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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 you heard the Cleveland Cavaliers won the top pick in the NBA draft – again. This time, despite relatively long odds (1.7 percent) of doing so.

This has led a large number of people to declare the NBA Draft Lottery is rigged so a particular team wins the lottery for some nefarious purpose that serves the NBA. The media’s desire to be as sensational 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 why, no matter which team won, people would say it was rigged.

NBA Draft Lottery

Year Probability of 1st Pick
2011 2.80%/19.90%
2013 15.60%
2014 1.70%


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 given 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 (see box above).

Note that in 2011 Cleveland had acquired the Los Angeles Clippers’ first round pick as well. The Clippers had a 2.80 percent chance and the Cavaliers a 19.90 percent chance with their own pick for a total of 22.70 percent.

As these are independent events, to determine the probability 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 percent probability of the Clippers pick.

When we do the calculation, we find 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 the odds of drawing to a Royal Flush using Expert Strategy are about 1 in 42,000.

This is roughly three times less likely as what happened to Cleveland. The odds of being dealt Four of a Kind from a 5-card Stud deal are 1 in 4,165. This is three times 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 first pick three times. Their true odds of winning it in 2011 were 22.70 percent. Had they won the first pick with their own pick, it wouldn’t change the questions being asked this week.

If we substitute 22.70 percent for the 2.8 percent, we find the odds of Cleveland winning all three picks were only 1 in 1,661. 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 percent 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 Cleveland would win the first picks in 2011, 2013 and 2014 and not get it in 2012, given their probability of getting the first pick in each of the years?

2) What was the probability Cleveland won the first pick three out of the last four 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 first pick in 2012. We find when we do this the probability is about 1 in 1,927. While not a common occurrence, it is 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 add it to the product of multiplying the probability of winning in 2011, 2012 and 2014 while losing in 2013, etc. There are four different ways Cleveland could have won three out of the last four first round picks.

When we perform this calculation the final probability that Cleveland won three out of the last four first round picks is a whopping 1 in 165. Quick, stop the presses. I have the proof 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 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 two out of the past three years, along with a three and a four and still not make the playoffs?

Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is Contact Elliot at [email protected].

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About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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