Tournament scoring for variable nbr of players a the table

[Phoxtrot]

In a swiss or round robin system tournament, it seems normal to give 1 or 2 points per player you defeated at the table.
This gives:

• 2 players table: 1 point to the winner, 0 point to the second
• 3 players table: 2 points to the winner, 1 point to the second, 0 point to the 3rd
• 4 players table: 3 points to the winner, 2 points to the second, 1 point to the 3rd, 0 to the 4th
• 5 players table: 4 ,3 , 2, 1 & 0 points

And in case of ex-aequos, you simply add the points of the ex-aequo positions and divide the sum by the number of players ex-aequo.
So for instance, in a 5 players games, if 2 players are ex-aequo for the second position, they both get (3+2)/2 = 2.5 points

Or you can, of course, multiply everything above by 2.
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One problem comes if you can't fill all the tables with the same number of players because some player left or because you did not enforce that the number of participants be a nice number.

As it stands above, 3p tables give an average of 1 point per player whereas 4 players tables give an average of 1.5 points per player.

So if you want it to be fair you would need to somehow scale the scoring.
One intuitive way of scaling would be to give in a 3p table: 3 points for the winner and 1,5 point to the second (everything multiplied by 1.5)

That is not however the most generic, nor in my opinion the fairest.
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My suggested scoring:
* score 1 point for each player that is ex-aequo with you (yourself included) and 2 point for each player you defeat, divide the total by the number of players at the table.

This is simple, generic (no need to have a different code for each table size) and fair:
* no matter how many players there are at each table, the average points per player is always 1.
* Winning in a table with many players is better than winning in a table with fewer players.
* Being last in a table with many players is worse than being last in a table with fewer players

So for example, in the absence of ex-aequos:

• 4p table: 1st gets 7/4 = 1.75; 2nd gets 5/4=1.25 ; 3rd get 0.75 ; 4th gets 0.25 ; average = 1.0
• 5p table: 1st gets 9/5= 1.8 ; 2nd gets 7/5=1.4; 3rd gets 1.0 ; 4th gets 0.6; 5th gets 0.2 ; average = 1.0

If says the 2nd and 3rd and 4th are ex-aequos in that 5 players table: 1st get 9/5= 1.8; the ex-aequos each get (2+1+1+1+0)/5=1.0 and the 5th gets 0.2 and the average remains 1.0

Tell me what you think...

[Phoxtrot]

A side point is this:

Suppose we are in a swiss system and a table start with 4p but one players leaves "very early on" ("very early on" to be defined) or later in the game, what do you do ?

The simplest would be to score the game as a 3p table and give 0 points to the player that left (even if the scoring would normally give a few points for the last player)

If the player left late in the game, you can do the same or you could pass his turns and take him into account in the scoring (but still give him 0). This however only makes sense in games where passing makes sense and is kind of neutral. (For example, passing is not allowed nor neutral in say Carnegie as it would give some other players more turns where they can choose an action than other players)

If all players leave but one, I would just give that player the equivalent of winning a 2p game.

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Note that in my experience, most players leaving a tournament actually leave before it really start: they registered some time ago and forgot about it.

So it would be very useful in my opinion to spare a few minutes at the start of real time tournament and turn-based tournament with a global time per match limited to 1h or less to make people confirm their attendance and throw away the leavers before assigning the tables.
This would be especially welcome in tournaments with more than 2 players per table.

[teff71]

Excellent suggestion
I posted another one, 3 weeks ago, in "Tournament module 2020 UPDATES: Swiss system v2" thread:
https://boardgamearena.com/forum/viewto ... 3&start=73

[Phoxtrot]

Excellent suggestion
I posted another one, 3 weeks ago, in "Tournament module 2020 UPDATES: Swiss system v2" thread:
https://boardgamearena.com/forum/viewto ... 3&start=73

Interesting.
By the way, we disagree on some points. I do think that winning in a 5p game should be worth more than in a 4p game (when a tournament has mixed table sizes).

I don't know how it is currently on BGA but normally, for live Swiss systems, it is always the last table(s) (those with lower scoring players) that might have a lower number of players (lower by 1) at the table so that it doesn't matter all that much.

On a side note, I don't remember if I already made a suggestion for it but some games could benefit from other scoring systems for tournaments (and some time for ELO as well). Like the VP scoring for bridge matches where there is a non-linear scale that gives you victory points depending how much you won by (30 VP points per match split up between the 2 teams depending on the score). But that would be a lot of work because it would have to be tailored individually for each game and it might be against BGA policy if it doesn't follow "official" tournaments rules.

Likewise, a few games could benefit from a duplicate system (games where the initial distribution of cards is an essential luck factor) but that is a lot of work... (you need some MP or IMP scoring tailored to the game and table movement schemes tailored to the number of concurrent tables in the tournament. And you need to explain it all to the players...)