MCC Tournament Break Point Analysis
Author: Alan Hodge
March 7, 2000

These thoughts and recommendations are offered in connection with the question of where the break points should be for two- and three-section tournaments played at the MCC. They are my personal observations, conclusions and opinions. Supporting data from 1999 are represented in the following attachments:

Attachment 1: Distribution of Tournament Participants by Rating Range, a bar chart showing (a) distribution of members by rating range (Note: Member ratings are snapshot data as of November 1999 [I think]. Only members who played during 1999 are represented, not the entire membership of the club.), and (b) average number of games played per tournament by rating range (Note: Averages are based on ten tournaments only; the December tournament [short time control] was excluded.)

Attachment 2: Section Participants by Rating, showing distribution by section and rating range of participants in every 1999 tournament

Attachment 3: Analysis of Three-Section Tournaments

Attachment 4: Analysis of Big-Event and Two-Section Tournaments

General Considerations

§ The MCC Board decided that four-round tournaments should be three sections and that five- and six-round tournaments should be two sections. The issue is to determine where break points might be fixed in order to optimize the number and competitiveness of players in each section.

§ Some players habitually play up, including particularly a few serious scholastic players who are presumably being advised or encouraged by their teachers to play up. These players are included in the “played up” numbers discussed below; however, because they are expected to play up regardless of what the break points are, decisions about where to fix break points should be made irrespective of these players.

§ Some analysis is based on the distribution of active members (those who played at least one tournament during 1999). Obviously the club attracts non-members. Attachment 1 illustrates that generally speaking the distribution of non-members by rating is very comparable to that of members. Anomalies are the Master range and the 1700s (and, in the opposite direction, unrateds), where we attract non-members disproportionately to our member population. Accordingly I concluded that the distribution of members by rating is a valid representation of the distribution of all players.

Three-Section Tournaments

The distribution of members by rating range (see Attachment 1) suggests that break points for a three-section tournament should be (1) either 1800 or 1700 and (2) 1400. The rationale for these breaks is as follows.

§ Higher break point: The population of players above 1800 is so sparse that the open section must include at least the 1800s to be large enough to work for Swiss pairings. The 1700 range includes only two players, and so will not have great affect whether it is included in the open section or not.

§ Lower break point: The greatest concentration of active members is in the range 1300–1699 (36 of 82 total players). Two considerations favor putting the break point at 1400 rather than 1300. First, the 1300s are not needed to make the middle section workable, considering the base of 25 1400–1699 players. Second, 1300s probably are needed for the lowest section, considering that below 1200 the population again is sparse and is artificially inflated by a high number of players (especially unrateds) who play only a tournament or two and don’t return.

Attachment 2 indicates the frequency with which players play up, and Attachment 3 is an attempt to take this factor into account rationally.

§ Break points at 1900 and 1500 (January and September tournaments): An average of 7 players played up in the open, with ratings averaging 246.5 points below the break point. Significantly, players playing up represented 44% (14 of 32) of the players in the open section. If these players had not played up, the open section would have been below “regulation” size for a Swiss (12 and 6 players respectively for January and September). An average of 6.5 players played up in the middle section, with ratings averaging 103.0 points below the break point. These players were likewise necessary to make the middle section large enough (13 of 34, or 38%). Despite the number of players that played up, the lowest section was well populated (18 and 25 for January and September).

§ Break points at 1800 and 1400 (July and October tournaments): An average of 8.5 players played up in the open, with ratings averaging 223.4 points below the break point. Players playing up represented 38% (17 of 44) of the players in the open section. Once again, if these players had not played up, the open section would have been below “regulation” size for a Swiss (13 and 14). An average of 5.0 players played up in the middle section, with ratings averaging 86.5 points below the break point. However, in July 9 played up, whereas in October only 1 did. In July these players were necessary to make the middle section large enough. The lowest section had 15 and 18, barely sufficient on average.

The numbers of players playing up was not greatly different between the two sets of break points. In fact, the total number is the same; the difference is how players playing up are distributed between the open and middle sections. Nor is there a significant difference in the rating “deficit” represented by the players playing up: –246.5 for 1900 versus –223.4 for 1800, and –103.0 for 1500 versus –86.5 for 1400. The average populations of the three sections did vary significantly, however:

Distribution of Players by Section	1900/1500	1800/1400
Open Section	16.0	22.0
Middle Section	17.0	18.5
Lower Section	21.5	16.5

From the standpoint of optimizing competition in the higher sections, break points at 1900 and 1500 appear to be preferable.

One of the arguments put forth in favor of varying break points was that those players persistently at the low end of the section range would have improved chances to win prizes, because in some tournaments they would be just below the break point rather than just above it. The data suggest that this has not been a major consideration for players. With the break point at 1900, 5 players in the 1800s played up anyway, as compared with 4 who played in the middle section. With a break point at 1800, 3 players in the 1700s played up, as compared with 2 who played down, while 7 players in the 1600s played up, as compared with 6 who played down. (See Attachment 3.) Moving the break points has not clearly not caused large numbers of players to stay in their “natural” section to compete for prizes. Presumably the players who played up were more attracted by the prospect of stiffer competition provided by Masters and Experts.

