# NBA Probabilities: Warriors, Spurs, Playoffs

At the close of the Pelicans – Warriors game tonight, we witnessed the Warriors set the record for fastest team to 60 wins with a 125 – 107 rout in Oakland. With the Warriors moving to 60-6 for the season with 16 games to go, the 72-10 record seems very well within their grasp. However, the Warriors have a very  tough schedule ahead of them.

Of the Warriors’ 16 remaining games, the Dubs find themselves playing the San Antonio Spurs (56-10) three times; two of which are in San Antonio. One of those Spurs games are sandwiched between a road and home series against the Memphis Grizzlies (39-28), who are looking more like the Grizzlies from the beginning of the season. Intertwined in the other 11 games are a pair of Dallas Mavericks games (home and away) and a single Clippers game at home. While the Warriors only need to go 12-4 to tie the record, in the NBA things can never be taken for granted.

Here, we have decided to estimate four sets of probabilities this go-around. First, we calculate the probability that the Warriors tie or break the illustrious 72-10 record set by the 1995-96 Chicago Bulls. We then calculate the probability that the San Antonio Spurs are able to scratch the 70 win mark, giving us a season where two NBA teams may hit the 70 win plateau in a single season.

Finally, we take a look at the probabilities for each team winning their respective division and/or making the playoffs. To calculate all probabilities, we consider building a rankings model where a weighted regression model is fit to each team, based on head-to-head match-ups and location of games. The resulting coefficients are then used to weight the probabilities. We then perform 1,000,000 Markov Chain simulations to estimate the resulting number of wins for each team.

# Probability of Warriors Getting 72+ Wins

To calculate this probability, we run the 1,000,000 simulations and count the number of wins. The simulation is simple. Suppose the Warriors have a weighted score of 1.0000 and their opponent, say the Oklahoma City Thunder have a weighted score of 0.602593. Since the home weighting is a value of .0022 (not much of an effect), we find that the Warriors have a probability for defeating the Oklahoma City Thunder of 0.62450 (home) and 0.623133 (away).  The fit of this model is a modest 0.6533; which is fairly good for sporting events. (Note: Our model that selected 65 of the 68 NCAA teams correctly for this year’s March Madness had a model fit of 0.5433).

Probability Warriors Do NOT Tie or Break the 72 Win Record:        59.8934%

Probability Warriors TIE the 72 Win Record:                                         19.5667%

Probability Warriors BREAK the 72 Win Record:                                  20.5399%

This suggests that the Warriors have over a 40% chance to tying or breaking the record; which are fantastic odds, given the hard road still ahead of them.

# Probability the Spurs Catch the Warriors

Another interesting probability to measure is that of the San Antonio Spurs catching the Warriors. It is very interesting to see two teams battle for 70 wins from the same conference. The Cavaliers and Lakers had 66 and 65 wins, respectively, in the 2008-09 NBA season. The Chicago Bulls and Utah Jazz had 69 and 64 wins in the 1996-97 season. The Chicago Bulls and Seattle Supersonics had 72 and 64, respectively in the 1995-96 season. What all these teams had in common is that they played in different conferences; therefore having a third of their season with different opponents, and only having two games against each other. The closest teams have both gotten to 70 wins within the same conference were the 1971-72 Western Conference Los Angeles Lakers and Milwaukee Bucks with 69 and 63 wins, respectively. Since then, we have never seen such a high win-total race for first in the conference.

The Spurs also have an uphill battle. For starters, of their remaining 16 games, they play three against the Warriors. However, the Spurs have two more games against Oklahoma City, a game against Toronto, and a game against the Clippers. The Spurs undoubtedly have a harder road than the Warriors for the remainder of the season.

Using the same set-up as above, we are interested in three scenarios. First, we are interested in whether the Spurs will catch the Warriors and claim first place. Next, we are interested in whether the Spurs can nab the 70 win mark; requiring a 14-2 or better finish to the season. And lastly, we look for the probability that the Spurs and Warriors both hit the 70 win plateau.

