Reliability of Masterpoints

The "Illusion" that Team Events are More Reliable than Pair Events

Impression from the Data

The few tournaments I have looked at strongly suggest that the correlation between ability and outcome is higher for a Swiss Teams than a pairs event. (In a stratified field, B players are more likely to get an A award in a pairs event than in a Swiss Teams.) The difference isn't huge, but it seems to exist.

The Mathematical Factor of Number of People

A mathematical reason for this difference is this. A team has four players, usually of about equal ability. A pair has only two players. The addition of the two additional players increases the correlation between ability and outcome.

For example, compare Meckstroth and Rodwell to some good-but-not-great pair, which I will call the Smiths. Meckstroth and Rodwell will probably finish ahead of Smiths in a pairs event, and they will probably finish ahead of the Smiths in a team event. But they are more likely to finish ahead of the Smiths in the team event than in the pairs event.

However, a big part of this is that Meckstroth and Rodwell have Soloway and Hammon on their team. In the team game, even if the Smiths somehow play as well as Meckstroth and Rodwell, they are likely to lose because their team-mates, the Thompsons, are not going to play as well as Soloway and Hamman.

Now imagine the following, which I will call the "coupled pairs". The pairs game is run exactly the same way as before, except that at the end, Meckstroth and Rodwell add their percentage to Soloway and Hammon's percentage, and the Smiths add their percentage to the Thompson's. The winner is the team with the highest average percentage. Now Meckstroth and Rodwell (and Hamman and Soloway) are a lot more likely to beat the Smiths (and Thompsons).

Are Meckstroth and Rodwell more likely to beat the Smiths at the Swiss Teams, or the coupled pairs? We don't know. There are still a lot of differences between the two events and I don't have any data.

Past Ability Versus Ability That Day

Masterpoint awards should, as much as possible, relect ability that day. We don't want them reflecting some overall ability. We already know that Meckstroth and Rodwell are better than the Smiths. If we wanted masterpoint awards to be based on ability, we could give first place to Meckstroth and Rodwell and not bother playing out the hands.

That day, the Smiths might be better. Maybe they play well and Rodwell has a cold. Because they played better, they are more likely to beat Meckstroth and Rodwell.

But they are much more likely to beat Meckstroth and Rodwell if they are competing in a pairs event. If it is a team event, we still have Soloway, Hamman, and the Thompsons to consider. On average, Soloway and Hamman beat the Thompsons. That substantially increases the chances that Meckstroth and Rodwell will beat the Smiths, even though we have as a given that the Smiths played better than Meckstroth and Rodwell.

To be more precise, there is a nice correlation between ability that day and outcome, even in a team event. However, in the team event, there is less correlation between Rodwell's ability that day and the team's ability that day. What we really want is for Rodwell's masterpoint award to reflect his ability that day, not his team-mate's ability.

An Illusion?

This then is the situation.
1. The correlation between ability and outcome is higher for Swiss Teams than pairs events.
2. There is a mathematical reason for this higher correlation -- a team event has four players and the pair event has only two.
3. However, while this factor produces a higher correlation between ability and outcome, it does not produce a higher correlation between ability that day and outcome.

So yes, the Swiss Teams has a higher correlation between outcome and ability than the pairs event. Without any analysis, we would look at this data and conclude that the Swiss Team is more reliable. However, with this analysis, we know that this better correlation could be an artifact -- we could see a better correlation between outcome and ability, but underneath it all, there might be no better correlation between outcome and ability that day.

In the Muller-Lyer illusion, which you have all seen, there are two lines with flanking arrows, like >-------< and <------->. The flanking lines make the first line seem longer. If the lines are the same length and you don't know the illusion, you will think the first line really is longer. Once you know the illusion, you know not to trust your judgment. Once you have discarded your judgment, you can't tell which line is really longer.

It's the same for the reliability of Swiss Teams versus pairs. There is a mathematical factor increasing the correlation between ability and outcome but probably/not necessarily increasing the correlation between outcome and ability that day. If you don't know about this factor, you will look at the data and conclude that Swiss Teams are more reliable. If you know about this factor, you can distrust the data, but now you can't tell which is more reliable just from looking at this data.

The sister essay to this topic (Factors Influencing the Reliability of Masterpoints looks at particular factors influencing the reliability of team versus pair events. If anything, the advantage seems to go to the pairs event. So it is plausible that for ability that day, the pairs events are as reliable as the team events.