We first need to work out the average PPIs of (1) your partners (which we will call "b"), and (2) your opponents (which we will call "c"). You will need to have noted all their suit symbols.
I recommend you assume 44% for a "Club", 48.5% for a "Diamond", 53% for a "Heart" and 56% for "Spades" that do not appear in the Top 100 ladder.
We will call our own PPI "a", the number of boards we have played "n", and we will call our session % Match Points "p".
We will also need to know our value for "m", which will often be 600 but will be less for less frequent players who would need to check the formula in the main text.
Our change in PPI will be approximately n [p - {(a+b-2c)/2 + 50}] / m
So let’s say I played 20 boards, my PPI is 47%, My "m" is 600, my partners were all diamonds and my opponents were 3 "Clubs", 4 "Diamonds" 2 "Hearts", and a "Spade" with a 58% PPI, and I scored 44% over the 20 boards.
b = 48.5
c = [3x44 + 4x48.5 + 2x53 + 58] / 10 = 49
Change in PPI = 20 x [44 - {(47 + 48.5 - 2x49) +50}] / 600 = -0.117%
For our PPI not to change, we would have needed on this occasion
p = {(a+b-2c)/2 + 50} = 47.5%
If all the players have the same PPI, then (a+b-c-d) = 0 {(a+b-c-d)/2 + 50} = 50 p = 100 [ p - {(a+b-c-d)/2 + 50}] = 50 The sum of this over 1 board = 50
(a) For a frequent player who has played more than 600 qualifying boards altogether, m=600
New PPI is an increase of 50/600% = 0.083% over previous PPI.
(b) For an infrequent player who has played more than 300 qualifying boards altogether, but less than 150 such boards in the last 90 days, m=300
New PPI is an increase of 50/300% = 0.167% over previous PPI.
(c) For a newcomer who has played just 100 qualifying boards altogether, m=100
New PPI is an increase of 50/100% = 0.50% over previous PPI.
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