarithmic manner. For example, the geometric mean of two players with 10 and 1000 MP respectively, is 100 MP not 505 MP. Less experienced players drag down the geometric mean more than the arithmetic mean. A field with a high geometric mean should in principle be uniformly fairly tough and offer few gifts.

The Eastlake payoff matrices are presented below in the order of decreasing field strength according to the table above.

## Eastlake Wednesday evening pairs

Club owner Kathie Angione and her regular partner John Lagodimos dominate the Wednesday evening game with a 59.17% average, well ahead of John and Linda John Dusharme’s 52.69% average in second place. Curiously, Kathie and John really take it out on John and Linda, scoring an almost 80% average against them over 13 boards. Nothing like demoralizing your closest rivals even if they are more than 6% behind you. The proles must be kept in their place.

Kathie and John also have far more masterpoints than any of the other regulars; without them the mean field strength would fall below 200 MP. In this case the geometric mean of 166 MP is a much more accurate indicator of the field strength. Not surprisingly Kathie and John are much better than the result of the field at a bidding and making slams (0.50 / session) though Cheryl Rankin and Carol Adair make an effort at 0.29 / session. But due to flighting and perhaps by sometimes flaggging themselves as Not Eligible (NE) in ACBLscore, John and Kathie did not haul in the most masterpoints. The Dusharmes won that race, collecting an average of 0.57 MP / session. But Judi Bunch and Hiroko Kitamura play more often and thus won the most masterpoints (13.60 MP) in this game during 2013.

There is a lot of payoff matrix data, an entry for every partnership-partnership interaction, over 400 interactions in the course of a year even for this small game. But many of the interactions only involve a few boards. The payoff matrix can be simplified by limiting it to the interactions between regular partnerships. However, this reduction still leaves us with 45 interactions. It helps to see the reduced results visually, as shown below.

Both axes list the partnerships in order of decreasing strength for partnerships who played at least 6 sessions in 2013. Each square shows how well the partnership listed on corresponding row does against the partnership in the corresponding column. The color scale runs from solid blue (30% or lower) to solid yellow (70% or better) with grey at 50%. White squares indicate partnerships that have never played any boards against each other. Pink squares indicate partnerships that can not interact because they have one or more players in common. The diagonal is always pink.

Move the mouse over the image to view the details for each square (matrix element). The hovering tooltip will show the names of the two partnerships, each partnership’s average against the field, the number of boards the partnerships have played against each other, and in bold the average results of those boards including an error. The average result shows how well the partnership on the row did against the partnership on the column. The matrix is anti-symmetric about the diagonal. Squares with a faint red X denote statistics based on relatively few boards, fewer than 10 in this case.

The upper right corner of the matrix is mostly yellow. This is because stronger partnerships usually have an advantage against weaker partnerships. Conversely the lower left corner is mostly blue. However, there are interesting exceptions, most notably the strong showing of Gary and Liz Piazzoni against Judi Bunch and Hiroko Kitamura.

### Over/Underperformance

Even a weak partnership might cause another partnership a lot of trouble by doing far better against that partnership than the difference in skill against the field would suggest should be the case. We could say that the weak partnership is overperforming against the stronger partnership.

The matrix below corrects for the difference in partnership skill, showing how much each partnership overperforms or underperforms against another partnership. The blue to yellow scale runs from -20% to 20% with grey at 0%. Move the mouse of the image to view the details for each square (matrix element). As before the partnership names and average percentage are shown. The over-perform / under-perform percentage is shown in bold. The ordinary percentage from the previous figure is also shown. Note: the previous figure also shows the over/under-performance statistics after ‘OU:’ as in ‘OU: 9.7%’.

The more yellowish and bluish square in the second matrix above are interesting because they indicate a pair that is strongly over/underperforming against another pair. The following table lists these relations in descending degree of payoff (or “exploitability”) where the pair-pair percentage is derived from at least 20 boards. Cnt is the number of boards that each interaction percentage based on.

