I get a big laugh when I see someone post about how Quick Picks are the greatest. Then they'll post some winning numbers and prizes with a "Look! See!... See! Look!... Loooook...seeeee." attitude. Well, there are a few problems with comparing Quick Picks to Self Picks (a.k.a. Personal Picks). It has to do with proportionality of work being done. From Powerball's Frequently Asked Questions page, under the heading WHICH HAS THE BETTER CHANCE OF WINNING: COMPUTER PICKS OR PLAYER PICKS? They say, "About 70% to 80% of purchases are computer picks." Computer picks are also know as Quick Picks. This is a fairly good representation of the population as a whole because it's based on actual data obtained on a Nation wide basis without regard to detailed demographics of the purchaser. 70% to 80% is the percentage of the total number of purchased plays, n. n can be any value for any given draw. p, the percentage, is the proportion of n purchases that are Quick Picks. p is represented as a value less than or equal to 1 and greater than or equal to 0, i. e. ( 70% = .70 and 80% = .80). Multiplying p times n gives the number of Quick Pick purchases for that draw, Qn. The number of Self Picked purchases is just the difference between n and Qn, Sn = n - Qn. During any draw there are Quick Pick wins, X, and Self Pick wins, Y. In order to offset the disproportionate number Quick Pick purchases to Self Pick purchases, we need to setup an equation of proportionality that states as Y is to B is the same as X is to A. This satisfies a lead in partial statement of, "All things being equal..." The equation of proportionality is then, Y is to Sn is the same as X is to Qn becomes (Y / Sn) = (X / Qn). This allows for a more equal comparison of which type of play has the advantage. We can solve for Y to find by proportion what a Quick Pick equals in terms of a Self Picked purchases based on the approximate percentage of 70% to 80%. As you'll see, the number of purchases becomes immaterial because that value factors out of the final equation.
n - total number of purchases
p - percentage of Quick Pick purchases
Qn = p · n , Qn - number of Quick Pick purchases
Sn = n - Qn , Sn - number of Self Pick purchases
X - Quick Pick wins
Y - Self Pick wins
(Y / Sn) = (X / Qn), equation of proportionality
Equation of Proportionality Solved for Y
(Y / Sn) = (X / Qn)
(Y / (n - Qn)) = (X / Qn)
(Y / (n - p · n)) = (X / (p · n))
(Y / (n (1 - p))) = (X / (p · n))
Y = ((n (1 - p)) / (p · n)) · X
Y = ((1 - p) / p) · X
Y = ((1 / p) - 1) · X
If we set X = 1, then we can see what one Quick Pick win equals in terms of a Self Pick win.
Y = ((1 / p) - 1) · 1
Y = (1 / p) - 1
Below is a table that shows what a Quick Pick equals for a few different percentages of Quick Pick purchases for any draw. A number less than 1 means the Quick Pick is less than effective as a Self Picked purchase. At 80%, a Quick Pick is only (1 / 4)th as effective as a Self Picked purchase.
Quick Pick % | Quick Pick's Self Pick Equal |
70% | 0.42857 |
71% | 0.40845 |
72% | 0.38889 |
73% | 0.36986 |
74% | 0.35135 |
75% | 0.33333 |
76% | 0.31579 |
77% | 0.29870 |
78% | 0.28205 |
79% | 0.26582 |
80% | 0.25000 |
This makes reasonable sense, Quick Picks out weigh the number of Self Picked purchases. This would be like having a football game and on the Quick Pick side you have all 12 players and on the Self Pick side you'd have only about 3 to 5 players. All the players have equal ability. Who do you think is going to win? Really, come on, all things being equal, it's obvious and unfair.
But, you also have to realize, with all those Quick Picks, if they are so great, wouldn't you see more wins per draw?
Self Picked numbers have the edge. Let's look at what 1 Self Picked purchase is equal to in terms of a Quick Pick.
Solving for X instead of Y, we get X = (p · Y) / (1 - p)
Set Y = 1, the equation is X = p / (1 - p)
Quick Pick % | Self Pick's Quick Pick Equal |
70% | 2.33333 |
71% | 2.44828 |
72% | 2.57143 |
73% | 2.70370 |
74% | 2.84615 |
75% | 3.00000 |
76% | 3.16667 |
77% | 3.34783 |
78% | 3.54545 |
79% | 3.76190 |
80% | 4.00000 |
As you can see, at 80% you'd have to have at least 4 Quick Pick wins in the same draw to be the same as 1 Self Pick win in the same draw.
Quick Picks can't match the power of Self Picks.