## Learn your lottery terminology

In tomorrow’s lottery, the Pistons will have the same number ping-pong balls as the Charlotte Bobcats, Washington Wizards, New Orleans Hornets, Miami Heat, Detroit Lions and any other team.

Zero.

Teams are assigned combinations, not ping-pong balls. Here’s how the process works, as explained by the NBA last year:

Fourteen ping-pong balls numbered 1 through 14 will be placed in a drum. There are 1,001 possible combinations when four balls are drawn out of 14, without regard to their order of selection. Prior to the Lottery, 1,000 combinations will be assigned to the 14 participating Lottery teams by a computer.

Four balls will be drawn to the top to determine a four-digit combination. The team that has been assigned that combination will receive the number one pick. The four balls are placed back in the drum and the process is repeated to determine the number two and three picks. (Note: If the one unassigned combination is drawn, the balls are drawn to the top again.)

The actual Lottery procedure will take place in a separate room prior to the national broadcast on ESPN with NBA officials and representatives of the participating teams and the accounting firm of Ernst & Young in attendance.

Following the drawing, team logo cards will be inserted into envelopes marked 1 through 14 by an Ernst & Young representative. These envelopes then will be sealed and brought on-stage, where the announcement of the Lottery results will be made by NBA Deputy Commissioner Adam Silver. A second representative from each participating team will be seated on-stage. Neither the Deputy Commissioner nor the team representatives will be informed of the Lottery results prior to the opening of the envelopes.

To review:

**Incorrect:**I wish the Pistons would’ve tanked to get more ping-pong balls.**Correct:**I wish the Pistons would’ve tanked to get more combinations.

## Leave a Reply

May 29, 2012• 9:56 pmby

HaanI don’t get it. If there were 9 balls with digits one through nine, wouldn’t that by itself allow for possibilities ranging from 1111 to 9999, i.e., way over the number of combinations you mention? Fourteen balls would make for additional combinations. Also, with balls up to 14 wouldn’t there be possibilities with (at least) five digits?

Maybe I’m misinterpreting. Perhaps 1000 combinations are designated in advance, corresponding with the 100% of different possibilities. For the top choice, 25% of the 1000 bals are somehow designated as being Charlotte’s, etc.

The explanation provided seems quite confusing, but maybe it’s just me.

May 29, 2012• 11:26 pmby

tom@Haan – You’re thinking of situations where order matters (eg. 1234 is a different number than 4321) but for what the NBA is talking about order does not matter. So whereas the combination of numbers 1, 2, 3 and 4 can be combined in 24 ways the NBA only counts each possible combination as the same.

May 30, 2012• 12:40 amby

HaanThat makes sense. Thanks, Tom. So if I could remember introductory stats, I’d remember that when 4 balls are drawn from a set of 14, there can be 1001 different combinations of balls (the number of sequences of digits being far greater).

If I understand that correctly, one minor problem that would remain with the explanation is that there could be combinations of balls with more than 4 digits. If each of 14 balls is numbered and four are drawn, one possibility would be a combination of the balls numbered 11, 12, 13, and 14, for instance. There are 1001 combinations — proportionately assigned to each of the lottery teams – but not each of those 1001 combinations consists of 4 digits?

Also, what happened to that one combination which separates the 1001 possible from the 1000 assigned?

Each of a 1000 possibilities is allocated according to the chance which each lottery team has for slots 1-3. Subsequently, the rest of the lottery slots are determined automatically by ranking the records of the remaining 11 lottery teams which fail to win one of the top three spots from worst to best. The numbers included in the envelopes simply report the results of the proceedings. Does that sound right?

May 30, 2012• 2:54 amby

oatsThe math is 14!/(10! x 4!). The end result is 1,001 possible outcomes. I could show the math, but that is kind of pointless if we already know the result.

The number of digits on the balls doesn’t actually matter. 10-3-2-1 is not significantly different from 4-3-2-1 as far as the process is concerned. All that matters is that the 4 numbers are different from each other. Since the drawing is done with only 14 balls in the hopper, there is no chance of 3-3-2-1.

