### Bucks Diary's 20 Spins: Volume 10

We have just as many pingpong balls today as we had yesterday, but my results, for some reason, just get worse and worse. Today I only got 3 results in the money picks (15%). And, get this, a whopping 15 of my results were below the Bucks rightful third spot (75%). Again, the fifth spot was the most frequent result.

One thing I didn't realize when I was doing my earlier post -- Atlanta's number one pick is owned by the Phoenix Suns. The Hawks, therefore, have no incentive whatsoever to play down to the third worst spot. That should help the Bucks, at least marginally.

A scary thought, though... what if Phoenix lands one of the money picks? Could you imagine them with Oden or Durant? It would be the equivalent of the Lakers getting Magic when they already had Kareem or getting Worthy when they already had Magic and Kareem. Or, of course, what the Celtics might have been had Len Bias lived. At any rate, they look like they will become an even bigger monster next year.

**Correction**: A very helpful reader has corrected me. It turns out the Hawks in fact DO have an incentive to play down to the third worst spot. The reader informed me that the pick they traded to the Suns is top three protected. That means the Suns haven't got a shot at Oden or Durant, and the Hawks have an incentive to increase the odds that they will land in one of the top three. But if the Hawks pick isn't in the top 3, the Suns still more than likely will get a very good player to add to their roster.

## 17 Comments:

Hey, just an fyi. The Hawks pick is actually top-three protected, so they actually have more of a reason to play into the top three. Only if they don't sneak into the top three does the pick go to the Suns.

I studied the lottery probability yesterday, you know what? The "competition" between Bucks and Hawks (3rd and 4th seat)is practically meaningless. Because for the 3rd worst seat, the probability of getting 1st or 2nd pick is:

.138+.142=28%

For the 4th worst seat, the probability is:

.137+.142=27.9%

So there is only 0.1% difference(!) between 3rd and 4th seat for getting 1st or 2nd pick in the draft lottery.

So I guess the most important thing is how to "catch" the Celts, because it'll make a huge difference in probability calculation.

1st or 2nd pick for 2nd worst seat:

.199+.188=38.7%

(Gee, I just kept posting on the wrong thread)

Frank, I'm sorry and I don't know how you found your numbers but that's crazy talk. #3 has 156 ping-pong combinations and a 15.6% chance at the top pick. #4 has 119 combinations and a 11.9% chance.

You are right that #2 has 199 combinations and a 19.9% shot at pick one.

I don't see how your probabilities change from pick to pick. It would seem with the way the combinations work that you'd have the same chance of getting any of the top 3 picks really.

Frank, you may be on the wrong post, but you are EXACTLY right. I mentioned that in an earlier post, but I just didn't get it quite as close as you did. But you're math is exactly right.

Anonymous, what Frank is talking about is the chance that the Bucks will land in EITHER the 1st or 2nd pick, and he's actually right. If you combine the two probabilities, they aren't that different from the third and the fourth pick. Check out "NBA Draft Lottery" on wikipedia.com. They have all of the probabilities.

Let me correct that last one... It should read "they aren't that different between the third and fourth worst record."

Okay, now I'm totally fucked up.

I'm back to thinking "Anonymous" is actually right. The probabilities I was siting, the ones laid out on the "NBA Draft Lottery" page on wikipedia.org, are based solely on the "2006 Lottery", a lottery in which two teams tied for the third worst record -- that's why the probabilities are so close for the two -- the NBA just split the pingpong balls between the two teams. So I was dead wrong in siting that as proof.

So there may yet be a statistically significant difference between 3rd worst and 4th worst.

Frank, is your math totally accurate? Because as Anonymous pointed out, you seem to be adding the same two probability amounts for both the third and fourth worst records when I know at least the 1st of those probabilities should be different for each. Unless I'm misreading your math, which is completely possible.

I'm confusing myself here. Somebody help me out with this.

Now I can see how a team's probability would go up from Pick 1 to Pick 2: If there's one less team (who already has Pick 1) then everyone's odds should go up for Pick 2.

