unless your opp (for the remaining games to be played) will have a sos higher than your ending sos then they will NOT hurt you (they will in fact help). In your example (I assume your SOS was around 56-57%) as that is likely what it owuld have been for you to finish above players and below players, your opp would have had to go 3-1 over their next 4 games in order to help your SOS. That seems pretty unlikely that someone who started out 0-2 will someohow make a rebound and go 3-1 over their next 4 games. I know that there are certainly a chance it could happen, but in general it will not happen.

We can find a scenario no matter what system we create that will have the wrong person make the playoff. We just need to find the one that is wrong the least. Chess has been using a version of SOS for 100+ years and MTG has been using our exact copy of SOS for nearly 20 years (with millions of dollars on the line over the course of that time).

--------------------------------------------------------------------------------
Buchholz (FIDE) or Solkoff (USCF)
This is the sum of opponents' scores. The idea is that the same score is more valuable if achieved against players with better performances in a given tournament. Looks like an ideal tie-breaking method and has been used since the Swiss system was invented. However it has some weaknesses which are addressed by other methods (see Median-Buchholz, Progress, Berger).

Back to Index


--------------------------------------------------------------------------------
Median-Buchholz (FIDE) or Median (USCF) or Harkness (USCF)
Same as above but discarding the highest and the lowest opposition's scores.

Its idea is to eliminate distortions in Buchholz values caused by taking into account games against run-away winners and bottom placed players.

Back To Index


--------------------------------------------------------------------------------
Modified Median (USCF)
Same as Median-Buchholz "for players who tie with even scores but modified for other scores to disregard the only the lest significant opponent's scores. The lowest scoring opponent is discarded for tied players with plus scores and the highest scoring for tied players with minus scores.

For tournaments of nine or more rounds, the top two and bottom two scores are discarded for even score ties, the bottom two scores for plus score ties, and the top two scores for minus score ties." (USCF Rules)

Back To Index


--------------------------------------------------------------------------------

PRINCIPLE: Player's Progressive Score



--------------------------------------------------------------------------------
Progress (FIDE) or Cumulative (USCF)
Calculated by adding points from a progress table eg if your scores were: Win, Loss, Win, Draw then your progressive scores are 1, 1, 2, 2.5 and your Progress tie-break value is 6.5

This is an attempt to put a higher value on scores which were achieved by scoring better in the initial rounds than by finishing from behind. It is common knowledge that the latter is usually much easier to achieve.

The problem is that the order of the Progress tie-breaks is known before the last round (last round scores will change the actual value but not the order within a point group). This may encourage some undesirable tournament "tactics" in the last round.

Interestingly the USCF Official Rules of Chess considers the above feature of the system an advantage on the grounds that it "avoids the problem, comon in Median and Solkoff, of having to wait for a lengthy last-round game between two non-contenders to end for top prizes to be decided".

Back To Index

I copied over some other alternatives (from wikipedia) that are basically SOS (one drops lowest score which is interesting but can punish a player who didn't play any weak opponents) and one drops lowest and highest (which seems interesting on the face of it) and the progressive method (but that seems to penalize people for losing early and since you don't control your matchups at all seems interesting but bad to penalize someone for losing to the 6-0 in the first rd so they are in the "losers" bracket all day long)

The NFL for example (once you get past head to head has conference records next "which we don't have) but then counts strengths of victories more than overall SOS. From my understanding this is what we want to avoid as it hurts the guy who played the 0-6 guy rd 1. It rewards you for beating players with good records but penalizes you for beating players with nad records and we cannot control how the matchups will be nor how any person will fare in later rds.

1.Apply division tie breaker to eliminate all but the highest ranked club in each division prior to proceeding to step 2.
2.Head-to-head, if applicable. (For ties between 3 or more teams, this step is only applied if there is a head-to-head sweep; i.e., if one club has defeated each of the others or if one club has lost to each of the others.)
3.Best won-lost-tied percentage in games played within the conference.
4.Best won-lost-tied percentage in common games, minimum of four.
5.Strength of victory (record of all the teams they defeated that season).
6.Strength of schedule (record of all the teams they played that season).

1-4 don't really apply to us at all as we don't have conferences and don't play enough games to have a significant number of common games (esp between all tied entrants).

Wow - I am impressed Jason. Obviously you have pulled up a lot of info here. It's actually a bit overwhelming. I am trying to sift through it all in my head.

