Bump for 2023 data.
Based on data from MTFWP, # of points and % chance to draw:
0 pts = 60.2%
0.2 - 1.8 pts = 0%
2 pts = 83.9%
2.2 - 3 pts = 100%
Buying points:
So, year one, you buy a point before and your odds of drawing is 0% (not drawing 100%) $100 spent.
You buy 2nd point before applying the next year, $200 spent. Your odds of drawing is 83.9% (not drawing 16.1%).
Odds of one of the other occurring should be:
Probability of not drawing either year: P(A and B) = P (A) x P(B) = 1.0 * 0.161 = 0.161 = 16.1%.
Probability of drawing in one of the two years = 1 - 16.1% = 83.9%.
You buy 3rd point before applying the next year, $300 spent.
Probability of not drawing in any year: P(A and B and C) = P (A) x P(B) x P(C)= 1.0 * 0.161 * 0.0 = 0.0 = 0.0%.
Probability of drawing in one of the three years = 100%.
Not buying points:
Probability of not drawing either of first 2 years: P(A and B) = P (A) x P(B) = 0.398 * 0.398 = 0.1584 = 15.8%.
Probability of drawing in one of the two years = 1 - 15.8% = 84.16%.
Probability of not drawing either of 3 years: P(A and B and C) = P (A) x P(B) x P(C) = 0.398 * 0.398 * 0.398 = 0.063 = 6.3%.
Probability of drawing in one of the three years = 1 - 6.3% = 93.7%.
Two-Year Comparison:
Buying points = 83.9%, Costs $200
Not buying points = 84.16%, Costs $0
Three-Year Comparison:
Buying points = 100%, Costs $300
Not buying points = 93.7%, Costs $0
Make your own call on buying points. With the cost of tag being around $1200, a $300 cost for points is 25% extra.