A New Tie-Break Method

I mentioned this idea in another thread - but I think its worth a separate discussion.

Every tie-break method attempts to discern the appropriate order of players within a score group by determining the relative value of their performance in a tournament. Different methods focus different approaches of doing this - and so different methods may produce different results.

Given the computer pairing era, there is an opportunity to create methods that in the past would have not been feasible. I think we should give thought to creating the following new method, where we allow the COMputer to indDEX the player rankings by using the other tie-break systems. This method I refer to as Comdex.

The Comdex method recognizes that all existing tie-break systems have positives and negatives. Therefore, under the Comdex method we look for AGREEMENT in these other systems with respect to a player’s indexed order of finish based on each system. (If desired, we can tweak this system by recognizing that some Tie-break systems seem to be more valid than others, and so we can weight the order, rather than using each order equally; additionally, weighting the systems, even slightly, seems to me to be more likely to break all ties on one shot, for reasons outlined below)

In current tie-breaks, the systems are used sequentially. A first system is used to break a tie, then if ties remain a second system, and then a third, and so on. In Comdex, we are using the various systems simultaneously.

So let’s suppose we start with the “standard order” of and do a VERY SIMPLE example. (Those of you with scholastic events know that we could easily have 10 or more ties in some cases - but the principles below would be the same.)

  1. Modified Median
  2. Solkoff
  3. Cumulative
  4. Cumulative of Opposition

Let’s assume we have 2 players, A and B, tie for first in a section with a trophy prize at 4-1. Let’s further assume that based on each of the standard tiebreaks the players finish as follows in their section:

A: 2, 1, 1, 1
B: 1, 2, 2, 2

Under Standard Tiebreaks - “B” would take the trophy. Comdex would say that A’s average finish was 1.25, and that B’s average finish is 1.75 - so by Comdex A would be ranked as 1, B as 2.

Further, we could decide to weight results. Let’s assume that we add "Average Rating of Opposition as #5; but we know this has some downsides (as described in the rulebook) So we could weight as follows:

1: 30%
2: 25%
3: 20%
4: 15%
5: 10%

Then with results:

A: 2, 1, 1, 1, 2
B: 1, 2, 2, 2, 1

We would get:

A: (.6 +.25 +.2 + .15 +.2)=1.4
B: (.3 + .5 + .4 + .3 + .1) = 1.6

So A would be ranked ahead of B again.

Weighting factors would have to be suggested by experience.

The idea here is simple: the players are INDEXED based on the results of each tiebreak system, and then the average Index determined - thus looking for agreement between systems.

And of course, this is all done withing the tournament management software.

Calculating Comdex based on the Unweighted Standard Order would seem to be the standard approach.

It’s not exactly a new system, but I discovered quite a few years ago the sum of the round numbers of losses plus half the round numbers of drawn games when compared to others with the same score will give the same result as cumulative and the differences will be the same. Compare someone who loses in the first round then wins four in a row with someone who had a perfect score before losing to the tournament winner in the fifth and final round.

The ComDex idea is interesting, I suppose. It’s not new, it’s just a combination of old. As such, it might be worth a look.

Bill Smythe

The only tiebreak method that makes any sense is performance rating based on either the opponents’ pre- or post-tournament rating. I’ll leave it to the statisticians to decide which is more accurate. Nothing else makes any sense to me.

Performance rating is a terrible measure, which is why the USCF no longer uses it except for someone’s first 8 games, when we basically have nothing else to go on.

Throw a really low or high rated player in the mix and the performance rating will be greatly affected.

Consider two players, both of whom are rated 1800 and score 3 out of 4.

Player 1 plays the following opponents:

W vs 1600
W vs 1800
W vs 1900
L vs 2000

Player 2 plays the following opponents:

W vs 1600
L vs 1800
W vs 1900
W vs 1990

Player 1 has a higher performance rating. Does that make any sense?

It should also be pointed out that this tie break method depends upon information the TD probably doesn’t have, which is someone’s exact pre-event rating. (Post-event ratings are even worse, as they won’t be available until after an event is rated.)

Also, what pre-event rating would you use for unrated players?

And of course both pre-event and post-event ratings can change due to a rerate.

I saw something in another topic on another forum decrying a TD who had apparently used Mr. Bachler’s method. The TD gave first prize to the player who had won the tiebreaks 3-2, apparently.

Alex Relyea