Couple initial thoughts:

1. We have a unique set of circumstances for our game, so we need to find something that works for us specifically, which either means creating it from scratch, or amending another system.

2. Some of them talk about keeping specific scores from games. I think that opens up something we don't want to get into for SWM. I can only imagine having to report and keep track of the score of each game (214 to 86, or whatever), and how that could get sticky. Something I don't think we should ever do.

3. I don't know how many rounds a typical chess tournament is, but it seems to me that full SOS would get more valid with more rounds. 6 isn't really enough (I think you pointed that out before).




So - Let's simplify our goals, and let's find the easiest path to get to them.

I know I keep going back to it, but I strongly believe this:

1. We don't want wins vs lesser players to weigh as heavy of a detriment as they are currently. How do we achieve this?

2. Higher positive weight should be given to beating better opponents

3. Higher negative weight should be given to losing to lesser opponents

Maybe it's an equation such as:

Average of opponents records who you lost to AND opponents with your same record or better who you beat.

We could call it "Modified SoS"

for each tied player you take the records of:
(opponents player lost to)
AND
(opponents at the tied levels record or higher which player beat)

Add them together.

So at WI - with this equation:

Jonny gets a score of (5-0 Tim) + (3-2 Bill) + (4-1 Matt) = 12-3 (80%)
Jason Gets a Score of (5-0 Tim) + (4-1 Jake) + (3-2 Bill) = 12-3 (80%)
Bill gets a score of (5-0 Tim)+ (3-2 Jason) + (3-2 Jonny) = 11-4 (73.33%)

Bill drops, and we recheck H2H with Jason and Jonny (they didn't face each other) so we move onto full SoS for Jason and Jonny.

This makes sense to me. In plain terms, Jonny beat 1 opponent that had 1 game better record than Jason's top win. Johnny also lost to an opponent that had 1 game worse record than Jason's lowest loss.

So this weighs them equally. If Jonny had lost to a 2-3, then he would have been edged out. If Jason had beat a 4-1, Jonny would have been edged out.




This seems as valid as anything, since it's really what we're after. And fairly simple too.

I like this since we don't have to answer the question, "Which do we weigh more, losing to lesser opponents or beating better ones?"

It's all in the same equation!

Heck this is all we need after H2H before SoS. I think I really like this simple equation.

It achieves my personal 3 goals:

1. We don't want wins vs lesser players to weigh as heavy of a detriment as they are currently.

2. Higher positive weight should be given to beating better opponents

3. Higher negative weight should be given to losing to lesser opponents

Maybe a multiplyer of sorts.

I'm not sure the exact numbers that would work best, so this is just for discussion.

At the end of a round, players are "weighted" by a multiplyer, that increases and decreases each round based on their ranking at the end of that round (by ranking, I'm referring only to points, you won't need to differentiate between ties for this).

So for example, at the end of round 1, all 3pt winners are worth 1.2, 2pts - 1.1 and 0pts - 1.0.

At the end of round 2:
6 - 1.3
5 - 1.2
3-4 1.1
1-2 1.0

and so on until the end of round 6 when it might look like this:
16-18 - 1.5
13-15 - 1.4
10-12 -1.3
7-9 - 1.2
4-6 - 1.1
1-3 - 1.0

Then you would take all of your opponent's wins only and multiply by the number. That number is then used as the denominator for determining SoS. The idea would be that having played higher point scoring players would further increase your total wins (which is the denominator) thereby inflating SoS since the total number of games (divisor in SoS) would not change. This would represent an "enhanced SoS" component that would put more emphasis on higher end games I believe.

Latest suggestion from me (it's actually gotten simpler)

1 Score
2 Record
3 H2H
4 Modified SoS: Record average of <opponents you lost to> PLUS <opponents your same record or better who you beat>
5 Full SoS
6 Roll-off

I kinda see where you're going, but at some point it's assigning an arbitrary value without knowing how accurately we should weigh it. It seems pretty complicated to figure it out (during a tournament) much less implementing it (the initial system - ie figuring out the multipliers)

Tim, I like the idea behind your system but I see a couple things we need to possibly address with it.
1.Your system would seem to punish people for bad losses (ie the kid who rolls 3 Disintigrations against you and loses every other game of the tourney or the game where you can't buy a save) and I am not really sure if you should get penalized additionally for a loss besides a loss. Also if you lose to someone who finishes higher than you, you should have lost to them in the grand scheme of things. (ie when a 10-5 nfl team plays a 5-10 team we expect the 10-5 team to win) so you seem to also be punishing people for achieving their respective results.