As for the 1001st combination, that is in fact the drawing of 11-12-13-14. That number is unassigned and would require a redraw. That number hasn’t actually happened yet, but that is the result if it were to be called. This is the same thing that would happen if a number assigned to a selection that has already won in the lottery were to be called. Redraws should be pretty obvious, the balls are replaced into the hopper and drawn again, just like a first time drawing, and the numbers get compared to available numbers.

They also don’t place numbers in the envelopes. They place team logos in envelopes that have the number of the pick on them. Yes, that is nitpicking what you said, but still. The envelopes are set up to make a more entertaining way of presenting the results than the process they use to determine the picks. That said, yes, only the first 3 picks are drawn, and the remainder assigned by the way the rest of the 11 teams placed in the regular season.

May 30, 2012• 12:51 amby

jonsince there are numbers 1-14….with each team gets 4 balls and lets say the pistons get: 1,5,7,8……what pick would they get

May 30, 2012• 2:29 amby

oatsThey don’t pick for the teams individually. They do the first pick, and compare that combination to a set of numbers assigned to various teams. Whichever team matches up gets the first pick. They are no longer eligible to win the lottery with the set of numbers assigned to them for that seeding (although if they have multiple lottery selections they could still get picked for the numbers assigned to the other selection). They then repeat the drawing for the 2nd and 3rd picks. After these 3 picks are assigned, the remainder of the picks are giving out in order of who had the worst record and did not win in the lottery. So, if 1-5-7-8 were selected the team who has that assigned to them gets whichever pick it was drawn for. Should the Pistons not get picked in those 3 picks, they will select 9th, or lower if a team below them got to jump them by winning one of the lottery selections.

May 30, 2012• 1:11 amby

Mike HerringtonPistons will get the first pick. I am a time traveler from the future.

May 30, 2012• 1:28 amby

Mike PayneWith regard to the draft lottery, the phrases “lottery balls” and “ping pong balls” are representational colloquialisms. They’re not intended literally.

“I wish the Pistons would’ve tanked to get [a greater number of ping pong ball combinations]“.

If someone says, “go ping pong!!!”, is their message not clearly communicated? Learn your social understanding of terminology.

May 30, 2012• 9:41 amby

tarsierThis was my initial reaction as well. But upon thinking about it, I am guessing many people actually don’t realize how the lottery works. Not that it really matters, but knowing more is never bad. That said, I will continue to say “________ are playing for ping pong balls” because it is simpler and less awkward sounding than “________ are playing for ping pong ball combinations.”

May 30, 2012• 1:39 amby

HaanI don’t think the public knows which specific combination(s) go with which team, Jon, just the likelihood of each team winning the top pick. We know the proportion of combinations for the top choice in advance, but not the particular combinations.

(btw, it’s dawned on me that the issue of the one unassigned combination has been addressed.)

The probabilities of the Pistons gaining the first, second, and third picks have been announced. It occurs to me, however, that depending on on the procedure, we may just know the probability regarding #1 with certainty because the probabilities concerning #2 and #3 become fixed only during the course of the drawing. Say Charlotte with its 250 combinations wins the first pick. According to one possible procedure, the Pistons would then have its opening share of the 1000 combinations minus the 250 of Charlotte’s which are now dead. That situation would be far more favorable to the Pistons than one in which the best lottery team wins number one, removing/deadening the fewest number of combinations. If the least likely team wins top pick, Charlotte would have its initial 250 combinations come the drawing for #2, leaving the Pistons with a much lower probability of winning #2 than if the best lottery team won #1. You can give a % in advance of the drawing, but you don’t know the Pistons’ odds at the moment of drawing for #2 or #3 until the earlier pick(s) occur(s). There would be other ways of doing it, but that strikes me as the most likely procedure. Of course the announcement counts down to #1, but the drawing must happen from #1 to #3.

May 30, 2012• 3:39 amby

oatsThat is the order they do it in. The odds we have now don’t have the benefit of knowing the actual results, so they have to determine the odds of all possible outcomes. In short, we know what the current odds of Detroit getting picks 2 or 3 are, but those odds will be different at the time of the drawing for those picks.

May 30, 2012• 9:20 amby

Victor FontanaPing pong balls are nice. If the Pistons don’t have one, they should get one.

May 30, 2012• 9:41 amby

HaanThanks for your lucid explanation, Oats. Big night!

Apr 9, 2013• 11:41 pmby

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