"Mega Carcassonne" at the 2016 UK Games Expo (maybe)

[ScottMoore]

I don't think it's a case of merely comparing winners against winners though. As you said yourself, anyone who wins all of their games will end up in the top 8 regardless of their tie-breaker score. What you really want to be measuring is how near or far non-winners came to winning and measuring total PD (versus winning score) is a good way of doing this.

If we assume that anyone who wins all their games will go through, what you really want to know is which of the rest of the players came closest to the winning scores/ lost by fewest points. Someone who won two games and then came second in the third by, say, 5 points will have an overall PD of -5. Another player who came 2nd by one point in all three games would have a PD of -3 but probably wouldn't have enough competition points to make it through to the top 8 even though they'd do very well on the tie-breaker.

For these reasons, I think PD will do everything you need it to.

Dan, I think it still is important to compare winners against winners. In the case of two players who each gained 1st, 1st, 2nd places then it is more important to compare their wins to their 2nd places (of course, each result should carry equal weighting).

Let's take an example.
Player A wins by 12 points and 8 points and gets a 2nd place 15 points behind the winner. His PD would be -15.
Player A wins by 2 points and 1 point and gets a 2nd place 10 points behind the winner. His PD would be -10.
In this example, it would not be fair for player B to be ranked higher than player A.
If we instead measured PD by comparing with the 2nd place score, then player A would have a PD of 20 (12+8+0) and player B would have a PD of 3 (2+1+0). This would be fairer in this example, but I could easily find another example where it would no fairer then measuring PD by comparing with the winner's score.

So, yes, I agree with PD, but not a simple PD of comparing with the winner's score or, for that matter, with the 2nd place player's score.

I think calculating PD by comparing with the mean of all player's scores would be better, but still flawed.

[Decar]

Could it be calculated as a % of the mean score?

[ScottMoore]

I think I was 3rd in this list and the reason I did so well was because I was involved in a couple of unusually high-scoring games which inflated my overall score. In the case above where 4 people got two 1st and a 3rd, I would have thought the score difference between first and third in these cases would be the best tie-breaking factor... ?

Now, I'm not sure what you mean by "the score difference between first and third in these cases". Surely it the strength of each player's two wins that is the best factor (if we take a single factor)? But we should also take into account the magnitude of those 3rd place losses. Indeed, there should be an equal weighting for all three game results. 

Anyway, we are not going to know beforehand how many points each player will get and where the critical cut-off point will be for getting into the top 8. So, we need to decide on the best tie-breaking factor in general terms.

This can all get very complex, which is the beauty of using score as a tie-breaker...

[ScottMoore]

Could it be calculated as a % of the mean score?

Which mean score? Let's say we have players A, B, C and D and their scores are S_A, S_B, S_C and S_D. I was suggesting that we use:

 Mu = (S_A+S_B+S_C+S_D)/4

PD (A) = S_A-Mu
PD (B) = S_B-Mu
etc.

Are you suggesting that we use:
PD (A) = (S_A-Mu)/Mu
PD (A) = (S_B-Mu)/Mu
etc.

[danisthirty]

My thinking was actually that since winning the game is your goal, if you do win a game then you've achieved your goal and there isn't much else to measure. I guess my approach focuses more on how far away you were from winning the game if you didn't win the game, so in the example above, it would only really be the game where the tied players came third that makes all the difference. Which I accept is flawed too, but relatively simple and better than calculating it based purely on cumulative score!

Ultimately there are so many factors that will swing things for the better or for the worse. For example, the luck of the draw may result in the four best players being drawn to play against each in the first round meaning that one of them will come fourth and stand no chance of reaching the top 8. Similarly, you only have to be better than 9 other people in order to win all 3 of your qualifying games. So, if you're fortunate enough to be drawn against all of these in 3 subsequent games then chances are you'll get 3 wins! But maybe I'm going off topic here, and maybe you have a more sophisticated system for choosing groups of players?

[Decar]

I was just thinking of making the PD:

PD(A) = S_A/Mu
...etc

That was you get a Score Factor that tells you how much better/worse the player was than average:  eg: more than 1 or less than 1.

It may also tell you how well 2nd places were between games and hopefully factor in 3 and 4 player games.

[danisthirty]

I was suggesting that we use:

 Mu = (S_A+S_B+S_C+S_D)/4

PD (A) = S_A-Mu
PD (B) = S_B-Mu
etc.

 

[ScottMoore]

My thinking was actually that since winning the game is your goal, if you do win a game then you've achieved your goal and there isn't much else to measure. I guess my approach focuses more on how far away you were from winning the game if you didn't win the game, so in the example above, it would only really be the game where the tied players came third that makes all the difference. Which I accept is flawed too, but relatively simple and better than calculating it based purely on cumulative score!

Ultimately there are so many factors that will swing things for the better or for the worse. For example, the luck of the draw may result in the four best players being drawn to play against each in the first round meaning that one of them will come fourth and stand no chance of reaching the top 8. Similarly, you only have to be better than 9 other people in order to win all 3 of your qualifying games. So, if you're fortunate enough to be drawn against all of these in 3 subsequent games then chances are you'll get 3 wins! But maybe I'm going off topic here, and maybe you have a more sophisticated system for choosing groups of players?

I don't agree with the logic of your argument. If the goal is simply to win the game, then surely a loss is a loss, no matter by 1 point or by 100 points? However, I would say that the goal is primarily to obtain as good a position as possible, and secondarily to get as good a score as possible vis-a-vis your opponents. However, surely the strength of a win counts for more than your relative scoring if you get a lowly 3rd place? If I win by 100 points then I'm going to feel much more of a winner than if I win by a mere 1 point. But if I get 3rd place then it is not going to make so much difference how far behind the winner. In fact, the difference between me and 2nd place is more important in that case.