2. Are you talking about taking counting wins against tied record or higher or tied points or higher because there could be some interesting interactions if someone beats other players with tied records but not tied pts

3. Just thought of this while writing the last one and it's biggest detractor.
Lose rd 1 to 5-1
Lose rd 2 to 5-1
win rest of rds pushing that person to at least 3rd loss
so my cool new tiebreak is (10-2) which % wise will be better than anyone else's by default.

Here is a question, should it matter in what round you win your games? Does the progressive type system as used in one of the chess formats have a chance at working for our game? or would it penalize players who lost in the first rd (to one of the 5-1 or to the 6-0) too much?

Tim,
I am just trying to find what the best system for us is. By best I mean the one that will get the correct person to the playoff most of the time as there is no system for tiebreakers that will work 100% of the time. Just doing research to see what other things that have ties similar to ours use.

Does anyone else have any of the other regional info available to analyze? I would hate to create a system that makes WI work out (personal oppinion is that it should have been Jonny) only to find out that WI was situation that actually broke the correct system (which may be the case).

I totally agree and I think we have the same goal.

I think Kokomo IN had all the results posted, but it wouldn't change much since only 3-1s or better made the finals.

This is true to a small degree, but I am actually OK with that. Someone who lost to the 1-5 kid (IMO) deserves to lose IN A TIE to someone who only lost to the 5-1 and 6-0. (More often than not SoS will show this anyway, but I'd rather catch this end than the other)

I think IN GAME luck will always be a factor, and is more valid than OUT OF GAME luck. Meaning if the kid rolls 3 disintegrations, that sucks. But it's still more valid to be weighed negatively IMO than getting screwed by beating chumps.

In WI you lost to a better opponent (by a degree of 1)

Jonny beat a better opponent (by a degree of 1)

So then drop down to the next tie-breaker, full SoS and Jonny wins.



Actually this isn't true. We're talking about 4-2s for the most part here, which means their level is 66.66% (4 out of 6 games won). If you lose to the undefeated then you average in a 100% to your score, thus it helps you. If you lose to the 5-1 you average in a 83.33 to your score also helping you. If you lose to a 3-3, you average in a 50%, which hurts you slightly. Lose to the 1-5 guy and yes, in this tie-breaker it hurts you. But I think that is valid.



Totally valid question, and I don't know the perfect answer. It almost seems like a coin flip, but I am leaning toward RECORD vs POINTS. Everything else is based on record (SoS), why switch here? Doubt it would change much either way.



if someone went 4-2 and only lost to two 5-1s, their tie-breaker should be strong. With your scenario they probably would have had to beat a 4-2 in the last round, so that would make them 14-4 (77.77%), still strong.

Player B beat a 5-1, and lost to the 6-0 and a 5-1, making them 16-2 (88.88%)

Player C lost to a 4-2 and the 5-1 and beat a 4-2, making them 13-5 (72.22%)

Player D lost to the 5-1 and a 3-3, but beat nobody at the same level or above, making them 8-4 (66%)

Ranking them B, A, C, D seems totally valid

I just think in the scheme of things it feels more right to say, "I missed the finals because I lost to weaker opponents" or "I missed the finals because the other guy beat better opponents".

-rather than-

"I missed the finals because I was unlucky to be paired with weak opponents that I thumped."

This got me thinking. Maybe we should not reward for beating someone at the same level. It can just be neutral.

So instead of averaging in records of <opponents your same record or better who you beat>
we simply average in records of <opponents with a better record who you beat>

So the same scenario in my last post would look like this now:

Player A lost to 5-1 and 5-1 (and beat a 4-2 in the last round - not counted here), so that would make them 10-2 (83.33%) <vs .77%>

Player B beat a 5-1, and lost to the 6-0 and a 5-1, making them 16-2 (88.88%) <same>

Player C lost to a 4-2 and the 5-1 (and beat a 4-2 - not counted here), making them 9-3 (75%) <vs 72.22%>

Player D lost to the 5-1 and a 3-3, but beat nobody at the same level or above, making them 8-4 (66%)

Ranking them B, A, C, D - same rankings here, but it seems a little more accurate.


This way a player cannot be hurt by beating another 4-2, where if we included it there are rare cases where it could. Good catch Jason.


This makes the wording simpler still, also a bonus.

