## Masterpoints or Glory

### The S-factor

Published: November 23, 2009

During the 2009 Memorial weekend sectional, we offered a two session event, open to all but oriented toward the strongest players. The event (session 1, session 2) drew a strong field of 20 pairs with an average masterpoint holding of 2850. Alex Prairie and I, arguably the weakest pair and certainly the one with the fewest masterpoints avoiding getting slaughtered which I considered a success. Remove us from the field and average field strength would have risen to nearly 3000.

And what did the two session winners receive? Just 5.00 masterpoints. At the same time we ran separate
morning and
afternoon open pairs events. The top awards for the *individual* sessions were 8.50 and 6.50 MP respectively. However, the single session open events had more pairs. To make a fair comparison it seems appropriate consider the average award per player per session, i.e. to divide the total number of masterpoints awarded by the number of players and the number of sessions. The morning single session event had 48 pairs and awarded 92.18 MP, an average of 0.96 / player. The afternoon single session event had 36 pairs and awarded 75.48 MP, an average of 1.05 / player. The two session event had 20 pairs and awarded 44.62 MP, an average of 1.12 / player, or just 0.56 / player-session. This means the payout was nearly 50% less in the stronger and fairer event!

Stronger and fairer? Let’s consider fairer first. A two session event with a Mitchell movement has the potential to expose each pair to 75% of the field. With 20 pairs and nine rounds per session, each pair meets 14 of its 19 opponents, or 74% of the field. In a single session event with a Mitchell movement, each pair meets at most 50% of the field. With 48 pairs and 9 rounds, each pair meets only 19% of the field. Of course directors try to balance the field, but still some pairs are destined to slice through the soft underbelly. But greater field exposure is only part of it. When the overall awards are determined from 54 boards instead of 27, the luck factor is reduced regardless of the movement.

Was the two session event really a stronger field? It sure felt like it. But we can be more precise. The average field strength of the two session event was 2850 MP while the average field strength of the open sessions was 1986 and 2068 in the morning and afternoon respectively. While it is certainly true that masterpoint totals partly reflect longevity and frequency of play and are distorted by triple point charity games, there must be some correlation between masterpoints and skill level especially when averaged over a large number of players. Moreover, if we compute the geometric average instead of the arithmetic average the results are more dramatic, 2035 vs. 1059 and 1040. Arguably, the geometric average is a more accurate metric because the geometric average is lowered more by weak players. A high geometric average means there are not many pairs to beat up and gifts will be infrequent further reducing the luck factor.

On account of this seeming inequity, I contacted Butch Campbell at the ACBL tournament department. I thought perhaps that the lack of stratification in the two session event created the problem. Maybe an A/X stratification would address the issue. No dice. Butch said there was nothing we could do and explained the “S” factor. The total payout for a multiple session event scales as 0.5 * (S+1)/S where S is the number of sessions. For a two session event this works out to only 75% of the payout from two separate single session events. For a three session event it is only 67%. One way to view this formula is that each additional session is only worth half of a normal session. Why my computations show something like 52% instead of 75%? I think that strictly speaking it is the top award that is scaled by the S-factor as well as the number of pairs. Stratification probably explains the rest of the difference and the difference may depend on specific details, for example if a C pair wins overall, receiving the highest award (the overall), that pair wipes out the overall C award, reducing the total payout. Conversely if pairs tend to perform according to stratification, the payout will be maximized.

I find it somewhat concerning that Butch concluded with, “Sorry, I do not know the reasoning behind the structure for the S-factor.” Is our award system really so arbitrary? My guess is that the S-factor is a sort of inbreeding penalty — that if you can beat a field once, how much more are you proving by beating them twice? Maybe there is some sense to this but I think that at least up to two sessions, the increased fairness more than compensates. Perhaps it is time to rethink the S-factor.

I like the idea of a strong event and as tournament chairman for the January 2010 La Jolla sectional, I have pushed to include a two session event. But as explained above, you will have to choose between masterpoints and glory. Honestly, if you want masterpoints, you should play in the single session open events. But I hope you’ll choose glory.

Jan 20, 2010: Today I discovered an excellent website about masterpoint reform written by Robert Frick. I am in close agreement with nearly all his conclusions, most importantly the rationale behind his proposed formula for masterpoints. It is worth noting that his first principle is that the masterpoints awarded per person should not depend on the number of contestants, the same consideration that I am implicitly suggesting in computing this value above. But his additional principles are also very logical.