Originally Posted by
Oldtimer
I have checked out a couple of websites and now believe I have an understanding of how the ping pong balls work.
There are 14 ping pong balls, numbered 1 through 14. The 14 ping pong balls are placed in a device that bounces them around and will eject one ball at a time. The device is turned off after four balls are ejected. The numerical order of the balls popping out of the device, i.e., which one comes out first, does not matter, just as in most lotteries. We now have four balls with four different numbers from 1 thorugh 14.
This - the four numbered balls picked - is one "combination" of numbers 1 thorugh 14 that is possible when 4 balls are randomly selected from 14 balls. It is a rule of probability that when there is no chance of repetition - the same ball twice - there are 1001 possible four ball combination when picking from a total of 14 balls. (1,2,3,4), (1,2,3,5), (1,2,3,6) . . . (1,2,3,14), etc.
One of the possible combinations is not used. That leaves 1000 possible combinations. The lottery teams are "assigned" their percentage share of the possible combinations. Miami will get 25% or 250 of the possible combinations; Seattle will get 19.9% or 199 combinations; and, as matters now stand, Minnesota will get 15.6% or 156 combinations; Memphis 11.9% or 119 combinations; with the Knicks and the Clippers tied for fifth worst and dividing the fifth place 8.8% (88 combinations) and the sixth place 6.3% (63 combinations). The total for the Knicks and Clippers to split is an is an odd number - 151. I am not sure how they would split it, but this would end up giving the Knicks about 75 combinations, i.e. a 7.5%
chance for the first pick.
All the possible combinations, 1000 of them, are "assigned" to the lottery teams. Miami is "assigned" 250 combinations, Seattle is "assigned" 199 etc. The "assignment" occurs before the lottery, but how it is done, I do not know. Probably through some random program. It does not matter because each combination is equally probable.
When the first four balls pop out of the lottery device, the team assigned the combination of numbers that matches the numbers on the four balls gets the first lottery pick.
After the first pick, they go to the second. All fourteen balls are placed in the device again and another set pops out one at a time. The team assigned this second combination of numbers that matches the numbers on the four balls, gets the second lottery pick. If the team that got the first pick also has the second combination, it is disregarded and they try again. This process goes one more time for the third pick. After that, the lottery order is set.
As a practical matter, we can forget about th ping pong balls. Its all in the percentages. And now it looks like the Knicks will have a 7.5% chance for the first pick.
One of the sites I checked did the math for last year which is the same essentially for this year. Carrying over to this year, Miami will have a 25% chance for the first pick; a 21.5% chance for the second pick; a 17.5% chance for the third pick; a 46.5% chance for any top 2 pick and a 64.3% chance for any top 3 pick. If the Knicks are fifth alone, rather than tied with the Clippers for fifth, their chances for the #1 pick would be 8.8%; for #2, 9.7%, for #3, 10.7%; for any top 2 pick, 18.5%; and for any top 3 pick, 29.1%. If they are tied with the Clippers for fifth and I have done my math right, the Knicks chances for #1 is 7.5%, for #2, 8.3%; for #3, 9.2%; for any of the top 2, 15.75% and for any of the top 3, 25%.
If the Knicks do not get one of the top three picks, we know they can not get the fourth. If they were fifth worst alone, their chances - after not getting one of the first three - for the 5th pick is 27%; for the 6th pick, 36%; and for the 7th pick 8%. It gets slightly worse if they are tied with the Clippers.
In short, that three game win streak hurts.
