Useful Scoring/Percentage Formulas

To calculate a useful winning percentage, to avoid 1/1 showing 100% and being better than 999/1000
(# of games won + 1) / (# of games played + 2)



Average score = [Score from Amazon] / ([Total # of reviews] / [# of Amazon reviews]) + [Score from Goodreads] / ([Total # of reviews] / [# of Goodreads reviews])


function GetRating( positiveVotes, negativeVotes ) {
    const totalVotes = positiveVotes + negativeVotes;
    const average = positiveVotes / totalVotes;
    const score = average - ( average - 0.5 ) * Math.pow( 2, -Math.log10( totalVotes + 1 ) );

    return score * 100;
}



There are three attempts (all will be taken individually).

The first is known to have a 60% success rate. The second is known to have a 30% success rate. The third is known to have a 75% success rate. What are the odds of a success occurring if all three attempts are made?

A: Probability of winning is probability of not losing all three: 1 - (1 - 0.6)(1 - 0.3)(1 - 0.75)



Regression Trendline #1
Calculating the Slope (m) of the Trendline
Consider this data set of three (x,y) points: (1,3) (2, 5) (3,6.5). Let n = the number of data points, in this case 3.

Let a equal n times the summation of all x-values multiplied by their corresponding y-values, like so:
a = 3 * {(1 * 3) +( 2 * 5) + (3 * 6.5)} = 97.5

Let b equal the sum of all x-values times the sum of all y-values, like so:
b = (1 + 2 + 3) * (3 + 5 + 6.5) = 87

Let c equal n times the sum of all squared x-values, like so:
c = 3 * (1^2 + 2^2 + 3^2) = 42

Let d equal the squared sum of all x-values, like so:
d = (1 + 2 + 3)^2 = 36

Plug the values that you calculated for a, b, c, and d into the following equation to calculate the slope, m, of the regression line:
slope = m = (a - b) / (c - d) = (97.5 - 87) / (42 - 36) = 10.5 / 6 = 1.75

Calculating the y-intercept (b) of the Trendline
Consider the same data set.

Let e equal the sum of all y-values, like so:
e = (3 + 5 + 6.5) = 14.5

Let f equal the slope times the sum of all x-values, like so:
f = 1.75 * (1 + 2 + 3) = 10.5

Plug the values you have calculated for e and f into the following equation for the y-intercept, b, of the trendline:
y-intercept = b = (e - f) / n = (14.5 - 10.5) / 3 = 1.3

Plug your values for m and b into a linear equation to reveal the final trendline equation:
Trendline equation: y = 1.75x + 1.3


Regression Trendline #2
SUBJECT	AGE X	GLUCOSE LEVEL Y	XY	X2	Y2
1	43	99	4257	1849	9801
2	21	65	1365	441	4225
3	25	79	1975	625	6241
4	42	75	3150	1764	5625
5	57	87	4959	3249	7569
6	59	81	4779	3481	6561
Σ	247	486	20485	11409	40022
From the above table, Σx = 247, Σy = 486, Σxy = 20485, Σx2 = 11409, Σy2 = 40022. n is the sample size (6, in our case).

Step 2: Use the following equations to find a and b where n is the same size (in this case 6).
a = (((Σy)*(Σ(x^2))) - ((Σx)*(Σx*y))) / (n*(Σ(x^2)) - ((Σx)^2))
b = ((n*(Σx*y)) - ((Σx)*(Σy))) / (n*(Σ(x^2)) - ((Σx)^2))

a = 65.1416
b = .385225


Find a:
((486 × 11,409) – ((247 × 20,485)) / 6 (11,409) – 2472)
484979 / 7445
=65.14

Find b:
(6(20,485) – (247 × 486)) / (6 (11409) – 2472)
(122,910 – 120,042) / 68,454 – 2472
2,868 / 7,445
= .385225

Step 3: Insert the values into the equation.
y’ = a + bx
y’ = 65.14 + .385225x


Wolfram Alpha derive quadratic equation from plots - equation {508,410}{595,370}{301,490}{175,520} or quadratic {508,410}{595,370}{301,490}{175,520}{190,520}