This page attempts to unravel the mysteries of the new GBQ column on some of the Tantrix group tables!

 

CONTENTS:

 

  1. The basics of GBQ
  2. The big assumption
  3. Examples of GBQs that may look odd at first sight (look here if you see something like that!)
  4. Comparison with the WBQ figures shown in the 2003 WTTC group phase
  5. Still not sure?
  6. Appendix – more detail on the calculations
  7. Updates

 

 

1. THE BASICS OF GBQ:

 

a) What is the new GBQ column on the Tantrix group results tables and why is it there?

 

GBQ means “games behind the last definite qualification place”. It is based on the “games behind” calculation shown on the results tables for most sports like baseball and ice hockey. It gives you an idea of how many wins you need to catch up with another player. This is something that is not always easy to work out from your TP %, especially when you and the other player have played different numbers of games.

 

b) But what does GBQ actually mean?

 

In simple terms, if you are +2.0 GBQ, it means that if your next match is against the player in the last qualifying place and you win the first two games against them by about 5 tiles each (see section 2 “ASSUMPTIONS”, below), you would then be approximately level with them in the table.

 

c) What does “last definite qualifying place” mean?

 

If, for example, three players from each group plus the two highest scoring 4th placed players qualify for the next phase of the competition, GBQ will be measured relative to the 3rd placed player in the group.

 

d) Going back to the player in the last qualifying place whom I am 2 games behind, GBQ = +2, what happens if I win some games and lose some games in my match against that player?

 

As far as changes in your GBQ go, winning 1 game & losing 0, winning 2 games & losing 1 and winning 1 game & drawing 1 are all equivalent. It is the number of wins less the number of losses that is important.

 

e) What if the player in the last qualifying place and I are playing different people tomorrow?

 

Even if you are playing different people, if you are 2 “games behind” them and you win your next two games while they lose their next two games, you will be approximately level.

 

f) What if only one of us is playing tomorrow?

 

In that case, you need to win two games for every 1 GBQ. So if you are 2 “games behind” and only you are playing, you would need to win 4 games to approximately catch up.

 

g) That sounds odd to me – wouldn’t it be better to say I was 4 GBQ if I need to win 4 games?

 

You can argue that this option would be more intuitive, but then it wouldn’t make so much sense if you were comparing GBQs for you and the player you were going to play next.

 

You can also look at it this way: if you are playing a game and the player you are comparing yourself with is not, then intuitively you need to draw your game just avoid going even more games behind. So you can think of a draw having zero effect on your GBQ, a win reducing it by 0.5 and a loss increasing it by 0.5. This means that the difference in your GBQ change if you win compared to if you lose is 1.0, which definitely makes intuitive sense!

 

Another important point is that the way I am doing it matches the convention used in other sports and games that use “games behind”. The last thing I want to do is to confuse or mislead those to whom “games behind” already has a very clear meaning, since they are the ones most likely to want to use it in the first place.

 

h) Why do the top players in my group has a minus sign before their GBQ figures?

 

This is because they are ahead of the player in the last qualifying place. If they are -2.0 WBQ, then they could lose two games against that player and still be approximately level with them.

 

i) Can I only compare myself with the player in the last qualifying place or with others too?

 

You can work out approximately how many wins you are behind (or ahead of) any other player in your group simply by subtracting their GBQ from yours. Remember that subtracting a number with a minus sign means that you should add it instead!

 

j) So why don’t you give the player in 1st place a WBQ of 0.0 and work down from there instead of having different signs for those ahead of and behind the last qualifying place?

 

Because usually most people are mainly interested in what they have to do to qualify, or how safe they are if they are already above the last qualifying place. However, if people prefer 1st place to be 0.0 instead, I’ll be happy to change it.

 

k) Why are the GBQ figures rounded to the nearest 0.5 rather than the nearest 0.1?

 

Because I think that gives a more intuitive interpretation and avoids giving an impression of spurious accuracy. If people feel differently though, I’ll be happy to change this.

 

l) If there are two to qualify from my group and I am in 1st place on -2.0 GBQ. If I play the 2nd placed player next and lose the first two games by 5 tiles each, they will catch me up but if they do, I will drop to 2nd place and still be in a qualification place. Shouldn’t the group leader’s GBQ (and perhaps the 2nd placed player’s GBQ for a similar reason) relate to how far they are away from 3rd place instead of 2nd?

 

This is a good point, but if the GBQ was calculated differently for the player already in qualifying positions than for all the other places, you wouldn’t always be able to take any two players and compare them by subtracting their GBQs from each other. Generally, at any one time, more players in a group will be interested in what they have to do to get into a qualifying place than what they need to avoid in order to stay in one, hence I think the convention used makes the most sense.

 

 

2. THE BIG ASSUMPTION:

 

a) Doesn’t the fact that all wins don’t score the same TPs in Tantrix mess all this up?

