Percentages and Points: Discussion Document
Percentages vs Club Points
This is the paper written by Helen Walker for the March 2020 meeting of the Committee to inform discussion about whether we should stay with percentages or revert to club points to decide winners for events at the Otaki Bridge Club.
Percentages vs Club Points
At an upcoming meeting we will be discussing the suggestion made to the AGM that the club revert to using “Club Points” to determine winners of series events rather than percentages. These notes (drawing heavily from notes prepared by Ian Sheen at the time that we changed to percentages) are aimed at providing some background to the issue.
Background
Up until 2017, Tuesday competitions were decided by “Club points”. The top five placings each night were awarded Club points, from 5 points for first place down to 1 point for fifth. The Club points were added up over the course of the competition, and the individual or pair with the most Club points won the trophy. If there was a tie, the result was determined by percentages scored. Percentages are a reflection of rankings for more technical detail I have included notes on this in an Appendix (thanks George).
Comment
There is no right or wrong answer as to whether we should use percentages or points.
The key issue is possibly whether you consider a series to be made up of three individual sessions or whether you think it is the total number of boards played over three nights. That is, for a 3 night series playing 24 boards per session do you think the best is the person (or pair) who played the 72 boards with the best result. If so percentages identify that person or pair.
At the AGM the main issue raised was that a pair might score 70% on one night and become virtually unbeatable, while other pairs have done very well over the whole series. It was considered that due to this, Club Points would reward consistent play rather than one good score.
It is possible for a pair to finish 2^{nd} NS with 50%, while on the same night another pair finishes 4^{th} EW with 56%. The pair with 50% would get 4 Club points, while the pair with 56% would get 2 Club points. The question is who played the best? Did the pair who scored 50% over 24 boards play better than the pair who scored 56%?
An example of this type of result was seen on Tuesday 4 February 2020 where the NS pair with 60% would get 3 points and the EW pair with 59% would get 5:
Rank 
Pair 
Name 
Matchpts 
% 
Club points 
1 
6 
302 
69.91 
5 

2 
1 
268 
62.04 
4 

3 
7 
261 
60.42 
3 

4 
10 
244 
56.48 
2 

5 
9 
194 
48.99 
1 









EAST WEST 



1 
4 
277 
59.19 
5 

2 
10 
273 
58.33 
4 

3 
2 
260 
55.56 
3 

4 
1 
259 
55.34 
2 

5 
7 
255 
54.49 
1 
This example also illustrates that Club Points can be just as misleading.
Pair 6 NS 69.91%
Pair 1 NS 62.04%
Pair 7 NS 60.420%
Pair 10 NS 56.48%
Pair 9 NS 48.99%
Pair 1 are getting twice the points (4) of Pair 10 (2 club points)for a difference of only 6.56%.
Pair 1 are getting almost as many club points as Pair 6 but are 7.87% behind
Both systems suffer from good/bad result playing a hand against good/weak opposition.
If you see a 3 night series as being 3 separate events then either percentages or points can be used to decide the winner. The winner should be the pair or person who has played the best and the debate is how to define “best”.
Factors that impact on Points and Percentages
When we play a Mitchell movement, Club points are awarded both for NS and for EW, so ten pairs get Club points each night. If there is a Howell movement there is only one result ladder, so only five pairs get Club points. (A Mitchell movement is what we usually play with players either playing NS or EW through the session. A Howell movement is when pairs play both NS and EW through the session.) A Howell movement could be considered unfair because only five pairs receive points while ten pairs get points under a Mitchell movement.
The argument for percentages is that if a pair score 70% they deserve to win, because over the 72 boards they have ended up with the highest average percentage.
Historic results
I have looked at previous recent results to see whether different people would have won. Of the 5 I looked at, two would have had the same winners (Championship pairs – the first three places were exactly the same; Hautere Individual Maree C won every session so was a very clear winner – but under % scoring Joyce came 2^{nd} and Anne 3^{rd}, under the points system Lyn came 2^{nd} and Bridget and Joyce were 3=).
Of the ones that changed the top 4 tended to be the same but in different order:
Mt Hector Pairs

Avg score 
Sess 1 
Sess 2 
Sess 3 
Points 
Dorothy & Naciye 
60.95 
56.48 
71.30 
55.06 
11 (3=) 
Bridget & Dave 
60.02 
59.62 
57.64 
62.80 
12 (2^{nd}) 
Joyce & Claudia 
59.09 
64.1 
56.02 
57.14 
11 (3=) 
Basia & Tim 
58.09 
58.56 
60.42 
55.25 
13 (1^{st}) 
 Tim and Basia won session 2 and came 2^{nd} on both session 1 and 3.
 Dorothy and Naciye won session 2 and came 3^{rd} on both session 1 and 3.
These results suggest that the comment above  that if a pair score 70% they become virtually unbeatable – may not be right, given the difference between 1^{st} and 2^{nd} is not insurmountable. All of the top 4 played equally consistently.
I only calculated one series for the handicap side – it was more complex due to needing to check eligibility. Similar to the open results the top 4 remained the same but the order changed:
Riverbank Pairs (Handicap section)

