Tie-break theory

Running Chess Tournaments
1

One tie-break that I would love to see implemented more is 34E11 Average rating of opposition. I’ve seen too many times when simple human reason can show that player A has played tougher opponents than player B, but Modified Median gives the trumps to B (a lot of times due to A’s opponents withdrawing, having off-days, etc.). Tim Just gives the obvious detriment to this rule: that player A might beat player B on this tie-break by a statistically insignificant margin (maybe they are consecutive pairing seeds and each time player A plays an opponent 15 measely points higher).

My proposal would be for any computer-calculated tiebreaks to have this rule as the first tie-break, then followed by Modified Median, etc. IF AND ONLY IF, the rating difference is “statistically significant” (USCF decides a number - 100, 200 points? Someone else with more talent than I can figure out the best rating difference to be used as the standard). If the number is “statistically NOT significant” then tie-breaks should revert to normal.

One simple case:
Player A beats 1500, beats 1600, beats 1700, draws 1800.
Player B beats 1500, beats 1600, beats 1750, draws 2400.
With modified median, Player A will win on tie-breaks more than a fair percentage of the time, simply because of opponents’ more-or-less random results. Here Tim Just’s nicely worded phrase “Each seeks to discover the first among equals (34D)” would show to any layman that a statistically significant rating differential should take first precedence.

Limitations:

  1. To a small degree, computers are helpful.
  2. A strictly defined statistically significant margin needs to be endorsed.

Benefits:

  1. It makes sense even to laymen.
  2. If the margin is insignificant, it can just be ignored for the next step.
  3. It rewards/compensates having to play against superior competition, rather than simply hoping that superior competition will match their theoretical likely tournament results. USCF ratings are much more secure predictions of a person’s strength than a random Saturday performance outing.

I hope some good discussion follows :wink:
Ben Bentrup

2

I like this idea in principle. Let me suggest a scenario and get your input:

Scenario:Player A and B play in a tournament of four rounds, with each player beating all other opponents, but their own games end in a draw. Player A is higher-rated than Player B, but Player A ends up playing a higher average opposition rating.

Example:

Player A: Beats an 1900, Beats a 1950, Beats a 2000, Draws a 1940.
Player B: Beats a 1000, Beats a 2000, Beats a 2100, Draws a 2150.

For instance, I could picture this scenario occurring when Player A is the top seed, and thus plays the people at the top of the bottom half in the score group, while Player B is located just above the first-round cut line, and ends up playing opponents just above the halfway mark for all subsequent rounds.

Note that in Player A’s case, his average rating is 1947.5.
Note that in Player B’s case, his average rating is 1812.5.

This is almost the size of the significant margin in the example given (a little bit less), but is similar in that both cases were above the 100 rating point difference boundary, and below the 200 rating point difference boundary.

I would argue here that Player B has had a significantly better tournament than Player A: while Player A has not played a single player higher-rated than himself, Player B has done so three times and scored 2.5/3. Further, when excluding the first round results, Player B’s average rating is 2083.33, while Player A’s average rating is 1963.33, which is as statistically signifcant as the original results (again roughly).

How do we present a statistical anomaly like a first-round pairing from messing with a tiebreak in a situation like this?

3

Excellent points, WA!

First of all, the more I think about it, the more I would urge for a higher rating difference as the standard (maybe even 300+), but again, I am not the expert. The higher it is, the more likely it will be implemented in only clear cut cases.

With regards to superficially negative or positive point spreads, I agree that that would bust my first draft as stated. However, if college football BCS can use diminishing return principles so as not to reward beating up on the low-tier schools, some math genius should be able to construct something similar for chess. I imagine that it would go something like this as an estimate: whenever someone has a statistical likelihood of scoring 90% or greater against someone, for this tie-break purpose only you treat it as 90%. If I am rated 2500 (in my dreams) and beat a 1500 first round, I might get this tie-break credit as if he were a 2000 because a 2500 has still 90% likelihood of beating a 2000 (I just made the numbers up, I’m sure the actual numbers are much different.) Or in reverse, if I were a 1500 and have a 1% chance of beating some GM, i get tie-break credit at 10%, or 2000 (again, a made up number) for my loss during that round. However, should I have beaten him, I would get full 2500 happy-dance credit.

If some kind of diminishing returns prinicpal (if that is the right term) gets included, then probably you can safely lower the statistically significant margin.

It seems like this addition makes a computer more necessary for this tie-break. Still, in no way is that unfeasible.

Other ideas?
Ben Bentrup