 

Sort of, but we can get around that and still produce a useful GBQ figure. We do this by assuming that all games are won by 5 tiles (a “standard win”), scoring 15.0-5.0 TPs, and working out an equivalent number of  “standard wins less losses” corresponding to your TP score. It makes the calculation more complex for Tantrix than for most games, but the interpretation is still simple and meaningful enough – it’s just approximate rather than precise.

 

For example, five 5-tile wins and one 5-tile loss in six games (i.e. wins less losses = 4) scores 80 TPs / 120. If instead you have managed four big wins and two very small losses and still scored 80.0 TPs, you will be treated as having the equivalent of five “standard wins” and one “standard loss” for WBQ purposes.

 

This also means that if your WBQ figure implies that you need to win N games, it means that you need to do the equivalent of winning those games by 5 tiles each.

 

N.B. If you are interested, there is more on the actual calculation in the Appendix at the end.

 

 

3. EXAMPLES OF THINGS THAT MAY LOOK ODD AT FIRST SIGHT:

 

I will add more examples here if/when people ask additional questions:

 

a) Player A won all 3 games against Player B by 5 tiles in the first match in a group, but it says on the table that A’s GBQ is -1.5 and B’s GBQ is +1.5. Shouldn’t it be +3.0 and - 3.0?

 

No. A is 3 games ahead of B, so their GBQ figures should differ by 3.0, and they do. A is 1.5 games ahead of the last qualifying place (e.g. 3rd) and B is 1.5 games behind the last qualifying place, so they are indeed 3.0 games apart altogether.

 

b) Player A managed a world record 3-game thrashing of Player B to score a 55.0-5.0 TP match win in the first match in my group. On looking at the table, I noticed that Player A’s GBQ was -2.5 and Player B’s GBQ was +2.5. Given the answer to the last question above, that means B is 5 games behind A even though only 3 games have been played in the whole group. That’s crazy, isn’t it?

 

No it’s not. Player A’s wins were so big that in TP terms, they were as good as winning 5 “standard” games against Player B. That doesn’t mean that Player A scored 5 * 15.0 TPs (obviously not, because the score was 55.0-5.0), instead it means that if these players carried on playing, Player B would need to win the next 5 games by 5 tiles in order to catch up with Player A:

 

Player A : 55.0 + 5 * 5.0 = 80.0

Player B : 5.0 + 5 * 15.0 = 80.0

 

c) The TP%s in my group’s table are in a different order to the GBQs. That’s got to be a mistake?

 

No mistake … but this can only happen when one player has played a lot more games than the other.

 

Imagine that Player A in the last qualifying position has played 4 games, won 2 by 5 tiles and lost 2 by 5 tiles so they are on 40.0 TPs, or 50%. Then consider:

 

Player B:

played 4 games, won 1 by 5 tiles and lost 3 by 5 tiles

total TPs 30.0, or 37.5%

GBQ = +1.0

If B played one game against A and won by 5 tiles, they would both be on 45.0 TPs, or 45%, so B would have caught up with A.

 

Player C:

played 16 games, won 5 by 5 tiles and lost 11 by 5 tiles

total TPs 130.0, or 40.6%

GBQ = +3.0

If C played one game against A and won by 5 tiles, C would be on 145.0 TPs after 17 games or 42.6%, so C would not have caught up with A. Hence C needs to win more games than B to catch up with A despite having a higher TP% than B at the start!

 

Looking at it another way, if you have played 3 games, won 1 (i.e. 33% of them) and lost 2, you only need to win one game to get back to 50%, whereas if you have played 20 games, won 8 (i.e. 40% of them) and lost 12, you need to win 4 games to get back to 50% despite starting with a better percentage. This is of course why people tend to shoot up and down the table much faster when they are just starting their games.

 

d) So why do you sort the table by TP% in preference to GBQ?

 

Although someone on 30% who has played very few games can get back to 50% quicker than someone on 35% who has played a lot more games, that will only happen if they win their next games. If they each lose their next games, the player who has played less games beforehand will move down much faster too, so GBQ is a double-edged sword. Hence:

 

- TP% is the best measure of your performance relative to the other players so far

- GBQ is simply the approximate number of games you need to win v another player to catch them up

 

TP% and GBQ both tell you something useful, but they are measuring slightly different things.

 

N.B. The TP%s and GBQs for players in any one group will always be in the same order as each other when all players have played the same number of games.

 

 

4. COMPARISON WITH 2003 WTTC “WBQ” FIGURES:

 

Is GBQ the same as the WBQ figure that was on the 2003 WTTC group tables?

 

Not quite. That was a similar concept, but instead of looking at the actual number of games played by each team, that calculation was based on each team’s TP% and the average number of games played by all teams in the group.

 

WBQ had the advantage that the TP%s and WBQs for the teams were always in the same order and it worked pretty well when all teams had played a lot of games (I only introduced it halfway through the group phase) but it gives crazy results when some players have played quite a few games and others have played none at all.