Place 
Avg 
Sess 1 
Sess 2 
Sess 3 
Points 
Tim and Andrew 
1 (2=) 
48.61 
51.08 
40.90 
53.86 
11 
Paul and Justine 
2 (4) 
47.80 
54.82 
52.28 
36.31 
10 
Clive and Alastair 
3 (1) 
47.70 
39.68 
52.87 
50.56 
12 
Pat W and Mary CC 
4 (2=) 
45.86 
49.21 
47.66 
43.72 
11 
In brackets are the placings using the points system.
The real point of these examples is – what is the most fair outcome? Who should have won?
When Ian did the same exercise at the end of 2016 – he noted:
“Out of eleven events so far this year, five would have been won by a different player or pair. Mostly this related to shuffling of positions between the usual suspects:
Club Points Winners changed to Percentage Winners
Dorothy Yuri
Naciye & Jane Noeline & Anne
Barry & Barry Naciye & Ron
Anthea & Jane Cheryl & Yuri
Yuri Lyn
Winners unchanged
Lyn; Dorothy & Jane; Dorothy; Anthea & Joyce; Ron & Graeme; Dave.
For handicap competitions, it seems to me that the lower ranked players did as well or better with percentage scoring.”
Other comments
All other clubs score club night competitions on percentages, Ian noted that he did not know of any other club that uses points (and nor do I)
Tournaments are scored on aggregate percentages. Tournaments usually offer session prizes but the tournament winners are on overall percentage scores from however many sessions were played.
A point to keep in mind when considering whether to stay with the current percentages approach or revert to “Club Points” is that bridge results might seem to be unlucky or unfair for various reasons. The types of reasons are:
 Meeting strong players when the board is a hard one – some boards for a variety of reasons may be hard to bid and/or play (often distributional). If you have strong opponents on that board you are likely to not do as well, if you have less experienced opponents you may get away with a bit more, giving you a better score. Whether we play Club points or percentages the outcomes are the same.
 Being phantom twice – some people believe there is an advantage to being phantom twice. I suspect you have to have played well to get any advantage and maybe the advantage comes if the boards you did not play were tricky… Basically if 24 boards are in play – each one is worth a maximum of 4.166% of the final score for the side that play all 20 (either EW or NS). (24 x 4.166 =100). If you are phantom once, you play 22 boards (assuming 2 boards a table), so each board is worth 4.545% and if you are phantom twice you play 20 boards, so each board is worth 5%. It does not matter if we are playing with percentage points or club points these calculations remain the same. In the days of manual scoring players would get 50% for unplayed boards.
Whether you use percentages or club points to find the overall winner will not correct for these factors.
Admin implications of Points
If we moved to points we need to consider:
 Friday night series: we introduced these last year. Would a point scale of 15 be appropriate when usually there are only 5 tables +/ 1 or 2. Tuesday night usually has 1012 tables. On Tuesday nights there are sometimes not 5 pairs (eligible to win the handicap section of the series) to award the points to.
A scale of 12 or 13 may be more appropriate for Friday night.
 The computer system, Compass cannot calculate the series winners ona points basis so that would need to be done manually, and though the open is fairly quick to calculate the handicap side is much slower (with checking for eligibility) and more open to error.
Appendix: Percentages are technically not percentages.
This appendix provides a bit more detail on how scoring is carried out.
The term percentage in bridge scoring is a misnomer because what we are calling Percentages are actually an arithmetic mean (the average) of the players rankings on each hand, then multiplied by 100 and called a percentage.
The scoring system we use for n tables (n = number of tables) gives 2xn2 points for a top, 2 less for the next pair, and so on down to 0 for the bottom scoring pair. So if there are 6 tables, each hand is analysed and the top pair scored 2x6  2 = 12  2 = 10 points, the next highest pair scored 8 on that hand and so on down to the bottom pair scoring 0. These are not ‘scores’ as such, they are a number representing a rank position. The difference between first and second could be vast or it could be just a smidgen but the top pair are accredited 10 and the second pair 8.
When the list is posted on the club noticeboard with 63.75% against a pair’s names it really means that their average ranking over the 24 boards was 0.6375. This does NOT represent 63.75% of anything meaningful  it is simply a number.