On the Tank, the Draft and Probability

These two players will definitely be at the top of the Pels draft board - Dennis Wierzbicki-USA TODAY Spor

The Pelicans are in a precarious situation that sounds eerily similar to another team's problem not long ago.

[Note: this was written last Thursday. Thus, the numbers used here are updated only through then.]

Two seasons ago, the Golden State Warriors owed the Utah Jazz a pick -- if it was outside the top 7, they'd retain it. Otherwise, the pick was headed to the Jazz. Luckily, the Warriors retained that pick and got for themselves a player who helped tremendously in their 2013 playoff run. Here's a summary:

In doing so, Barnes has become a symbol for Warriors optimism and also, indirectly, a symbol for the practicality of tanking. Just as the "Thunder Model" compelled various teams to ardently pursue awfulness (see Bobcats, Charlotte), Barnes' playoff run is all the reason another franchise needs to pack it in.

It wasn't so long ago that the Warriors had a shot at another playoff run. On March 14 of 2012, Golden State was only three games under .500 with 27 left to play. Instead of making one final playoff push, the Warriors went the other way, consciously. Monta Ellis and Ekpe Udoh were traded for Andrew Bogut, who was out that season with a fractured ankle. In the short term, a deal like that could only hurt the Warriors. The upside had something to do the Utah Jazz and a protected NBA lottery pick.

- Ethan Sherwood Strauss, ESPN TrueHoop

It was quite the tank job really. That year, Curry played just 26 games while Bogut NEVER suited up for them (effectively trading Monta Ellis and +/- King Ekpe Udoh for nothing. Doing so allowed the Warriors to strike two (maybe three) birds with one stone.)

  1. They gambled to solve their center issues by trading for Bogut.
  2. Rested Bogut and Curry, both tagged as injury prone players at that time, and gave them ample time to rehabilitate their injuries.
  3. Retained a much needed asset (2012 1st Round Draft Pick).


Not so long ago, the Pelicans were sitting 5 games below .500 at 22-27, a good 6 or 7 games behind the last playoff seed at that point (Memphis was 27-23, Dallas was 31-21, Golden State was 30-21, 30-20). With 33 games left to be played, the playoffs were an unlikely possibility. We had to finish with approximately around 48+ wins to even have a CHANCE at a playoff spot which meant winning 26+ more games.

So fans naturally looked the other way. I.e. #TankForWiggins #TankforParker #TankforInsertProspectHere

There have been numerous articles written about the draft (mine are here and here).

To summarize our situation, we keep our pick if it falls in the Top-5, we award it to Philadelphia if not (Holiday trade). No use discussing the merits of the trade (since it's been done so many times before) so instead let's analyze that draft pick.

These are the odds of us keeping our pick if we land at certain spots:

Slot Pr (Keeping Pick)
1st 100%
2nd 100%
3rd 96%
4th 82.8%
5th 55.3%
6th 21.5%
7th 15.0%
8th 10.0%
9th 6.1%
10th 4.0%
11th 2.9%
12th 2.5%
13th 2.2%
14th 1.8%

Those are some pretty bad odds outside the Top 4 (even the 5th worst record has just a 55% chance at getting a Top 5 pick). Currently, the race to be the worst stands like this:

Team Record
Milwaukee Bucks
Philadelphia 76ers
Orlando Magic
Los Angeles Lakers
Boston Celtics
Sacramento Kings
Utah Jazz
New York Knicks
Cleveland Cavaliers
Detroit Pistons
New Orleans
Denver Nuggets
Minnesota Timberwolves
Memphis Grizzlies

We're currently slotted 11th with Detroit looming (0.5 games ahead or behind, depending on your perspective). The 5th worst spot is Boston and they're 4 games away and Los Angeles - currently slotted 4th -- is 4.5 games away with 25 games left. This means that over that 25 games span, we need to be worse than how they'll play over the same span. Even if our last 25 games are similar -- i.e. example, the Lakers finish the season 8-16 over their last 24, we'll need to lose more than 66% of our games to catch up. That means over 25 games, we'll need to win just 4 (FOUR) games for us to match LA in terms of W/L. Some might say -- well, 4-21 is a very believable tank job, considering AD just had another injury. Well, let's look at the numbers.