Choosing groups of players in the first round can only be by chance (unless we use the results of last years tournament to seed the top players). We could seed the second round positioning based on the first round scores and the third round based on previous round's scores (I think this is called the Swiss system). But this would require a huge leap in complexity and/or time involved - we would need a computer application to calculate the positioning for us and a way to communicate these positions to all players -ideally each player would consult the results that we instantaneously post on a Website using their smart phone

[ScottMoore]

I was just thinking of making the PD:

PD(A) = S_A/Mu
...etc

That was you get a Score Factor that tells you how much better/worse the player was than average:  eg: more than 1 or less than 1.

It may also tell you how well 2nd places were between games and hopefully factor in 3 and 4 player games.

So, not really a score differential but a relative score...hmm, this would seem to be a good solution. Possibly a bit better than my suggestion, because it also takes into account the actual scores. A possible criticism could be - it would be easier to get a high factor in a low scoring game than in a high scoring game (and easier in a 4-player than a 3-player game). But then this does give the winner an incentive to keep all other player's scores as low as possible rather than, for example, just that of the 2nd place player (which would be attractive if we were just using the differential score relative to the winner's).

[Decar]

Without some concrete results to apply a model too, I think any way will have failings.  As you said the problem with the relative Score is that isn't a linear scaling; so in a low scoring game [52,49,48,32]  vs a high scoring game [122,110,77,60] the Relative Score would be:

Mu(1) = 45.25

RS(A1) = 1.15
RS(B1) = 1.08
RS(C1) = 1.06
RS(D1) = 0.71

Mu(2) Mu = 92.25
RS(A2) = 1.32
RS(B2) = 1.19
RS(C2) = 0.83
RS(D2) = 0.65


I've made these numbers up, but we're saying that Second Place in Game2 did better than First Place in the previous game.  Yet they scored a lot more points, but I suspect that it was a much tougher game and players were not sharing so many features.  I problem with taking the mean-score is that results can be skewed and not show how close the players were - for example: [100,99,99,1] , the average score is: 74.5 so 3 of the players would score: 1.34 which seems like a high number because 1 player didn't score very well, it could be beneficial for 3 players to gang up against one player and then score a huge number of points together

Maybe you need to compare relative scores between players per game to weigh how well a particular player is doing (ie: what was the average relative score?)

[danisthirty]

I don't agree with the logic of your argument...

Neither do I anymore. I was just trying to explain my initial thoughts in more detail!

Whilst I understand the difference (mathematically at least) between:

PD (A) = S_A-Mu and PD (A) = (S_A-Mu)/Mu

I don't necessarily understand the relative merits/ drawbacks in the context of the tournament anymore, so I'm going to bow out at this point...

Good luck!

[ScottMoore]

Well, I think we can say it is best to replace absolute score as the tie-breaker. But it is still not clear what the best alternative is.

It would better to have more qualification rounds and, indeed, to have only 2-player games. That way, we could just use PD in the rarer number of cases where players tied on points from game positions. But neither is possible at the Expo for reasons of practicality...

[danisthirty]

I guess it becomes impractical for a variety of reasons, but do you foresee there ever being a case for having regional qualifiers and then the final at the UK Games Expo?

[ScottMoore]

I guess it becomes impractical for a variety of reasons, but do you foresee there ever being a case for having regional qualifiers and then the final at the UK Games Expo?

Yes, but it all depends on one thing - having a sponsor who wants regional qualifiers. The same goes for 2-player games - if there's a sponsor and the sponsor wants that format then we would be only too happy to oblige. There have been regional qualifiers in the past for Ticket to Ride and Catan, because sponsors organised them with Esdevium Games. Having said that, the Catan regionals weren't qualifiers in the strictest sense - winning a regional just got you a "first round bye", which meant you got the maximum 4 points for the first round in the nationals.

In fact, there was some talk last year of having an event running over 2 days at the Expo. On the Saturday there would be the "qualifying rounds" and then on the Sunday, the 2-player knockout rounds - we could easily handle 16 players in the knockout rounds if they were held on a different day to the qualifiers. We did this with Ticket to Ride a couple of years ago, because that's what the sponsor wanted.

[danisthirty]

In fact, there was some talk last year of having an event running over 2 days at the Expo. On the Saturday there would be the "qualifying rounds" and then on the Sunday, the 2-player knockout rounds - we could easily handle 16 players in the knockout rounds if they were held on a different day to the qualifiers. We did this with Ticket to Ride a couple of years ago, because that's what the sponsor wanted.

I like this idea a lot. The most obvious drawback is that you can't just come for a day, take part in the competition and go home afterwards. And you would have to be relatively sure of yourself if you booked a room in advance assuming you were going to qualify for the knock-out stage of the competition! However, I guess there is a bigger picture to take into account and the organisers of the UK Games Expo probably want the competition to fit into a single day so that it can appeal to as large a crowd of gamers as possible?

Since we've spent some time talking about ways to calculate a tie-breaker such that the competition is fair for 3 and 4 player games alike, I wonder if there will be any system for determining which player starts? In the past we've literally just worked it out between ourselves via whatever method and it hasn't been a problem. But as you know, being the 4th player is a bit of a disadvantage since you get to place one fewer tile than everyone else so I wondered if there were any plans to formalise this process at all? Starting last in all 3 of your games would represent a major disadvantage, and if my practice against iOS AI opponents is anything to go by, ruin my chances completely! (but that's just me)