# Stop the Presses

I'm going to skip over what was supposed to be my topic for this week (continuation of Free Bet Blackjack), because there is another compelling and timely topic that simply requires, well, debunking.  For those of you who are sports fans, there is little doubt that you heard that the Cleveland Cavaliers won the top pick in the NBA draft - AGAIN.  This time, despite relatively long odds (1.7%) of doing so.  This has led a large number of people to declare that the NBA Draft Lottery is rigged so that a particular team wins the lottery for some nefarious purpose that serves the NBA.  The media's desire to be as sensationalist as possible has led to some very shoddy math work in an attempt to keep the discussion going.  Ironically, earlier in the day on Tuesday (the day of the draft), I read a parody column that declared the draft rigged BEFORE the draft even took place and showed how that no matter which team won, why people would say that it was rigged.

For those of you not familiar with the NBA Draft Lottery process it goes something like this.  The teams that finished with the worst records are giving positions in the lottery with the teams with lesser records given a higher probability of winning the top pick in the draft.  So, let's take a look at what Cleveland's probabilities were for 2011, 2013 and 2014:

Year   Probability of 1st Pick

2011    2.80%/19.90%*

2013    15.60%

2014    1.70%

* Cleveland had acquired the Los Angeles Clippers first round pick as well.  The Clippers had a 2.80% chance and the Cavaliers a 19.90% chance with their own pick for a total of 22.70%.

As there are independent events, the probability that Cleveland would win all three of these, we simply need to multiply these numbers together.  In 2011, the first pick was actually won by the Clippers who had traded the pick to the Cavaliers.  So, for the moment, we'll use the 2.80% probability of the Clippers pick.   When we do the calculation, we find that the odds of Cleveland winning all three picks was about 1 in 13,467.  These are relatively long odds, but hardly astronomical.  For anyone who plays video poker, they know that the odds of drawing to a Royal Flush using Expert Strategy is about 1 in 42,000.   This is roughly 3 times less likely as what happened to Cleveland.   The odds of being dealt Four of a Kind from a 5-card Stud deal is 1 in 4165.  This is 3x MORE likely than what happened to Cleveland.

This calculation provided us with most 'outlandish' probability and yet it hardly proves anything was rigged.  There have been stories of people hitting Lotto more than once.  The odds of winning once in any particular week is tens/hundreds of millions to one.  So, if someone wins twice does this mean the whole lottery is rigged?

To make matters worse, people aren't really focused on the details, only that Cleveland won the 1st pick 3 times.  Their true odds of winning it in 2011 was 22.70%.  Had they won the 1st pick with their own pick, it wouldn't change the questions being asked this week.  If we substitute 22.70% for the 2.8%, we find that the odds of Cleveland winning all 3 picks was only 1 in 1661.  This is now almost three times as likely as being dealt that Four of a Kind.

Let's keep going.  Some of you may be wondering what happened in 2012, which was conveniently ignored by, well, just about everyone.  Now, if Cleveland had made the playoffs, they would have had NO chance to get the top pick and it would be appropriate to ignore it.  But, that isn't even close to what happened.  Cleveland had a 13.80% chance of getting that first pick, but didn't.  So, now let's ask the PROPER questions.  In my mind, these would be the following:

1)  What was the probability that Cleveland would win the first picks in 2011, 2013 and 2014 and NOT getting it in 2012, given their probability of getting the first pick in each of the years.

2)  What was the probability that Cleveland won the first pick 3 out of the last 4 years given their probabilities of winning the pick in each of those years.  Because let's face it, we'd be having this same discussion if they had won in 2011, 2012 and 2014 or 2012, 2013, 2014.

Question #1 is resolved in a similar manner to the problem presented earlier.  We multiply the probabilities of the independent outcomes together.  This time we use the probability of NOT getting the 1st pick in 2012.  We find when we do this that the probability is about 1 in 1927.  While not a common occurrence, still far from proving a conspiracy.

Question #2 requires that we multiply each of the combinations of winning 3 out of 4 and summing up these values.  So, we multiply the probability of winning in 2011, 2013 and 2014 and losing in 2012 (result from Question #1) and adding it to the product of multiplying the probability of winning in 2011, 2012 and 2014 while losing in 2013, etc...  There are 4 different ways that Cleveland could have won 3 out of the last 4 1st round picks.

When we perform this calculation we find that the final probability that Cleveland won 3 out of the 4 last 1st round picks is a whopping 1 in 165.  Quick stop the presses.  I have the proof that the NBA's lottery system is most assuredly completely legit.  1 in 165.

I have frequently written about how people don't understand how probabilities work and this week we have gotten an incredible real world look at this phenomenon.  I have seen countless posts on Facebook with people decrying how the NBA Lottery is rigged and yet when you look at the real numbers, you realize that what happened here while on the rare side was completely within the 'norm'.

To me, the only real question that should be asked is how in the world can the Cleveland Cavaliers have the top pick 2 out of the past 3 years, along with a #3 and a #4 and  STILL not make the playoffs??  It would appear with the return of LeBron, we won't have to worry about this a year from now.