An NBA Draft Lottery analysis: Is getting worse than we are really necessary?

[nickagneta]

This reminds me of this recent article:

"Via Andrew Sullivan, Chris Dillow points us toward a weird experiment in a fourth-year finance class at the Autonomous University of Barcelona. One student flipped a coin five times and a group of 20 students predicted heads or tails for each toss. Then a second group of students was told that there would be another set of five coin tosses. The best and worst guessers from the first group would try their luck again, and everyone in the second group would earn money for each coin flip that the worst guesser got right.

But there's more! If students in the second group were willing to pay for the privilege, they could instead earn money for each coin flip that the best guesser got right. There's no reason to do this, of course, since guessing is just guessing. Nonetheless, 82 percent of the students paid to switch to the better guesser."


Please take a statistics class.


250 combinations, 25.0% chance of receiving the #1 pick
199 combinations, 19.9% chance
156 combinations, 15.6% chance
119 combinations, 11.9% chance
88 combinations, 8.8% chance
63 combinations, 6.3% chance
43 combinations, 4.3% chance
28 combinations, 2.8% chance
17 combinations, 1.7% chance
11 combinations, 1.1% chance
8 combinations, 0.8% chance
7 combinations, 0.7% chance
6 combinations, 0.6% chance
5 combinations, 0.5% chance
Here are the odds for each seed to get specific picks if there were no ties (rounded to 3 decimal places):
Seed   Chances   1st   2nd   3rd   4th   5th   6th   7th   8th   9th   10th   11th   12th   13th   14th
1   250   .250   .215   .178   .357                              
2   199   .199   .188   .171   .319   .123                           
3   156   .156   .157   .156   .226   .265   .040                        
4   119   .119   .126   .133   .099   .351   .160   .012                     
5   88   .088   .097   .107      .261   .360   .084   .004                  
6   63   .063   .071   .081         .439   .305   .040   .001               
7   43   .043   .049   .058            .599   .232   .018   .000            
8   28   .028   .033   .039               .724   .168   .008   .000         
9   17   .017   .020   .024                  .813   .122   .004   .000      
10   11   .011   .013   .016                     .870   .089   .002   .000   
11   8   .008   .009   .012                        .907   .063   .001   .000
12   7   .007   .008   .010                           .935   .039   .000
13   6   .006   .007   .009                              .960   .018
14   5   .005   .006   .007                                 .982

Every ounce of information you need is right here. Combing through the past data is ridiculous. Like breaking down the data in the first 20 coin flips out of a million.

That goes for the conspiracy theories as well. Unless you think Stern really wants great players to end up in Orlando and Cleveland - 2 of the 4 or 5 worst markets in the league.  Don't get fooled by the randomness.

Just so you know I have a BME and am two semesters away from a BA in Mathematics and then plan to get my MA in Applied Mathematics. I've taken a stats class or four in my life.

This was a historical look at expectations and not a future look per se. My guess is the NBA won't be around for a million years for every possible outcome to come to fruition. So why not look back and see what outcomes have occurred and take a look at those results to see what might transpire if recent results are any indication. It gives a great window to look through for expectations.

[LooseCannon]

That doesn't change the fact that the players most likely to help a team to multiple 50+ win seasons and a chance at a title are taken in the top 5 of the draft, and by far the easiest way to get such players is to get a top 5 draft pick, and by far the most likely way to get a top 5 draft pick is to be one of the 5 worst teams for at least one season.

I don't think anyone has proven to my satisfaction that being one of the 5 worst teams is easier than trade or free agency for acquiring such a player.

[Boris Badenov]

That doesn't change the fact that the players most likely to help a team to multiple 50+ win seasons and a chance at a title are taken in the top 5 of the draft, and by far the easiest way to get such players is to get a top 5 draft pick, and by far the most likely way to get a top 5 draft pick is to be one of the 5 worst teams for at least one season.

I don't think anyone has proven to my satisfaction that being one of the 5 worst teams is easier than trade or free agency for acquiring such a player.

I do think GM ability in different areas is important. This just occurred to me, but in some sense advocating a tank is a riskier move - we don't know anything about Danny's ability to draft well in the top 5. We do know that he's capable of drafting well later in the draft, and trading drafted assets for bigger stars.

Of course he could end up moving a top 5 pick like he did in 2007, so maybe that doesn't matter quite so much.

[syfy9]

Let's say there is a prize in a thing. And to get the prize, you need to bet on which color (red, blue, yellow, green) ping pong ball will be picked out of a totally random assortment of balls.

In that assortment, there are 25 red balls, 20 blue balls, 16 green balls, 14 red balls, 12 purple balls, and 10 white balls.

You know that in the last 20 draws, a red ball has only come up once.

If you knew that winning the bet would change your life forever, what color do you bet on?

Probably orange.

[nickagneta]

Let's say there is a prize in a thing. And to get the prize, you need to bet on which color (red, blue, yellow, green) ping pong ball will be picked out of a totally random assortment of balls.

