FCFS "proof"

FCFS "proof"

Mar 12, 2010, 9:01 PM |

I have copied this explanation of the merits of a First Come First Served system for Team Matches in general and the World League in particular from one of the World League HQ forums. I copied them because I reckon I might need it again. Credit must go to Artfizz for the original idea.

(FCFS means that rather than the highest rated to join a given match get in, the first people to sign up get in. This is supposed to prevent the unfair pairings that eventuate when a large group plays a smaller one.)


First Post:

OK, here we go.

The following is a graph for the ratings of the players on the boards of a Team Match between Team Spain and Team Italy, the stats for which were provided by Kokino. As you can see, the statistics were taken slightly after the match started, but that shouldn't make that much of difference.

(you can see a graph of the players in order of their current ratings here, but that is not relevant)

Next, we see a graph of the players (current) rating distibution (including those who didn't get to play).

And finally, the Spanish figues in the above diagram minus the Italian ones, to get the differance:

That was part one: the graphs that we shall interprit. Stay tuned for part two.


Post two:

FCFS Proof Part II:

Some more stats:


Team Spain Team Italia
Number of Members 385 595
Average rating of all members 1554 1543
Number of Members signed up for Match 108 74
Ave rating of members signed up 1708 1787
Members who missed out on match 34 0
Ave rating of members who got in 1878 1787
Ave rating of members who didn't get in 1340              N/A


Part III soon


Post Three:

FCFS Proof Part III

We shall start with the stats from part II

First, I seems that even though Team Italia has more members, it was Team Spain who put in more people to play. Again I say well done to Kokino and their fellow admins for keeping Team Spain interested in the League.

Ave rating of members signed up 1708 1787

This is a very interesting statistic in many ways. For one, it shows that Team Italia on average put in a higher rated team than Spain. Unfortunetly for them, because Team Spain had the larger team, they got to cream off from the bottom their lowest rated people, bringing their average up to 1878, 101 points over the unchanged Italian one.

A second point that this raises is that both teams have average ratings more than 150 points under the average that they have in the match. this suggests that the lower rated players are getting disinterested in the League, as they play a hopeless game or none at all.

Finally, 34 people missed out on this match. They had an average rating of 1340 - the final pairing is 1613 to 1068!

I'm sorry, but there will be a part IV


Post Four:

FCFS Proof Part IV:

So where does FCFS come in?

One thing I haven't done the math for, but are pretty certain about is that rating bands wouldn't help in this match. While you could ensure that many at the bottom got a game, it would be at the expense of those at other stages.

Under FCFS, however, the people who missed out are the ones who turned up late, so to speak. Would you prefer this or FIDE's attempt to make latecomers pay a fine of several hundered euros? Wink

In theory, these latecomers will be distributed randomly over the players. No group will be unfairly left out, and those who are left out can just turn up sooner the next time.

Another thing about FCFS is that there only need be one match. We don't have any confusion nor can we have admins refusing to send multiple challenges.

Now, the significance of the second graph:

In theory (ie if we had enough data - the entire members of the groups would do it) the second graph should be what is called a Bell Curve. The point is that if the curve is in the same place for each team the match should be even under FCFS.

The third graph shows this in more detail. In a totally fair match (under FCFS) this graph would be almost completely flat, only having a slight bulge in the middle. The point is that the match would be fair no matter where the line actually was - near the top or at the bottom, not just at dead zero in the middle, the only fair match under the current system.

"Unfair" matches are still possible, of course, but only happen when the average rating of the team is the higher, rather than the team has more players, and in such a situation you could call that team the undisputed best anyway.

Such an, er, unbalanced match would be seen in graph three as a rough slope going from one extreme at the end of the higher ave rated team to the other being the lower rated team's increase in numbers ar the lower end of the boards. As you can see, the above match does not resemble that and therefore I would say that in a FCFS system the match would indeed be "epic" as would all the others.

I might add as a post script that FCFS would mean that a small team could overcome great numerical odds and even possibly win the League. You might not even need divisions and you could certainly have allot more than one team advancing at the end of each year.

Now, any questions?



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