Lotteries are typically really tough to win.
Powerball, Mega Millions, and even state lotteries are all damn near impossible claim the jackpot. Even winning anything is pretty unlikely. Getting a Pick 5 (numbers 0-9) exactly right is 1 in 100,000. Getting luck enough to draft the next phenom like LeBron, Anthony Davis, or perhaps Zion Williamson? That's much, much easier than getting a few digits in the right order.
The NBA trade deadline is fast approaching and that means teams will be dealing a bunch of picks and players. Sometimes big contracts will be off-loaded by teams looking for salary cap or luxury tax relief (both of those are topics for a later post) for draft picks and expiring contracts. Other times picks will be traded for a player a team hopes will help in the playoff push. When these deals are made you may hear a pick is "top 10 protected" meaning if that particular pick ends up within the first 10 overall then the team that gave up the pick gets to keep it. Why would any team agree to let a pick be protected? Well, the NBA draft can often be very top-heavy in transformational talent, so it is worth protecting such an asset. Additionally, heavily protecting a pick may lessen it's value. Right now the Lakers have the second best record in the NBA. If they decided to trade their first round pick (which you can't always do because of rules, blah blah blah) the receiving team would expect it to fall in the 26-30 range. The Lakers protecting that pick in the top 14 or 20 wouldn't make much difference, the pick will more than likely convey. However, look at the Golden State Warriors this season, who very unexpectedly have the worst record in the league at this time. They traded their first round pick to the Brooklyn Nets in the sign-and-trade deal for DeAngelo Russell. The Warriors made the pick top 20 protected, so they won't have to send their likely top-4 pick this year. What do the Nets get this year? Nothing, but next year the process may start again with lesser protection, depending on the details of the trade.
Back to assuming the Warriors are going to have worst record. We can say they have the best "seed" for the lottery. Now let's make change the parameters of their trade with Nets and make the pick only top-4 protected. In this scenario, what is the probability the Warriors keep their pick (i.e. it's in the top four)? What is the probably they would lose it (i.e. they get the 5th pick)? If they end seeded second in the lottery by having the second worst record, does that change the probability of keeping their pick? Below is an interactive table and bar chart (created using Tableau Public) that shows the probability of each team by their seed in the lottery getting each of the 14 lottery slots. If you're on a mobile device, rotate it to a landscape for a better view.
Using the table above we see that the Warriors will have a 47.86% chance a losing their pick as it would not be in the top four. And actually, since the top three seeds all have the have number of combinations they all have the same probability of getting slotted within the first four; there's no difference between seeds 1 - 3 in this scenario. A couple of interesting questions: If the top three seeds have the same number of combinations, why do they have differing probabilities after the 4th slot? What if the pick in our original scenario was top-5 protected?
The number of combinations and the number assigned to each team was changed in 2019 to the current system shown in the table above. We saw in the Warriors example that the team had no incentive to have the worst record and as long as they were seeded 1 - 3 they has the same probability of keeping their top-4 protected pick. This was done to reduce team's incentive to tank. Some think this should be extended to the first five seeds having the same number of combinations. So what if the number of combination and how they're distributed changes? I've got you covered. Click the link below customize your own draft scenario and see how it would change the teams' lottery slot probabilities.
https://mathwithjerome.shinyapps.io/nba_lottery_probabilities/
What do you think is the best way to determine draft order for the NBA? What about for NFL, MLB, or NHL drafts? Should there be no drafts at all and let player go where they want? What about a draft salary cap (sort of like auction drafting in fantasy sports)?
Tweet to @MathWithJerome Follow @MathWithJerome
Powerball, Mega Millions, and even state lotteries are all damn near impossible claim the jackpot. Even winning anything is pretty unlikely. Getting a Pick 5 (numbers 0-9) exactly right is 1 in 100,000. Getting luck enough to draft the next phenom like LeBron, Anthony Davis, or perhaps Zion Williamson? That's much, much easier than getting a few digits in the right order.