 

The old WBQs and the new GBQs are, however, the same when all teams have played the same number of games, e.g. at the end of the group, for reasons that are hopefully obvious.

 

 

5. STILL NOT SURE?

 

I’ve read all this and it still makes no sense!

 

That’s a pity. Maybe someone else can explain it in a way that will make more sense to you once they get used to GBQ themselves.

 

In any case, don’t worry, GBQ is just a non-essential extra bit of info that some players will find helpful. You can safely ignore the GBQ column and just concentrate on the TP%s if you want.

 

 

6. APPENDIX – more details on the calculations:

 

How does the calculation work in basic terms?

 

To calculate “games behind” In games where you can only win or lose, you simply:

 

-          find Player A’s number of wins less number of losses, Wa-La

-          find Player B’s number of wins less number of losses, Wb-Lb

-          then work out the difference between these numbers and divide by two

 

So if A has W 20 L 15 and B has W 16 L 15, A has 5 more wins than losses and B has 3 less wins than losses, so B is said to be ( 5 - (-3) ) / 2 = 4 games behind.

 

But game wins in Tantrix don’t always score the same number of TPs!

 

That’s right, so what we do is to assume that the average (non-drawn) game is won by 5 tiles (a “standard win”), giving a TP score of 15.0-5.0 (i.e. a difference between winning and losing of 10 TPs) and we convert each player’s TP score into a number of “standard wins” less “standard losses” for GBQ purposes.

 

Say you have scored 80.0 TPs from 6 games. The only way to do that if all games are decided by 5-tile margins is to win 5 games and lose 1 (because 5 * 15.0 + 1 * 5.0 = 80.0), or in other words to win 4 more games than you lose. Or you could draw 2 games and win the other 4 (because 2 * 10.0 + 4 * 15.0 = 80.0), again giving you 4 more wins than losses.

 

If on the other hand you win 4 games by 20-tile margins and lose 2 games by 9-tile margins, you will also score 80.0 TPs (because 4 * 18.0 + 2 * 4.0 = 80.0), so this is effectively just as good as 5 “standard wins” and 1 “standard loss”, so although you have only won 2 more games than you lost, for GBQ purposes you would be treated as having won 4 more “standard games” than you lost.

 

So, the GBQ figures are based on converting your TP score so far into an equivalent number of “standard” 5-tile wins less “standard” 5-tile losses and then assumes that you will win or lose any future games by 5 tiles as well, so if you win games by less than 5 tiles and lose them by more than 5 tiles, you will need to win more games to catch up. If that sounds like stating the obvious, well, it is!

 

And if I want to work out GBQs myself or check that you aren’t doing anything stupid?

 

Feel free, I probably am. J The calculation in the spreadsheet goes like this:

 

Da, player A’s equivalent number of “standard” (wins – losses) = (TPs scored – 10 x games played) / 10

 

The number of games player B is behind player A = Da – Db

 

7. UPDATES:

 

a) There are two definite qualification places in my group, yet while the 2nd placed player has a GBQ of 0.0 as you would expect, both the 1rd and 3rd placed players have negative GBQs, i.e. they are both 'games ahead' of the player who is in 2nd on TP%s. How is this possible?

 Let's look at an example of how this could happen. Assume every player has to play 10 games and, for simplicity, every game played so far has has a 5-tile margin of victory and no time penalties. The player in 2nd place on TPs has played 4 games, won 3 and lost 1, giving them 50 TPs or 62.5%. The player in 3rd place has won 6 and lost 3, giving them 105 TPs or 58.3%. However, the latter has won 3 more games than they have lost while the former has only won two more games than they have lost, so the player in 3rd place is ahead of the player in 2nd place on GBQs.

One way of looking at it is that the player on the higher TP% has done better in their games than the other player so, but the other player is more certain to finish above 50%. In fact, GBQ tends to favour the player who has played more games when both players are above 50% and favour the player who has played less games when both players are below 50% because in that case, the player who has played more games is more likely to finish below 50%.

N.B. For the 2004 WTTC, I have made sure that the team what is in the second qualification place on TP% has a GBQ of 0.0 and the other teams' GBQs are worked out relative to that, whereas in the Euros, the player in the last qualification place in GBQ tems was used as the 0.0 point. It does not really make much difference, but I get the impression from talking to people that it will look slightly less odd when the kind of situation described in this example occurs.

Obviously when the group has finished everyone has played the same number of games, so at that stage, TPs, TP% and GBQ will all be in exactly the same order.

 

At the moment, GBQs are calculated either side of the player with the 2nd best GBQ, rather than the player with the 2nd best TPs, which is why Garry is on 0.0 not Paul. It’s simpler to do it that way and apparent (but not actual) anomalies like this should only appear near the start of a group phase, so I hope you don’t mind if I leave it as it is and let it sort itself out as more games get played!

 

- ENDS -