That doesn't explain how the 2nd-worst team's probability would go down for the 2nd pick in Frank's work though.

Also the only reason I've been assuming they still draw #1 first, then #2 and #3 is because of an old ESPN.com article about the year they first opened up the lottery to reporters (Yao draft).

It sounds confusing to try to calculate because of the way they number the balls.

I almost want to superstitiously cool off on thinking about any of this so it would hurt a little less if say Indiana and Chicago via NY cruise in on the combinations.

OK. I'm totally fucked up too. Because I used the "wrong" (which is not exactly wrong but who remembered there was a tie for 3rd and 4th worst seat last year?) probability on the wiki link which Mike showed just then.

I'll come back with the correct calculation later (hopefully).

Here is the answer first:

If Bucks stays at 3rd seat, the prob of getting 1st or 2nd pick is 31.34%.

If Bucks beats the Celtics, the prob raises to 38.71% (this number matches the one I posted earlier and the one on the wiki link, because the calculatoin there is correct for 1st and 2nd seat)

If Bucks go back to the 4th seat, the prob drops to 24.50%

so, 24-->31-->38. I guess it is still worthy to tank.

If anybody is interested in this, the detailed calculation is here:

The probability of getting one of the first two picks is:

P(1st)+Sigma_i P(2nd)-->The sum of two probabilities since it is mutually exclusive (unless master Harris pull up some shocking trade!). Sigma_i means that you need to sum up all the possible scenario that the other 13 teams get the first pick then Bucks get the second one.

So if the Bucks have the second worst record, P(1st) eqauls to

199/1000

Sigma_i P(2nd) equals to

(199/1000-250)*(250/1000)+

(199/1000-156)*(156/1000)+

....

...

(199/1000-5)*(5/1000)

The first line is the worst team gets the 1st pick, etc.

If you really want to be hard on yourself, here is an excellent academic paper which compared the old and current nba lottery system and anlysis.

http://www.ajur.uni.edu/v2n3/Florke%20&%20Ecker.pdf

Thank you, Frank. That's great work. Holy shit, you just blew me away. That's awesome.

Have you been following my 20 Spins deal? Its a fun little meaningless exercise, but its also meant for nonmath people like me who understand better through concrete example.

Anyway, the point I'm getting at is the results I'm getting with my 20 Spins are clearly underperforming the odds. I don't think I've hit 31% in the money picks(1-2)yet. So, the better odds you just provided brighten my outlook considerably.

Yeah, good looking out Frank

Hey Ty,

First, your blog is awesome and I'm just doing my little contribution as a submarine daily reader. Orz

Second, I followed every daily spin. I think it perfectly shown the nature of the lottery draft. The only thing predictable is its unpredictability. If we have 1000 spins, yeah yeah, we may have some advantage, but not in one spin, or 20 spins (well, that's why we got Bogut, didn't we? :-))

As a Buck's fan who never been to Bradley Center (yaya, I know is blasphemy, don't punch me), can I make a humble request here? I would love to see you write an article titled "top 10 DOs and DON'Ts at Bradly Center".

(submarine dives........)

First of all, thanks for the nice compliment, and the contributions. My spins have reflected the odds, eh? Shows how strong my mathematical acumen is.

You've never been to the BC? Gotta get there. I think the first thing on my list would be, don't order the "soft" pretzels. Its like eating your shoe (LOL).

The second thing would be, if you don't have tickets, and you're dealing with the legendary Kilbourn street scalpers, know your BC seat layouts. A couple of times I have asked them for lower seats, and they'll say "I got em right here". I'll look at the tickets and they say 400 something. Anything 400 is second level. If you want lower level its 200. Oh, and beware of the scalpers thumb. Many of them also work the Brewers game, and one time they tried to sell my brother and his buds some tickets to a Saturday game on Sunday afternoon. When they showed the tickets, they displayed them with a strategic thumb over the date. I still crack up about that one.

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