Biggest Over/underperforming partnership interactions in the payoff matrix
Overperforming Pair Underperforming Pair Cnt OU%
Gary Piazzoni - Liz Piazzoni Judi Bunch - Hiroko Kitamura 26 16.46
Judi Bunch - Hiroko Kitamura Fred Goodsell - Dave Cleary 32 10.79
Judi Bunch - Hiroko Kitamura Dan Bloch - Richard Keplinger 23 10.43
Gary Piazzoni - Liz Piazzoni Fran Hunter - Doral Hunter 24 9.50
Fran Hunter - Doral Hunter Fred Goodsell - Dave Cleary 35 9.15
Thomas Ciolli - Jim Ciolli Judi Bunch - Hiroko Kitamura 40 8.32
Cheryl Rankin - Carol Adair John Lagodimos - Kathie Angione 91 8.11
Fran Hunter - Doral Hunter Linda Dusharme - John Dusharme 21 6.96
Roy Shepard - Tom Turner Thomas Ciolli - Jim Ciolli 49 6.93
Fran Hunter - Doral Hunter Cheryl Rankin - Carol Adair 94 6.50
Fred Goodsell - Dave Cleary Cheryl Rankin - Carol Adair 37 5.97
Fred Goodsell - Dave Cleary John Lagodimos - Kathie Angione 34 5.20
John Lagodimos - Kathie Angione Dan Bloch - Richard Keplinger 29 5.18
Cheryl Rankin - Carol Adair Thomas Ciolli - Jim Ciolli 52 4.93
Dan Bloch - Richard Keplinger Fran Hunter - Doral Hunter 39 4.87
Cheryl Rankin - Carol Adair Roy Shepard - Tom Turner 37 4.60
Judi Bunch - Hiroko Kitamura Cheryl Rankin - Carol Adair 73 4.58

The table gives us much to speculate about and yet it is still a lot to absorb. Part of the difficulty is that many pairs are listed multiple times. A graph may be a better representation.

Unlike the Social Network graphs, the payoff graphs are directed, i.e they represent flow, the transport of over/underperformance around the partnership network. An incoming arrow represents a payoff to a partnership; an outgoing arrow represents payoff from a partnership.

It should be noted that although these are directed graphs, they are not directed acyclic graphs (DAGs), an important and well studied class of graphs. Cycles are easy to spot. For example Judi Bunch and Hiroko Kitamura payoff to Thomas and Jim Ciolli who payoff to Cheryl Rankin and Carol Adair who complete the cycle by paying off to Judi Bunch and Hiroko Kitamura. So turns the wheel of exploitation.

## Eastlake Wednesday morning pairs

Wednesday morning is a new story. James and Shay Andrews are clearly leading this game with a 59.61% average, ahead of Sharon Gordon and Kathleen Hennessy (56.54%) and Barbara Schafer and Hiroko Kitamura (56.49%). Kathie and John bring up fourth place at 54.61%. The Andrews are clearly an established partnership and James Andrews finished 2013 at about 3500 MP which is quite a large holding for an Eastlake game player. Statistical arguments identical to those in performed in Payoff Matrix writeups for other games allow us to state with 94% confidence that the Andrews are a better partnership than Sharon and Kathleen and with almost 99% confidence that they are better than Barbara Schafer and Hiroko Kitamura. The greater confidence in the second case despite the very similar percentage of the second and third place partnerships is due to the more consistent results of Barbara and Hiroko (σ = 1.03%).

The matrices below are limited to pairs that played at least 10 sessions in 2013. The red X flagging remains at fewer than 10 boards.

Here is the Over/underperformance table where the pair-pair percentage is derived from at least 20 boards and OU ≥ 5 is shown. Cnt is the number of boards that each interaction percentage based on. Or view the graph. It is interesting that the top pair, James and Shay Andrews, has so many large inflows and outflows. This suggests their top position is not secure.