NBA Draft System and Protected Picks
A quick refresher: The NBA determines the selection order of the first 14 (of 30) teams for an upcoming draft of new players by a lottery system. These are teams that didn't make the playoffs. The rest of the draft order is determined by inverse order of regular season record. The NHL also has a lottery system for non-playoff teams but differs for teams in the post season where order is determined partially by playoff performance and regular season point total. In the NFL, non-playoff teams are ordered purely by regular season record (worse record means better draft slot) with the rest of the order determined by when the team loses in the playoffs. MLB determines their draft order by the inverse of regular season records and don't include any playoffs results.The NBA trade deadline is fast approaching and that means teams will be dealing a bunch of picks and players. Sometimes big contracts will be off-loaded by teams looking for salary cap or luxury tax relief (both of those are topics for a later post) for draft picks and expiring contracts. Other times picks will be traded for a player a team hopes will help in the playoff push. When these deals are made you may hear a pick is "top 10 protected" meaning if that particular pick ends up within the first 10 overall then the team that gave up the pick gets to keep it. Why would any team agree to let a pick be protected? Well, the NBA draft can often be very top-heavy in transformational talent, so it is worth protecting such an asset. Additionally, heavily protecting a pick may lessen it's value. Right now the Lakers have the second best record in the NBA. If they decided to trade their first round pick (which you can't always do because of rules, blah blah blah) the receiving team would expect it to fall in the 26-30 range. The Lakers protecting that pick in the top 14 or 20 wouldn't make much difference, the pick will more than likely convey. However, look at the Golden State Warriors this season, who very unexpectedly have the worst record in the league at this time. They traded their first round pick to the Brooklyn Nets in the sign-and-trade deal for DeAngelo Russell. The Warriors made the pick top 20 protected, so they won't have to send their likely top-4 pick this year. What do the Nets get this year? Nothing, but next year the process may start again with lesser protection, depending on the details of the trade.
The Probability of Ping Pong Balls
Let's assume the Warriors do end up with the league's worst record (not a stretch). It's a lottery so what draft slots can they get? Aren't there ping pong balls involved? The first draft lottery was in 1985, used envelopes, and also thought by some to be rigged so the Knicks would get to draft Patrick Ewing. Since 1990 the ping pong balls were used in a weighted lottery system and now the first four picks are determined by lottery where all 14 teams have a chance, with the rest of the slots being assigned by record. That means the Warriors can get no worse than the 5th pick. It also means that the team with the best record of the lottery teams has a small chance of getting into the top-4, but if they don't they will pick 14th, there's no in-between. There are 1000 lottery ball combinations which are assigned to teams with the three worst teams getting the same number of combinations. The rest of the combinations decrease as records get better. A quality quick reference for draft order and procedures is tankathon.com.Back to assuming the Warriors are going to have worst record. We can say they have the best "seed" for the lottery. Now let's make change the parameters of their trade with Nets and make the pick only top-4 protected. In this scenario, what is the probability the Warriors keep their pick (i.e. it's in the top four)? What is the probably they would lose it (i.e. they get the 5th pick)? If they end seeded second in the lottery by having the second worst record, does that change the probability of keeping their pick? Below is an interactive table and bar chart (created using Tableau Public) that shows the probability of each team by their seed in the lottery getting each of the 14 lottery slots. If you're on a mobile device, rotate it to a landscape for a better view.
Using the table above we see that the Warriors will have a 47.86% chance a losing their pick as it would not be in the top four. And actually, since the top three seeds all have the have number of combinations they all have the same probability of getting slotted within the first four; there's no difference between seeds 1 - 3 in this scenario. A couple of interesting questions: If the top three seeds have the same number of combinations, why do they have differing probabilities after the 4th slot? What if the pick in our original scenario was top-5 protected?
The number of combinations and the number assigned to each team was changed in 2019 to the current system shown in the table above. We saw in the Warriors example that the team had no incentive to have the worst record and as long as they were seeded 1 - 3 they has the same probability of keeping their top-4 protected pick. This was done to reduce team's incentive to tank. Some think this should be extended to the first five seeds having the same number of combinations. So what if the number of combination and how they're distributed changes? I've got you covered. Click the link below customize your own draft scenario and see how it would change the teams' lottery slot probabilities.
https://mathwithjerome.shinyapps.io/nba_lottery_probabilities/
What do you think is the best way to determine draft order for the NBA? What about for NFL, MLB, or NHL drafts? Should there be no drafts at all and let player go where they want? What about a draft salary cap (sort of like auction drafting in fantasy sports)?
Tweet to @MathWithJerome Follow @MathWithJerome