In that assortment, there are 25 red balls, 20 blue balls, 16 green balls, 14 red balls, 12 purple balls, and 10 white balls.

You know that in the last 20 draws, a red ball has only come up once.

If you knew that winning the bet would change your life forever, what color do you bet on?

Probably orange.

Orange. My favorite flavor and yet not my favorite color.

[PhoSita]

That doesn't change the fact that the players most likely to help a team to multiple 50+ win seasons and a chance at a title are taken in the top 5 of the draft, and by far the easiest way to get such players is to get a top 5 draft pick, and by far the most likely way to get a top 5 draft pick is to be one of the 5 worst teams for at least one season.

I don't think anyone has proven to my satisfaction that being one of the 5 worst teams is easier than trade or free agency for acquiring such a player.

It's not something that really needs to be "proven."

It's self-evident.

Drafting a player requires no investment of resources other than being bad in the first place, which usually requires only that you spend less money and don't give up assets to be better in the short term.

Free agency requires a LOT of money to sign that kind of player, and such players rarely are available in free agency anyhow.  Having max cap space to spend often requires that you give away players for very little or nothing, so that's an additional cost.

Trading requires you to give up a bunch of assets, and typically the kind of players who get traded in those deals are themselves top 5-10 draftees.

[LooseCannon]

That doesn't change the fact that the players most likely to help a team to multiple 50+ win seasons and a chance at a title are taken in the top 5 of the draft, and by far the easiest way to get such players is to get a top 5 draft pick, and by far the most likely way to get a top 5 draft pick is to be one of the 5 worst teams for at least one season.

I don't think anyone has proven to my satisfaction that being one of the 5 worst teams is easier than trade or free agency for acquiring such a player.

It's not something that really needs to be "proven."

It's self-evident.

Drafting a player requires no investment of resources other than being bad in the first place, which usually requires only that you spend less money and don't give up assets to be better in the short term.

Free agency requires a LOT of money to sign that kind of player, and such players rarely are available in free agency anyhow.  Having max cap space to spend often requires that you give away players for very little or nothing, so that's an additional cost.

Trading requires you to give up a bunch of assets, and typically the kind of players who get traded in those deals are themselves top 5-10 draftees.

It's not evident to me.

One could quantify this by looking at the top 15 or so players in each of the past ten seasons who were taken with a top 5 pick and see how many of those seasons were spent with the team that drafted them.  I haven't run the numbers, so I don't know what the answer is, but I am not willing to predict whether or not more or less than half of the players fit that description.  Are you?

[PhoSita]

That doesn't change the fact that the players most likely to help a team to multiple 50+ win seasons and a chance at a title are taken in the top 5 of the draft, and by far the easiest way to get such players is to get a top 5 draft pick, and by far the most likely way to get a top 5 draft pick is to be one of the 5 worst teams for at least one season.

I don't think anyone has proven to my satisfaction that being one of the 5 worst teams is easier than trade or free agency for acquiring such a player.

It's not something that really needs to be "proven."

It's self-evident.

Drafting a player requires no investment of resources other than being bad in the first place, which usually requires only that you spend less money and don't give up assets to be better in the short term.

Free agency requires a LOT of money to sign that kind of player, and such players rarely are available in free agency anyhow.  Having max cap space to spend often requires that you give away players for very little or nothing, so that's an additional cost.

Trading requires you to give up a bunch of assets, and typically the kind of players who get traded in those deals are themselves top 5-10 draftees.

It's not evident to me.

One could quantify this by looking at the top 15 or so players in each of the past ten seasons who were taken with a top 5 pick and see how many of those seasons were spent with the team that drafted them.  I haven't run the numbers, so I don't know what the answer is, but I am not willing to predict whether or not more or less than half of the players fit that description.  Are you?

That's irrelevant.

I'm talking only about the resources required to get the player in the first place.

[guava_wrench]

So if the metaphor is that a tanking C's team is risking the franchise's future by decimating the current team for the sake of more Ping-Pong balls in the lottery, it may well be a risk not worth taking.

The team was already decimated.

[guava_wrench]

Just so you know I have a BME and am two semesters away from a BA in Mathematics and then plan to get my MA in Applied Mathematics. I've taken a stats class or four in my life.

This was a historical look at expectations and not a future look per se. My guess is the NBA won't be around for a million years for every possible outcome to come to fruition. So why not look back and see what outcomes have occurred and take a look at those results to see what might transpire if recent results are any indication. It gives a great window to look through for expectations.

The past is irrelevant for expectations. We know exactly what to expect with the math. The small sample size of all the lotteries doesn't change that.

I understand that sometimes it is nice to put the lottery in terms that are understandable for the less mathematically competent, but mentioning things like the mean record position of lottery winners is incredibly misleading to those same people. They might end up confusing the mean with the mode and thinking that 4th worst record is better.

