Masterpoint Notes

by Matthew Kidd

A small blog on masterpoint issues.

Basing masterpoint awards on the strength of the field

On page 27 of the January 2011 Bulletin, the new ACBL president Craig Robinson says his plans include working on changes to the ACBL masterpoint plan.

Currently, the strength of the field is considered in only the crudest possible manner, e.g. awards in BCD event are less than those in an AX event (where the number of tables is also factored in). I think Mr. Robinson is moving in the right direction. Even a simple adjustment based on the geometric mean of the masterpoint of the players in a field would be a big step forward.

The first 1000 masterpoints are the hardest

It is no surprise that on average the more masterpoints you have, the more you gain per year. But what do the actual numbers look like and is there more to the story? The first figure below shows the average number of masterpoints gained for players grouped in each of 30 logarithmically spaced bins, six per decade. No one has yet crossed into the final bin starting around ~68,000, though Jeff Meckstroth and Mike Passell are very close. The first bin contains all players who started the year with less than 1 MP.

In order to get a handle on the impact of playing frequency, the data set is split into three components: players who played at least once every month (blue), played in 8-11 months (green), and in 1-7 months (red). Players who did not play during the last year, i.e. were not active, were excluded from the analysis. The lower stacked bar chart shows the number of players in each category in each bin. The ~35,000 blue players are the true “regulars.” Error bars are included for the regulars; they represent the error on the mean, i.e. the standard deviation of the bin divided by sqrt(N-1).

The most striking feature of this plot is the sudden steeping of the curve around 1000 masterpoints, highlighted in gold. This steeping suggests a qualitative difference in the players above that level. My guess is that after ~1000 masterpoints one has truly mastered the fundamentals of the game. Alternatively, it could also mean these players are fiends who play nearly every day of the week and attend many tournaments. But I do not lend as much weight to the second explanation because the steeping of the curve happens ~1000 MP rather than say ~10,000 MP; while it is true that 1000+ MP players are certainly enthusiastic, they are by no means largely pros. Approximately 600 players have more than 10,000 MP; ~32,0000 have more than 1000 MP and ~12,000 have more than 2000 MP. Taking the conservative cut of 2000 MP, there are perhaps 20 potential superstars (12,000 / 600) for each actual superstar, probably limited more by desire and other considerations, than raw talent.

Ah but to get to a 1000 MP, there’s the rub! The first thousand are the hardest; the 18% of active players with 1000+ MP are swallowing up 48% of the masterpoints. How many masterpoints should you expect in a year? That depends on your frequency of play. If you are a regular player starting with fewer than 10 MP, you should expect to earn about 40 MP. If you have between 10-1000 MP (silver highlight) you should expect between 40 and 95 MP. It is possible to be more precise by fitting a line to each region. However, a linear fit on a log-log plot is actually an exponential fit. This leads to the two formulas for the expected earnings per year where mp is the number of masterpoints at the start of a year, ln is the natural logarithm, and exp is the natural exponent.

expected mp earnings = exp( ln(mp) * 0.1919 + 3.2170 )     for players with 10-1000 MP
expected mp earnings = exp( ln(mp) * 0.7223 - 0.4755 )      for players with 1000+ MP

Are District 22 players different? Not really. The purple line shows the D22 regulars. It tracks the blue curve quite closely except where the statistics are small.

Analysis details: The analysis period was from masterpoints recorded at the start of October 2009 to those recorded at the start of October 2010. This period is slightly impacted by the curtailment of triple point charity games which went into effect July 1, 2010. It will be interesting to regenerate this figure a year from now to fully understand the impact of that change. Because I was missing one of the monthly reporting files, a regular player is not actually someone who has played in 12 of the last 12 months but rather someone who has played in all 12 of the last 13 months for which I have activity data; the meaning of 1-7 and 8-11 months is similarly altered. This detail should have negligible impact on the results and does not affect the calculation of total masterpoints gained for the year.

