Cartref,
Well I'm back, and have been catching up with stuff over the past few days. You asked how I came about my weighting formula. Well for the recent example, I couldn't remember exactly how I arrived at my original heat scores 22 years ago and could not find the original excel file. So I had to improvise, and came up with that version because I happenned to have some skip values to hand and wanted a quick way to generate scores. I knew that my original method took into account both frequency and recent appearances, but the skip method was much simpler. I did not regard the method of arriving at a score as important as converting the scores to a heat chart, and that was the main purpose of that spreadsheet.
I did stress that everyone will have their own view of how to define hot or cold and could devise their own method of working out a score. The essence of the scoring system is to acknowlege the difference between a ball drawn one draw ago and one drawn say five draws ago. The problem with skip charts is that they don't explicitly define when a ball was drawn, so much as to count how long it's been absent ,and you find yourself dealing with figures in descending order going back in time until they reset at zero in the past. So long overdue numbers have high skip values over recent history and result in (high score = cold balls) and vice versa.
The problem with the skip values is this :-
Suppose the the skip value in the most recent draw was 25. Then 10 draws ago it was 15. In terms of cooling down between 15 and 25 it's percentage cooling based on skips is 10/15 which is a factor of 66%. I don't think that is much over 10 draws, I think it should be a multiple much more than 100%. I'm saying that I think cooling should be exponential not linear.
Thats why weighting was employed for that version of heat calculation, to force cool the ball the further into the past you go without it being drawn. For brevity I did not look back very far, ideally one should look a lot further back than four draws.
Since then I have recovered an old copy of my original work and now remember my method from all those years ago. For the 649 lottery, I looked back 12 draws and instead of using skips, I had a grid of 0's and 1's. 0' meant a ball was not drawn, 1 meant it was drawn. I calculated what I called 'recency rating' from this grid. So if the recent history of a ball was:- ( leftmost is most recent)
0,0,1,0,1,1,0,0,0,1,0,1 my weighting favoured the most recently drawn balls, 12 points for the most recent, 11 points for the previous one, etc down to one point for 12 draws ago. But points only score where there is a 1' in its history. So this would have a recency rating of 0 + 0+10 + 0 + 8 +7 + 0 +0 +0 +3 + 0 + 1. = 29.
You should notice that this method, instead of force cooling overdue balls, boosts the heat of more recently drawn balls instead.
I also calculated another figure based on the balls frequency and the expected frequency for the current draw. This had to be weighted to make it of comparable value with the recency figure ( hence having influence on the final score). For 49 balls my 'occurrence' figure was (actual F X 50) /expected F . Usually a figure in the range 45 to 55 would result for all the balls.
My heat score was the sum of the two components, e.g 29+ 47 = 76. How much importance F had could be varied by changing the multiplier ( currently 50) to say a lower value 20 , making recency of a ball more influential.
You should notice that this way of doing it, high score = hot balls and vice versa, unlike my previous example. This only works with an upside down lookup table as VLOOKUP doesn't like the first column to be sorted descending. There are other display issues too, which can be overcome.
Like I've said all along, there is no right answer to this. It's what you feel is most important:- Frequency ( be that over lotto history or over the past year) or recent appearances, or both - you can massage fiddle factors to reflect your view on this.