Probability the Spurs Win the Western Conference:                1.9557%

Probability the Spurs Win 70 or More Games:                            1.4809%

Probability the Spurs and Warriors Win 70+ Together:           0.9004%

So it looks as if the Warriors will be safe, barring any historic collapse, to win the conference outright; despite only a 4 game lead with 16 games to go. The most important probability to take away here:

Probability the Spurs/Warriors Set a Record for Most Combined Wins In the Same Conference (Breaking the 1971-72 Bucks/Lakers Record):      95.0482%

# Playoffs? Who’s Making the Playoffs?

Lastly, we take a look at the remaining 234 NBA games this season and run our Markov Chain to estimate the probabilities for each team to make the playoffs. First, we simulate the number of wins for the remaining 234 games. Then, we identify the division champions. Finally, we separate out the remaining 5 teams from each conference. The probabilities we give are then the Probability of Winning the Division (PWD), the Probability of Wild Card (PWC), and the Probability of Making the Playoffs (PMP).

 Team Score PWD PWC PMP Atlanta 0.525967 19.462900 76.955300 96.418200 Boston 0.513101 1.099600 98.819400 99.919000 Brooklyn 0.203504 0.000000 0.000000 0.000000 Charlotte 0.517984 25.012000 73.379800 98.391800 Chicago 0.462458 0.000000 62.781500 62.781500 Cleveland 0.647040 100.000000 0.000000 100.000000 Dallas 0.481343 0.000000 69.704400 69.704400 Denver 0.400446 0.000000 0.990900 0.990900 Detroit 0.491252 0.000000 42.446300 42.446300 Golden State 1.000000 100.000000 0.000000 100.000000 Houston 0.473919 0.000000 83.895000 83.895000 Indiana 0.509098 0.000000 94.625100 94.625100 LA Clippers 0.600783 0.000000 100.000000 100.000000 LA Lakers 0.176505 0.000000 0.000000 0.000000 Memphis 0.479135 0.000000 99.947400 99.947400 Miami 0.501849 55.520900 43.623000 99.143900 Milwaukee 0.399017 0.000000 0.150500 0.150500 Minnesota 0.285581 0.000000 0.000000 0.000000 New Orleans 0.350957 0.000000 0.001000 0.001000 New York 0.372437 0.000000 0.033200 0.033200 Oklahoma City 0.602593 99.999800 0.000200 100.000000 Orlando 0.393102 0.000100 0.122000 0.122100 Philadelphia 0.040989 0.000000 0.000000 0.000000 Phoenix 0.229407 0.000000 0.000000 0.000000 Portland 0.441287 0.000200 92.644300 92.644500 Sacramento 0.366869 0.000000 0.108500 0.108500 San Antonio 0.823037 100.000000 0.000000 100.000000 Toronto 0.606783 98.900400 1.099600 100.000000 Utah 0.441108 0.000000 52.708300 52.708300 Washington 0.395122 0.004100 5.964300 5.968400

Here, we see that the Warriors and Spurs have already won their divisions outright, therefore having a 100% chance of winning their respective divisions and making the playoffs. Oklahoma City (45-22) are holding onto a 10.5 game edge over Portland (35-33) and therefore haven’t clinched yet, but the 99.9998% probability suggests its coming soon.

Cleveland’s (47-19) magic number for winning the division is 4; which effectively gives them a 100% probability of closing out the division on top. Toronto (44-21) is holding onto a 5.5 game lead over Boston (39-27) with 17 games to go, but are looking at a 98.9004% probability of winning the division. The Southeast Division, however, is a mess with the Heat, Hornets and Hawks all sitting within 2 games of each other. Miami is clinging to the best odds of winning the division with 55%, but this is slightly better than a coin flip.

The playoff hunt is effectively a pair of 9-horse races as the Utah Jazz and Detroit Pistons have significant probabilities of making the playoffs (52.7083% and 42.4463%, respectively) but are 9th in the respective lists. The Wizards have a promising probability of 5.9684%, but are finding themselves running out of real estate when it comes to games where they can pick up wins.

Who do you have making the playoffs? My team has been long knocked out for months (Lakers). So I can sit back and enjoy watching some great basketball.