The ACBL tracked about ~289,000 player numbers as of October 2010 but only had around ~165,000 members. Presumably the additional ~124,000 player numbers are retained in case players decide to rejoin the ACBL. Of the ~165,000 members, only ~138,000 (84%) played during the last year. Around ~9,000 active players were excluded from consideration because they were not members during the entire period examined either because they joined the ACBL part way though or dropped their membership. 82 players were excluded from consideration because they lost masterpoints during the examined period. I don’t know how these individuals lost masterpoints. Perhaps it was due to a combination of scoring revisions, administrative errors, and the use of out of date versions of ACBLscore with the wrong masterpoint formulas. Some may have been penalized for cheating. 60 players were excluded because their gain in masterpoints was due to transferring their lifetime accumulated points and/or achievements from another bridge organization to a roughly equivalent number of ACBL masterpoints. In some cases the transfer is obvious, for example a gain of 5000+ MP. However, to automate the process, I assumed any player who gained more than 120% of the masterpoints achieved by the 2009 Mini-McKenney winner of the appropriate bracket, was a transfer.

In any given month ~93,000 (56%) players are active. The number of months per year that active players play is shown in the histogram below. I am using the number of months in which a player plays as a surrogate for the frequency of play because it is the data I have available. I do not have direct access to the ACBL database. It would be interesting to regenerate these results using the actual number of sessions per player and possibly with distinction between club and tournament play.

From October 2009 to October 2010, the ACBL gained ~15,000 members and lost ~8,000. Of the members lost ~1,800 died, ~1,700 had never played, and ~5,200 had not played during the last year. There may be some overlap between the categories, particularly the first and the third. As for the ~27,000 players who did not play during the last year, some had never played, e.g. they had received a student membership and never used it. Others may be on their way to dropping their membership and still others may no longer easily be able to play anymore but still enjoy receiving the magazine and continuing to be part of an organization in which they have long held membership.

Download plot data as tab delimited text.
Download plot data in Excel format.

Masterpoint inflation reversed

The impact of the new rules curtailing triple point charity games which went into effect July 1, 2010 is beginning to show up in the masterpoint statistics. The plot below shows the total number of masterpoint awarded each month from August 2009 though September 2010. These numbers are based on the reporting released around the 6th of each month; thus the September bar represents matchpoints recorded between September 6, 2010 and October 6, 2010. Since clubs are often a couple of weeks behind in reporting masterpoints, it is only now that the full impact of the new regulations becomes apparent.

Compared to last September, masterpoint awards are down 24%. Compared to the 2010 average before the new regulations went into effect masterpoint awards are down 21%. Since both clubs and tournaments award masterpoints and the new regulations only affect clubs, club masterpoint awards have probably fallen at least 30% though I do not have the numbers to say this conclusively.

The data show a few other curious features. I don’t know what explains the Dec to Jan discontinuity. Maybe people play a lot of bridge during the holidays to escape their in-laws and then get busy in the new year and can not play as much bridge. Hopefully, they are not resolving to cut back on bridge though if they are the resolutions are being broken about as quickly as any other New Year’s resolution. The discontinuity could also be explained by a reporting issue; perhaps clubs are extra careful to get up to date at the end of the year even if they are a couple of months behind. Ignoring the discontinuity, the awards during the first half of 2010 already seem lower than the second half of 2009. Maybe some other change went into effect that I don’ know about. Finally the similarity of the October 2009 and November 2009 peaks is a data massaging artifact because I only had the delta between October and December and simply divided by two to generate monthly data.

Towards a Rating System

The June 2010 issue of the ACBL Bulletin contains a letter from Rona Goldberg in New York, who proposes replacing the masterpoint system with a rating system.

I basically agree. Moreover I have a decent technical understanding of the how the chess rating formulas work and I have tracked down the statistician, Mark Glickman, who probably knows more than anyone about the United States Chess Federation (UCSF) rating system and a hell of a lot about rating systems in general. I’ve been thinking over a few details that I would like to bounce off him when the they are more fully baked.

Unlike chess, bridge has the added complication that the fundamental competitive unit is usually a pair rather than an individual and yet of course we seek to rate individuals. One approach would be to simply rate established pairs and leave it at that. This is computationally feasible and would by itself be interesting. Maybe San Diego could have the Oakley-Walters Top 50 list… or should the list be named differently?