Regarding another post, the draft is not as "random" as some are making it out to be. There are guys like Duncan and Lebron who were no brainers. Guys that generate the tank buzz are usually clear perennial all-star talent. Oden was the same, but injuries stopped him. When he plays, he is clearly a difference maker. Guys like Irving or Bargnani didn't tempt anyone to tank, even though Irving has become an amazing pro. You can't just crunch numbers when there are actual players involved. Tanking last season obviously would have been pointless since the players coming out were quite underwhelming.

Some people keep talking about analyzing players taken top 5 or so. That is all irrelevant when you have a guy of a certain caliber in a draft, like Duncan or Lebron, or, many would say, Wiggins. I admit, I know little about Wiggins because I don't follow high school basketball.

One this is sure, the worse your record is, the more players you get to choose from when you pick.

[Tr1boy]

Unless you are a brutal team from head to toe, you are not getting the 1st pick. Or 1-5.

Celts will next draft based on need more then talent. Anybody really think wiggins will be that much superior to jeff green? Unless green goes back to being green of the starting of last year , he is a long term solution at the sf spot. He has the height, iq, skills to be a top 5 guy in the league. He wont be the issue this upcoming year.

Its going to be either we are short that one inside presence though i have faith in olynyk and sully, ab is not the long term starting sg or rondo is never the same / gets traded and we need a stud pg.

No freaking tanking allowed. Dont care what management does with trades but on the court the team has to try their best and the best players left on the court in the final moments of the game

[nickagneta]

Just so you know I have a BME and am two semesters away from a BA in Mathematics and then plan to get my MA in Applied Mathematics. I've taken a stats class or four in my life.

This was a historical look at expectations and not a future look per se. My guess is the NBA won't be around for a million years for every possible outcome to come to fruition. So why not look back and see what outcomes have occurred and take a look at those results to see what might transpire if recent results are any indication. It gives a great window to look through for expectations.

The past is irrelevant for expectations. We know exactly what to expect with the math. The small sample size of all the lotteries doesn't change that.

I understand that sometimes it is nice to put the lottery in terms that are understandable for the less mathematically competent, but mentioning things like the mean record position of lottery winners is incredibly misleading to those same people. They might end up confusing the mean with the mode and thinking that 4th worst record is better.

Regarding another post, the draft is not as "random" as some are making it out to be. There are guys like Duncan and Lebron who were no brainers. Guys that generate the tank buzz are usually clear perennial all-star talent. Oden was the same, but injuries stopped him. When he plays, he is clearly a difference maker. Guys like Irving or Bargnani didn't tempt anyone to tank, even though Irving has become an amazing pro. You can't just crunch numbers when there are actual players involved. Tanking last season obviously would have been pointless since the players coming out were quite underwhelming.

Some people keep talking about analyzing players taken top 5 or so. That is all irrelevant when you have a guy of a certain caliber in a draft, like Duncan or Lebron, or, many would say, Wiggins. I admit, I know little about Wiggins because I don't follow high school basketball.

One this is sure, the worse your record is, the more players you get to choose from when you pick.

Your premise is not exactly true as empirical probability with the return distribution of past data could theoretically give expectations of short term future(in other words not using the law of large numbers). I could have done all that but this simple approach was easier to understand and a lot less work. Though still a lot of work.

[EDWARDO]

Typically like your posts Nick, and enjoyed reading this one, too. But agree with the Guava Wrench on this one-- his first 2 paragraphs above are spot on. The math is plain and simple. Fun to look at the past, but don't let that get in the way of the raw math.

Also agree that there are good and bad years to have high picks and that we can in fact know if a year has a higher probability of having more high level pros and which guys they will be. Again-- probabilities and not definites. To think otherwise is to bury your head in the sand to some degree. So, if Cleveland (theoretically) could have traded this tear's #1 overall to be guaranteed next year's #1 overall, they would have and should have done it. It's not a guarantee that next year's #1 overall will be better, it's just some knowledge about the players that leads EVERYONE to believe that he is LIKELY to be better.

[indeedproceed]

Restating what others have said because I like the sound of my own text:

Looking at every draft of the last 20 years, or since the weighted system became the norm, you're neglecting the context of the quality of each draft (and still not getting statistical significance) If you only look at similarly hyped drafts your sample size becomes so small, the trend is meaningless.

Darned if you do, darned if you don't. Neither one really gives you a picture of a outcome that is terribly impossible to judge anyways. The best we can do is look at what we know.

1) Alledgedly historically good draft on the top end

2) Being terribly bad is the best way according to the system to get a higher pick, giving you the best choice of players.

It becomes a cost-benefit of what we have to give up to be really bad (not much, unless it involves dealing Rondo) vs what we hope to gain in the lottery.

[LooseCannon]

Unless you are a brutal team from head to toe, you are not getting the 1st pick. Or 1-5.

You can be a team with talent that gets hit hard by injuries.  Or you can get lucky in the lottery.