Biggest Over/underperforming partnership interactions in the payoff matrix
Overperforming Pair Underperforming Pair Cnt OU%
Sharon Gordon - Kathleen Hennessy Rose Vogt - Bjorn Syversen 41 11.49
Manu Chaganlal - Dan Bloch Alice Frades - Richard Schubert 28 10.87
Manu Chaganlal - Dan Bloch Francie Collins - Alice Hurley 21 10.36
Francie Collins - Alice Hurley Linda Dusharme - John Dusharme 28 10.24
Sandra Buffington - Judy Shepard Richard Keplinger - Donna Rafenstein 27 10.23
Alice Frades - Richard Schubert Laurie Dodson - Terry Moy 23 10.17
Rose Vogt - Bjorn Syversen Don Bonney - Janet Bonney 25 10.16
Gary Piazzoni - Liz Piazzoni Francie Collins - Alice Hurley 34 10.08
Alice Frades - Richard Schubert Jan Schottle - Judi Swift 27 9.32
Richard Keplinger - Donna Rafenstein Shay Andrews - James Andrews 25 9.08
Jan Schottle - Judi Swift Gary Piazzoni - Liz Piazzoni 35 9.03
Lois Richards - Liz Cogdill Manu Chaganlal - Dan Bloch 31 8.71
Fran Selder - RoseMarie Lofgren Lois Richards - Liz Cogdill 23 8.40
Manu Chaganlal - Dan Bloch Fran Selder - RoseMarie Lofgren 25 8.36
Francie Collins - Alice Hurley Sandra Buffington - Judy Shepard 33 8.24
Sharon Gordon - Kathleen Hennessy Alice Frades - Richard Schubert 22 8.06
Shay Andrews - James Andrews Barbara Schafer - Hiroko Kitamura 36 7.70
Fran Selder - Ellie Elphick Manu Chaganlal - Dan Bloch 27 7.51
Shay Andrews - James Andrews Cheryl Rankin - Donna Rafenstein 21 7.19
Jan Schottle - Judi Swift Don Sandweiss - Beverly Sanchez 23 7.19
Sandra Buffington - Judy Shepard Gary Piazzoni - Liz Piazzoni 55 7.15
Lois Richards - Liz Cogdill Rose Vogt - Bjorn Syversen 31 6.69
Gary Piazzoni - Liz Piazzoni Barbara Schafer - Hiroko Kitamura 38 6.56
Don Bonney - Janet Bonney Sandra Buffington - Judy Shepard 20 6.51
Gary Piazzoni - Liz Piazzoni Laurie Dodson - Terry Moy 21 6.46
Bruce Zissen - Jim Ciolli Shay Andrews - James Andrews 22 6.38
Linda Dusharme - John Dusharme Laurie Dodson - Beverly Sanchez 23 6.25
Fran Selder - RoseMarie Lofgren Shay Andrews - James Andrews 28 6.19
Jean Chene - Marilyn Wolf Manu Chaganlal - Dan Bloch 34 5.97
Manu Chaganlal - Dan Bloch Linda Dusharme - John Dusharme 41 5.73
Sandra Buffington - Judy Shepard Barbara Schafer - Hiroko Kitamura 33 5.63
Francie Collins - Alice Hurley Lois Richards - Liz Cogdill 24 5.62
Sandra Buffington - Judy Shepard Lois Richards - Liz Cogdill 25 5.47
Shay Andrews - James Andrews Jan Schottle - Judi Swift 40 5.20
Don Sandweiss - Beverly Sanchez Linda Dusharme - John Dusharme 23 5.19
Letha Couch - Beverly Stebbins Alice Frades - Richard Schubert 24 5.18
Francie Collins - Alice Hurley Alice Frades - Richard Schubert 24 5.15
Linda Dusharme - John Dusharme Jan Schottle - Judi Swift 35 5.04

## Eastlake Thursday afternoon pairs

Kathie and John again dominate this weakest of the Eastlake pairs games with a 65.71% average, way ahead of Barbara Schafer and Linda Dusharme’s 60.38% average and Judi Bunch and Martha Walker at 56.66%. But Kathie has always flagged her and John as Not Eligible (NE) in ACBLscore so they won no masterpoints for it. I think they only play in this game if it is necessary to prevent a half table.

The matrices below are limited to pairs that played at least 7 sessions in 2013. The red X flagging remains at fewer than 10 boards.

Here is the Over/underperformance table where the pair-pair percentage is derived from at least 16 boards and OU ≥ 4 is shown. Cnt is the number of boards that each interaction percentage based on. The corresponding flow graph is shown below the table.

Biggest Over/underperforming partnership interactions in the payoff matrix
Overperforming Pair Underperforming Pair Cnt OU%
George Vegter - John Dusharme Fred Goodsell - Ginny Potter 23 10.94
Barbara Schafer - Linda Dusharme George Vegter - John Dusharme 39 10.05
Laurie Dodson - Beverly Sanchez Francie Collins - Alice Hurley 25 7.96
Fred Goodsell - Ginny Potter Terry Cleary - Dave Cleary 22 7.72
Fred Goodsell - Ginny Potter Gary Piazzoni - Liz Piazzoni 20 7.40
Terry Cleary - Dave Cleary Laurie Dodson - Beverly Sanchez 21 6.64
Laurie Dodson - Beverly Sanchez Barbara Schafer - Linda Dusharme 36 5.62
Fred Goodsell - Ginny Potter Laurie Dodson - Beverly Sanchez 27 4.94
John Lagodimos - Kathie Angione Laurie Dodson - Beverly Sanchez 19 4.92
Kalpana Parikh - Kamal Parikh Barbara Schafer - Linda Dusharme 16 4.65
Jan Schottle - Judi Swift Barbara Schafer - Linda Dusharme 18 4.39
George Vegter - John Dusharme John Lagodimos - Kathie Angione 18 4.36

## Get the data

Download a zip file (1 MB) of all the tab delimited text files created by the Payoff Matrix software and used to generate the payoff matrix images above. For convenience, an Excel version of some files is also included. A filename such as Eastlake-2013-Wed-Mor-min-10-payoff-matrix.txt means the 2013 Eastlake Club payoff matrix data for the Wednesday morning session after restricting to partnerships that have played at least 10 sessions. If min-# is not included in the filename, no minimum session cut has been applied. The definition of each column is explained in the Payoff Matrix software documentation. The zip file also includes the images and the image specific JavaScript files.