Modified SoS

Average records of:
a players opponents with lesser records who they lost to
AND
a players opponents with better records that they beat


I also realized that this whole system will really help Jedi Challenge and Sith Trials.

What we probably need to do now, is run a bunch of scenario's with the system. Where's Brad

My one concern would be if it's possible for a person to play only two losses better than they are, with a SoS of a 11-1 and end up at 4-2.

This would be by definition the person with the worst SoS of the group, yet this tie breaker would easily vault them into the lead.

The thing is, just because you played the top 2 players in the first two rounds (someone in the game will be this person) then went on to play a bunch of low ranked players, ending up in the very bottom 3-2 match up in the final round, you did not have a better day than the guy who went 3-0 before losing.

Agreed that scenarios are in order.

I do think the guy who only lost to two 5-1s and then worked his way up the losers bracket still had a better day than the guy who lost to a 4-2 and a 5-1. Or a guy who lost to someone worse. If someone lost to a 5-1 and a 6-0, they advance over the first guy. This all seems as fair as anything else.

I do see the concerns here.

Honest question - would it be better to separate the two (losses) vs (wins against greater), and weigh wins vs higher record opponents slightly more. That way in WI Jonny would have won the tie-breaker before even going down to SoS, since he beat a 4-1.

So for our purposes, since it's impossible to have beaten the 6-0, the only possibility is to have beaten a 5-1. So if you did that you get elevated. If not, onto the next tie-breaker.

If we did it this way, then we could add wins vs same record opponents next. That way if it were a 4 way tie, and nobody beat the other three, and nobody beat anyone with a better record, BUT if someone beat 2 out of the other three, they advance. That is as it should be (IMO).


So then it would be:

A. Number of games you won vs opponents with a better record than you

Then

B. Number of games you won vs opponents with the same record as you

Then

C. Average of records from opponents you lost to

Then

D. Full SoS

LOL - a bunch of nerds playing with math to come up with a system to rank a bunch of nerds playing their nerd game.

We RULE!

Believe it or not, this isn't all just circular arguments. I think we are making real progress towards an excellent solution. This is just the process that it will take. I like the brainstorming.

ran through this a couple more times at the shop, and came up with a couple more ideas.

1. SOS (but take out the first round entirely). Would penalize people for losing 1st rd but would take care of the problem of guy who beat the 0 fer in the first rd having a bad SOS. This actually makes sense as the first rd is the only rd you have zero control over who you play. Every other round your opponent is determined how you have done in the tourney.

2 nd idea. SOS against people you have beaten (minus the lowest 1) so basically in a tiebreak at 4-2 it would be comparing your top 3 wins vs all the other tied people's top 3 wins. This puts much more emphasis on who you beat (which you control in a sense) and because you drop the worst one doesn't penalize you for playing against a guy who goes 0 fer.

But yes, need to run through some scenarios and see if any of them actually come up with different outcomes than each other lol.

1st idea - Another problem with this one is if you face and beat a tough opponent in round 1. What if you beat a 5-1 in round 1? That doesn't get factored in? That sucks!

2nd idea - I like this better between the two. But it still doesn't hold you accountable for who you lost to, which makes this suggestion less valid IMO. Lose to chumps and it should factor in. I can see someone slipping through here that was not the best player.


It seems like a lot of these suggestions are trying to find a circuitous route to certain things, and in doing so making it more complex and creating loopholes.

I am thinking more and more that a simple direct approach is the way to go.


I will refer back to what I think the goals of the system are:

1. We don't want wins vs lesser players to weigh as heavy of a detriment as they are currently. How do we achieve this?

2. Higher positive weight should be given to beating better opponents

3. Higher negative weight should be given to losing to lesser opponents


Your first suggestion sorta will take into account #1 a little over half the time, but will frequently have the opposite of the desired effect. It is just too arbitrary to work IMO

Your second suggestion takes into account the worst cases of #1, but stops there. What if someone beats the 0-6 and the 1-5, along with a 5-1 and a 4-2? Let's say he only lost to the 6-0 and a 5-1. He is still getting screwed by that 1-5, and he is obviously a good player. So this suggestion somewhat does #2, but completely disregards #3.


Do you disagree with #3 as a goal?



I think the first step for us need to be to decide what the goals are of the system. What deserves merit, and what ranks higher in that merit hierarchy?

Jason, Bill, Brad, whoever else wants to chime in - I think we should each delineate this first and see where they cross over.