I think there are two fundamental approaches to determining individual ratings, what might be termed the forward and backward approaches. The forward approach starts with individual ratings which adjust depending on the implied strength of the partnership versus the implied strength of the opponents and the results. I think this is the approach the online services generally take; certainly it was what OKbridge did in its early days, in the early 1990s when I dabbled in online bridge, and it is computationally relatively simple. The problem is that the implied partnership strength is just a guess based on the typical performance of a pair of players with Rating A and Rating B, even if the formula is more sophisticated than the average of their ratings. Such a system does not account for individual partnership synergies, positive or negative. And that can lead to practical problems; for example stronger players who will not play with weaker players because they feel their rating will drop even given the rating system’s accounting for the expected performance of their partnership.

The backwards approach is to infer individual ratings from partnership ratings. This amounts to solving a very large but sparse system of over-constrained equations, which is typically done by using a least squares fit. If the implied average partnership rating is assumed to be a linear function of the individual ratings, we enter well trod mathematical territory. How well would this work in practice and is it computationally feasible for all ~160,000 ACBL members? I don’t know yet. But I am considering running some simulations in Matlab with different assumptions about the distribution of the number of regular partnerships per player and the general network topology, i.e. the extent of non-local interactions. Non-local connections, which are helpfully promoted by sectionals, regionals, and nationals, are important for establishing a globally meaningful ratings. If the calculations look plausible on say a $5000 dual quad core box with 48 GB of memory, which the ACBL could readily afford, it would be worth trying to get the ACBL to perform the calculation using real data.

Should a rating system replace the masterpoint award system? Probably. But I wouldn’t hurry to do it as Ms. Goldberg suggests. It’s not computationally burdensome to run the old system in parallel with a new system for a few years. We can afford the luxury of easing into a rating system as the quirks are ironed out.

Rex Latus Speaks Out Against Excessive K.O. Team Awards

In the June 2010 issue of the Contract Bridge Forum, Rex Latus, the District 22 President, reviewed masterpoint history, masterpoint inflation, and the recent curtailment of the triple point charity game madness. He noted in part the following:

Then he went on to address the excessive awards for K.O. Teams:

I’m happy to see Rex taking on the other big masterpoint distortion. Although the definition of a level playing field may seem subjective, Robert Frick has done some serious thinking on the matter and stated the principle that, “the total number of masterpoints awarded should not depend on whether they [the players] organize themselves into teams or pairs. They are not suddenly better bridge players, or more deserving of masterpoints, just because they decide to play teams rather than pairs.” This seems obvious to me. He notes in part:

Since Mr. Frick’s website appears to be a few years old, his calculations may be slightly out of date but qualitatively the problem is still very much the same.

Deep down I think the ACBL knows what it needs to do. And there are clearly ACBL members who grasp the principles and mathematics behind a logical award system. It is just a question of whether the ACBL finds the willpower to tackle the problem head on.

Why did communism collapse? Was it the economic punishment exacted by the arms race with the U.S. (the Jeane Kirkpatrick school of thought), the U.S.S.R.’s hard currency crisis when Saudi Arabia flooded the world with cheap oil in the 1980s (see Gaidar, 2007), the inability to compete technologically while restricting information flow? All these reasons were probably contributing factors. But in part many people seemed to have simply stopped believing in the system. Even the leadership. Masterpoints should not be allowed to suffer the same fate unless they are to be replaced with something better.

Triple Point Charity Games Curtailed

The ACBL finally took action on the triple point charity game distortion at the Reno NABC (March 2010). Hooray. The following is excerpted from Ken Monzingo’s remarks, published in the May issue of the Contract Bridge Forum and also on his website.

Ken’s comment that, “neither of those extremes is viable” is curious. What exactly would happen if the ACBL went cold turkey? Would people really stop playing? Yes, the Junior Fund and International Fund, which support bridge activities widely seen as desirable, would have to be funded in some other manner, either by a direct increase in dues or more stealthily by raising sanction fees. But that seems more desirable than a major distortion in the award system.

At times, discussions of masterpoint inflation recall those stories of one’s grandparents about having to walk uphill each way in the snow to and from school. Moreover, in principle the inflation could be calculated quite accurately year to year and used to calculate “real masterpoints” just as economists calculate real dollars indexed to a given base year. I even suggested this once to Richard Oshlag, who is responsible for the databases and backend web services at the ACBL. He thought it was a fine idea though spending time on it is not his call to make.