I attempted some consideration of lowering the higher break point to 1700. There are no actual data to consider, because 1700 was used as a break point only in two-section tournaments. I assumed that the rating deficit of players playing up would be comparable to those discussed above; I used –230.0 for the open section, and –95.0 for the middle section. I assumed that half the player population within these deficit ranges would play up on the basis that the lower break points would encourage some to play up who otherwise would not. Given the population of the ranges immediately below those breakpoints, I derived the following hypothetical section populations:

Distribution of Players by Section	1700/1400	1700/1300
Open Section	25.3	25.3
Middle Section	14.2	20.1
Lower Section	15.8	9.9

My conclusion is that dropping the upper break point to 1700 will produce results contrary to our intention, i.e., it will encourage more people to play up, thus both further “diluting” the rating strength of the open section and increasing its population, which probably will lead to unsatisfactory pairings (from a competitive point of view) and more shared prizes.

On the basis of this analysis, which is admittedly very limited, my conclusion is that the best break points for a three-section tournament are 1900 and 1500. There is some risk inherent in this conclusion, however, in that sections defined by these break points will work well only if players continue to play up in numbers comparable to our 1999 experience. I have already noted the apparent incentive of competition, but I would suggest as a further encouragement/assurance that an “under 2000” class prize be considered in the open section additionally to the three place prizes. Our resident Masters almost without exception claim the first and second prizes; third place provides something for the Experts (typically). A class prize for Class A players will reward their participation in the open section. Moreover, having two avenues for Class A players to pursue prizes (open section class prize and middle section place prizes) might attract other strong area players to the club (if there are any to be attracted within a reasonable drive radius).

Big-Event Tournaments

These are two-section, six-round tournaments (April and November) and the break point for both is 1800. Analysis of these is more speculative because they attract an unusually large number of non-members. I noted the following, however, from the 1999 data (see Attachment 4):

§ Numbers of players playing up was comparable to three-section tournaments (8 in April and 7 in November), and the average rating deficit for these players was also comparable or even a little smaller (190.3 for April and 249.9 for November).

§ Again, without the players who played up (8 of 26 in April, 7 of 26 in November), the open section would have been too small.

§ Players in the top ranges below the break point did not play up in unusual numbers; in fact, given the presence of additional Masters and Experts, I would have expected more to play up than did. For both tournaments, 4 players in the 1700s played up and none played down, but for the 1600s only 2 played up and 10 played down; in the 1500s, 4 played up and 7 played down.

§ Players were evenly split between sections in April (26 and 27), whereas in November 26 played in the open and 44 played in the under 1800. Given that the tournament was six rounds, 44 was not an unwieldy number of players, but in case we attract larger numbers in the future, perhaps we should be prepared to make either of these tournaments three sections.

My conclusion is that a break point of 1800 is appropriate for these tournaments. A lower break point, if a third section were justified, could be determined (if rules of published notice permit) at registration depending on the actual turnout.

Two-Section Tournaments

The February and December tournaments were excluded from this analysis. I believe the February tournament was intended to be three sections, but the low initial turnout made it necessary to combine the lower two sections. The December tournament used an unusual time control and drew an unusually small number of players; for these reasons I did not consider it appropriate to include it in an analysis intended to resolve issues pertaining to the club’s usual tournaments. The two-section tournaments considered are June, with a break point at 1900, and March and August, with a break point at 1700.

In the June tournament 14 players played up, including 5 of 7 players in the 1800s and the only 1700 player. In the 1600s, however, only 3 players played up while 6 played down; in the 1500s, 2 played up and 5 played down. The data indicate that 1700 was a pretty clear line of demarcation.

In contrast, only 6 players played up in March and 7 in August. For these tournaments in the aggregate, 2 players in the 1600s played up while 7 played down. In the 1500s 6 played up and 5 played down; in the 1400s, 3 played up and 11 played down. These data, in my opinion, confirm 1700 as a serviceable break point for two-section tournaments.

It is worth noting the population of the sections in these tournaments (see Attachment 2): 25 and 25 for March, 20 and 34 for June, and 20 and 40 for August. Once again, we should be prepared to make any of these tournaments three sections in case we attract larger numbers in the future.

Summary

My conclusions regarding break points are as follows:

§ Three-section, four-round tournaments: break points at 1900 and 1500, with consideration for adding an “under 2000” class prize.

§ Two-section, six-round (“big event”) tournaments: break point at 1800, but acknowledging the potential need to add a third section at a break point to be determined.

§ Two-section, five-round tournaments: break point at 1700, but acknowledging the potential need to add a third section at a break point to be determined.

§ Some thought should be given to defining the criteria on the basis of which a section will be split into two sections, and the method and policy for determining the relevant break point.

§ The above recommendations are made independently of any considerations particular to a club championship tournament.