There are 1230 games in a regular 82-game NBA season. To calculate this, you just have to understand that each team has 41 home games (or 41- road games, if you will). 41*30 = 1230. VOILA!

This late into the season, there are still 370 games left to be played. Which means, this season can still go 2^370 ways (which means a LOT). Insane right?

For this particular analysis we'll use a relatively simple but tedious variation of one of my fave statistical models called the "Monte Carlo simulation". Put simply, this is a model that tackles a specific mathematical problem by random sampling. Based on the last 370 games, I calculated a very simple win probability for each team from here on out. We divided a team's W/L% by the sum of the two teams' W/L% to get a VERY simple Win Probability for each team. The idea is that superior teams have a better chance of winning against an inferior team. Also, I added a "3%" homecourt advantage/disadvantage. To provide a sample:

The Pelicans -- currently sitting with a W/L% of 40.4% -- have a game against the Suns -- a team with a W/L% of 57.9% -- on February 28 at US Airways Center. To calculate my Win Probability, I add 40.4 and 57.9 = 98.3. I then divide 40.4 by this sum to arrive at 41.1%. Subtracting 3% from this (since we ARE on the road) and we arrive at my simple Pr (Win) of 38.1%. Phoenix, of course, has a 61.9% chance of winning that game.

This isn't necessarily true since some teams are better on the road than others, others are better at home than others and match-up issues that are yet to be considered (example: Pelicans vs Grizzlies). But for the sake of simplicity, this will do.

Now, I generated a random number (this is where the "random" sampling takes place) between 1 to 100 (decimal places included) which I used to determine which team wins or loses. In the example above, if the random number generated is greater than 38.1, then the Pels lose. If it's less than or equal to 38.1, we win!

In doing the above for the 370 games remaining and I arrived at ONE random "league standing". Tiebreakers have yet to be included in the spreadsheet (that's AWFULLY hard to do since it requires a matrix) but even if we don't consider that, my point later will still stand.

Next, I did this 10,000 times to arrive at 10,000 random league standings. From here, I counted how many times the Pels finished with a bottom 5-worst record (note: no consideration for "tiebreakers." I.e. if two teams are tied for 5th worst record, they'll both be ranked as "5" instead of "5.5". Another note: I considered inter-conference positioning. I.e. Minnesota will still be in the lottery considerations even if they get a better record than 4 playoff teams in the East).

In order to understand the next few lines after this, you have to understand how to interpret these results. The basics are: the bigger the sample size, the more accurate the random sampling will be. If say I run just 1,000 scenarios, it won't be as accurate as say running 10,000 scenarios (which also won't be as accurate as running 1M scenarios). Similarly, results of trials derived from multiple scenarios tend to hover around a certain number -- more often than not, this is the actual answer. If say I run 1 million trials of a 1 million scenario Monte Carlo Model, the answers that will come up in the 1 million trial will tend to cluster around a specific region (which means, the answer will be somewhere in that region).

At our current W/L% (40.4%), this is how the 1,000 trials of a 10,000 simulation model is distributed:


Confused yet?

What that table gives us is an indication of the odds of where the Pels will currently be slated. This means if most of the 1000 was in the 0 to 5% bin, we're probably NOT going to be in that place at seasons end. The odds of us finishing with either the 14th, 13th, 5th, 4th, 3rd, 2nd or worst record are slim to none. In fact, the average probability of us being in the 14th are 0.01% (as I said negligible), 1.02% for the 13th, 3.82% for the 5th, 1.6% for the 4th, 0.33% for the 3rd, 0.01% for the 2nd and 0.0% for the 1st.