But triple point charity games introduce a fundamental inequity not across time, but rather amongst clubs. For example, how much meaning does the Ace of Clubs ranking have if it turns out that most of the winners picked up most of their points in charity games? Maybe those masterpoints should be recalculated as ordinary club awards for the purpose of this ranking. But the more one attempts to correct for an inequity piecemeal, the more one wants to tear down the entire edifice.

Triple point charity games also kick off an arms race between clubs. If one club runs frequent charity games, other clubs come under pressure to do the same despite their principles, lest their attendance fall. Yet in the end when all clubs have caved in, no one is better off than before because the value of masterpoints is relative. Meanwhile tournaments lose some of their luster because the charity game awards are 70% of a sectional award. Actually someone is better off than before, namely the wealthier regions whose players can readily afford the extra $1 per game. It’s easy to scoff at this if you have lived in wealthy San Diego for a long time but I have played bridge in other parts of the country where I can assure you that each dollar increase in card fees caused serious clamoring from people on fixed incomes.

I have no trouble with the ACBL engaging in charitable activities but those activities should not be entangled with the award system.

2010 San Diego Regional Statistics

For the second year in a row I have worked with Ken Monzingo, Betty Bratcher, and Sergio Mendivil to post all the results from the San Diego regional online (2010, 2009) with integrated hand records using ACBLmerge. This is a significant but manageable task though it always turns out to be a bit more work than “anticipated” because I end up making improvements to the program.

One new thing this year is the computation of field strength. Since the masterpoint system is really an award system rather than a rating system, one might question how meaningful such statistics are. However, despite the entanglements of longevity, frequency of play, and grade inflation (especially triple point charity games), masterpoint holdings must have some correlation with skill level, especially when averaged over all players in an entire event. And in a Rumsfeldian sort of way it is the system we have if not the one we want to have.

Still, should one use an arithmetic mean (the ordinary average), a geometric mean, or something else entirely? There is no perfect answer but the first two have the advantage of being easy to compute so I presented both of them. But intuitively I feel the geometric mean is more meaningful than the arithmetic 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 fact that the histogram of masterpoint holdings on a logarithmic scale for tournament attendees (see below) is approximately Gaussian (bell curve shaped) lends support for considering the geometric mean. Notice Jeff Meckstroth and Eric Rodwell filling in the bin centered at ~56,000 MP. Arguably to get a feeling for the entire population, the histogram should be calculation for player-sessions rather than players. This is done in the second plot where the distribution shifts to the right because on average the stronger players play more sessions. This plot is also approximately Gaussian. For comparison consider the logarithmic distributions for all ACBL players ever and all ACBL players who have played during the last two months, the latter constituting 66% of the current membership of ~164,000. Both distributions are quite far from Gaussian.

Note: as a practical matter, all the masterpoint distributions below exclude players with fewer than 1 MP.

February 2010 Bridge Bulletin Letters

As if on cue, the February 2010 Bridge Bulletin arrived two days after writing the previous entry and has five letters to the editor touching on masterpoints and the meaning of the life master rank.

Lou Stern suggests that passing a test or series of tests should be a requirement for the gold card. Henry Francis reminds us what a herculean task making life master once was. Frank Walsh notes that ~50 years ago he received a club rating point slip for 0.06 MP for coming in third; this year the same result was worth 1.50 MP in a club charity game. He suggests a ~7500 MP requirement for Life Master would rollback the clock, accounting for masterpoint inflation. Dennis Cohen also cites masterpoint inflation as a major shock when returning to bridge after a 17 year hiatus.

Masterpoint Reform

As a lead up to the 2010 January sectional, I wrote a couple of articles about the ACBL reward system (Masterpoints or Glory, Against 499er, 799er, 999er Events). Since then I found Robert Frick’s masterpoint reform website that covers the matter in detail. Mathematically inclined visitors may wish to head directly to the page titled A Formula for Masterpoints. If you care about this issue, bear in that we have a new president, Rich DeMartino, at the ACBL. Now is a good time to speak up.