## How The Ping Pong Balls Work

This is, quite simply, for those of you that are still curious/confused about the whole ping-pong ball aspect to the lottery. I've attempted to explain the whole thing using numbers, words and a random number generator.

I've explained, in a previous post, how the Jazz have 75 combinations for them (through the #6 pick; #12 has a some as well) when the lottery process starts. A fair second question, and one I didn't really hit on, is "how do the combinations work?" How do the 75 combinations magically (we hope) land us a top-3 pick? I'll try to explain more about the actual aspects of it all here.

If you're interested, I hope this helps. And if there are any more questions, just ask.

PING PONG BALLS

So, the balls are numbered 1 through 14. So (just for clarity's sake)

• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10
• 11
• 12
• 13
• 14

They are put into a machine, which spits a ball out every 10 (or something like that) seconds. So they let it spit out four balls and record the combination. That combination corresponds to some team in the top 14.

COMBINATIONS BY TEAM

The top 14, along with the number of combinations they have.

• Minnesota, 250 shots out of 1000 to have the top pick
• Cleveland, 199
• Toronto, 156
• Washington, 119
• Sacramento, 76
• Utah (New Jersey), 75
• Detroit, 43
• Cleveland (LA Clippers), 28
• Charlotte, 17
• Milwaukee, 11
• Golden State, 8
• Utah, 7
• Phoenix, 6
• Houston, 5

Generally the 5 spot (Sacramento) would have 88 combos and the 6 spot (Utah through NJ) would have 63. But since the teams tied (record-wise), they add the two numbers (88 and 63) up and average them out (75.5). Since you can't have half of a combination, they make it 76 and 75. Then there is a coin flip - Sacramento won, so they got the 76 and the Jazz ended up with 75. But even with that loss, the Jazz picked up 12 more combinations more than they normally would've had. (More on that in a second.)

FROM 24K to 1001

So, if you were to do the math, there would be a total of 14 X 13 X 12 X 11 combinations of numbers. 14 possible numbers can come out first, then 13 (because the first ball is not put back into the machine), then 12 and then 11. That ends up being 24,024 combinations of 4 numbers. To make things easier, they decided to make each set of the same four numbers the same.

1,2,3,4 is one combination. As the way its set up, and combination with those 4 numbers counts as the same combination. So whether the machine spits up 1,2,3,4 in that order, or 2,3,4,1 or 3,1,4,2, they're all the same - and they all correspond the one team.

Then that 24,024 can be reduced. (For the numbers 1,2,3,4, there are 24 possible way with which you could set them up, going from 1234 to 4321.) So with 24 possibilities for each combination, you divide the 24,024 by 24 and get 1001. (I hope that makes sense.)

So now we're down to 1001 unique combinations, each with 24 different ways in which it can show up. I won't list out all 24,024 or even all 1001, but they range from 1,2,3,4 (or any combination of those four numbers) to 11,12,13,14 (or any combination of those four numbers). Any combination of 1,2,3,4 is regarded as being the same as any other, which becomes important a bit later. (Sorry that I keep harping on this.)

THE COMBINATIONS BREAKDOWN

Okay, so the breakdown. Now, I'm not going to type them all out because it would take forever, but I hope I get enough to help you understand the gist of it.

So for Minnesota to have 250 combinations, they have (I'm assuming they're assigned in order, but either way, it should explain the basics)…

1,2,3,4

1,2,3,5

1,2,3,6

1,2,3,7

1,2,3,8

1,2,3,9

1,2,3,10

1,2,3,11

1,2,3,12

1,2,3,13

1,2,3,14

(that's 11 combinations out of the 250)

1,2,4,5

1,2,4,6

1,2,4,7

etc.

all the way down to

1,7,12,13

1,7,12,14

That's 250 combinations. So everything "starting" (more like containing, but yeah) the numbers 1 & 2, or 1 & 3, or 1 & 4, or 1 & 5, or 1 & 6, and down to 1,7,12,14 (so all the 1 & 7 combos except the 1,7,13,14 combination) belongs to Minnesota. Then the next 199 combinations, starting with 1,7,13,14 and then going on to the 1,8,9,10 and so on, belong to the next team (Cleveland in this case).

Again, I could write out all 1001 combinations, but I don't know if you want to read all that.

So the list goes on, down by teams as each team gets its allotted combinations. In the case of Houston, #14, they have 5 combinations. So they will get…

9,11, 12, 14

9,12,13,14

10,11,12,13

10,11,12,14

10,11,13,14

Phoenix, #13, will get the 6 combinations immediately preceding that. And so on. That last possible combination - 11,12,13,14 (or any combination with those 4 numbers) is unassigned. If that combination comes up (which it never has), then they just ignore it and pick again.

The benefit for the Jazz picking up the 12 extra combinations - normally they'd have a 6.3% chance of landing the top pick with that spot. With the 12 combinations, its now 7.5%. It doesn't seem like much, but when you get down to random number generators (which is pretty much what the machine is), its enough to make a difference.