In reality, the biggest probability for our record is finishing 12th, 11th, 10th, 9th or 8th. That was just if we finish at that spot. We have yet to consider the odds of us keeping our pick if we finish at THAT spot. Here are the calculations for the "expected probability" of us keeping our pick.

Place Average Pr (being in that place) Pr (keeping pick if we land in that place) Pr (keeping the pick)
14th 0.01% 1.8% 0
13th 1.02% 2.2% 0
12th 10.27% 2.5% 0.3%
11th 18.40% 2.9% 0.5%
10th 18.25% 4.0% 0.7%
9th 16.15% 6.1% 1.0%
8th 13.24% 10% 1.3%
7th 10.05% 15% 1.5%
6th 6.82% 21.5% 2.1%
5th 3.82% 55.3% 2.1%
4th 1.6% 82.8% 1.3%
3rd 0.33% 96% 0.3%
2nd 0.01% 100% 0
1st 0.00% 100% 0
Total 100%

So in reality, at our current pace, we have a 10.6% chance of keeping the pick. Now you may be saying "but we WON'T be playing at the same level as our first 57 games!"

I tried doing the same thing with our W/L% (in the calculation of Win Probability) set at 25% i.e. for the remainder of the season, we'll be playing right around the level of Philadelphia. Here are the results:

Distribution at 25%


Place Average Pr (being in that place) Pr (keeping pick if we land in that place) Pr (keeping the pick)
14th 0.00% 1.8% 0
13th 0.06% 2.2% 0
12th 1.36% 2.5% 0
11th 4.44% 2.9% 0.1%
10th 7.61% 4.0% 0.3%
9th 10.89% 6.1% 0.7%
8th 13.90% 10% 1.4%
7th 16.07% 15% 2.4%
6th 16.88% 21.5% 3.6%
5th 14.87% 55.3% 8.2%
4th 10.08% 82.8% 8.3%
3rd 3.55% 96% 3.4%
2nd 0.30% 100% 0.3%
1st 0.00% 100% 0
Total 100%

So there is some truth to what people were saying -- that if we did play worse (and everybody played at about the same rate), the odds of us keeping that pick increases (by more than 150%). But what if Anthony Davis got injured and we played at a historically bad rate? Like, 9-73 bad (i.e. W/L% of 10%)


Place Average Pr (being in that place) Pr (keeping pick if we land in that place) Pr (keeping the pick)
14th 0.00% 1.8% 0
13th 0.00% 2.2% 0
12th 0.00% 2.5% 0
11th 0.03% 2.9% 0
10th 0.12% 4.0% 0
9th 0.39% 6.1% 0
8th 1.14% 10% 0.1%
7th 2.96% 15% 0.4%
6th 7.43% 21.5% 1.6%
5th 16.65% 55.3% 9.2%
4th 31.50% 82.8% 26.1%
3rd 32.04% 96% 30.8%
2nd 7.62% 100% 7.6%
1st 0.12% 100% 0.12%
Total 100%

NOW we're talking. Right?! A 76% chance of keeping our pick? Hell yeah!

Slow Down Matey

Now, I think there's a need to temper expectations here. Since going 23-34, the Pels have lost 3 more (by an average of 17 points per game, I might add). So is there a really big chance for us to keep the pick with Jrue Holiday and Ryan Anderson being out for the season? (Not to mention Jason Smith?)

RyNo's last game was January 3, and since then the Pels have been 8-20 (28.5%). Jrue last played last January 8 and since then, the Pels have been 8-19 (29.6%). It's also worth noting that RyNo and Jrue were not playing anymore since January 8. At that rate (29.6%), the probability of us keeping our pick is actually just at 20.8%.

In reality, we have about a 1 in 4 chance of keeping that pick. You think that's enough to cheer for the tank? You decide.

Personally, I don't think we'll ever get to 10% bad. I mean, that's historically bad. We may all hate Monty but one thing he does know is to make a bad group overachieve (and a good group, underachieve). So no, I don't think we'll be bad enough to retain our pick. So let's talk about something else, yes?

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