TO CONFUSE YOU A BIT

I guess, technically, if you want to look at it this way, each combination above is technically counting for 24 different possible draws. So, if you don't like thinking of 1,2,3,4 and 3,4,1,2 and 2,4,1,3 as the same combination, then you don't have to. Instead, you just multiply each teams possible combinations from above by 24 to get how many combinations they have out of 24,024 possibilities. That does become uglier though, and much more messy - especially if trying to make a list of all the combinations by team. 1001 is bad - 24,024 would be horrible. But technically that's what it is. All 24 combinations of 1,2,3,4 belong to the same team - so they're able to cut it down and just use 1,2,3,4 to represent ALL of those combinations. I won't do that though - this is just an "FYI" in case you prefer to look at it this way.

PICKING THE TOP SPOTS

Okay, so when they get into the room with the machine and turn it on, the first spot they're deciding is the #1 pick. So - well, assume you have a random number generator that doesn't repeat numbers. And you've set it from numbers 1 through 14. (They have ping pong balls and a machine - I don't have that though, so my calculator will have to do.)

Lets say the first 4 numbers that pop out are 7,9,3,6, which is 3,6,7,9 numerically (not that it matters). Then they go down the list (or whatever they have) and figure out who that number belongs to. Lets say Washington (#4 in this draft) - again, I don't know who it would end up with, I'm just guessing. So yeah, Washington in this case. Then, using that process, Washington is given the number #1 pick in the draft, moving them up from #4.

Those 4 balls are returned to the machine, and they do it again - for the #2 spot now. This time, lets say they get 11, 14, 13, 12. That happens to be the 11,12,13,14 combination, so it is disregarded. The balls are put back into the machine, and they pick for #2 again.

Say this time they get 6,8,10,5. Lets say that belongs to the Jazz (the #6 pick). Yay! … Then the Jazz are given the #2 pick in the draft. The balls are returned to the machine and they do it again - this time for the #3 pick.

So this time, assume 4,6,7,9 come up. Lets say that belongs to Washington as well (I don't know if it does or not  in such a scenario - I'm just pretending). Since Washington already has the first pick, they can't pick again. So the draw is disregarded, the balls replaced, and they do it again.

(Worth noting, since the Jazz (and Cavs) have 2 picks each - if the Jazz #6 pick had another combination come up again, it would be disregarded since they already have moved up to the #2 pick from that spot. On the other hand, if the Jazz #12 pick had a combination drawn there, then that pick would become #3 and the Jazz would pick #2 and #3.)

But assuming it got the Washington pick again and they're redrawing. This time, 3,2,1,6 comes up. That combination is of the 1,2,3,6 (just ordering them numerically) variety, which as you can see from above belongs to Minnesota. So then the Timberwolves get the #3 pick. After that, everything is just decided based on the pre-set order.

So yeah, pretty much its like a random number generator. It spits outs 4 numbers, and you match it up to the team. I haven't figured out what the Jazz's 75 numbers are (assuming they use the same numbering system I do); I can't figure it out if you want.

ORDER

So, in that situation, the order would go…

• Washington (previously #4)
• Utah (previously #6)
• Minnesota (previously #1)
• ---------------- (after this point, everyone just shifts down until #6)
• Cleveland (previously #2)
• Toronto (previously #3)
• Sacramento (previously #5)
• ---------------- (since only teams in the top 6 jumped into the top 3, everyone below 6 stays in the same spot. … If #9 had moved into the top 3 instead of Washington, then everyone down to #8 would've then moved down a spot to correspond for the moving up)
• Detroit (still #7)
• Cleveland from LA Clippers (still #8)
• Charlotte (still #9)
• Milwaukee (still #10)
• Golden State (still #11)
• Utah (still #12)
• Phoenix (still #13)
• Houston (still #14)

HOW IS IT DONE?

Again, as far as I know, they use some sort of machine that pops out (or something) ping pong balls one at a time. So then they have 4 numbers, which will correspond to some team (maybe they have a chart, or a list, or something). A representative from the NBA and a representative from each team is in the back room, where this process takes place. An unaffiliated member then puts the teams logos into envelopes and places them in the slot in the other room. This room, which we see at halftime, has a different NBA representative (Stern, maybe? I don't remember) and a different representative from each team. So no one in this room knows the results or what happened in the back room. So to everyone there, every opening is a surprise.

BENEFITTING THE WORST TEAMS, BUT NOT TOO MUCH

Minnesota has 250 chances to end up with the topic pick, a nice 25%. But then, due to the "top 3 only" picking, they also have a 21.5% shot at the #2 spot, 17.8% shot at the #3 spot and 35.7% shot at the #4 spot. Because of the set up, Minnesota can't drop below #4. If three teams below #3 jump into the lottery, thus displacing #1 Minnesota, the furthest they can fall (based on bad record) is #4.

The benefit comes from that aspect. If they had just allowed the worst team to have the #1 pick, that would encourage tanking. On the other hand, if they gave every team an equal shot at the #1 pick (1001/14 = approximately 71 picks per team), then that would increase the chance that a "better" team would land the #1 pick - which would definitely not help the bad teams. Not to say it doesn't still happen (again with Orlando winning the Chris Webber lottery despite having just 1 combination out of the 66 at the time), but its much rarer now. The goal is to have the top teams near the top of the lottery, without just giving it to them.

All comments are the opinion of the commenter and not necessarily that of SLC Dunk or SB Nation.

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