Scheduling for the playoffs: who has the easiest path?

We are almost two thirds of the way through the 2012-2013 NBA season, and once again our Rockets are locked in a tight race for the 8th spot of the always competitive Western Conference. The fact that the Rockets are holding a tenuous lead on the last playoff spot at this point in the season is nothing new to the fans of the Rockets as they've been in a similar position each of the past 3 seasons, but this year, things are a bit different. We have a far more exciting team and a better chance than we've had in years. For the first time in what seems like ages, the Rockets are without major injuries and subtractions entering the All-star break, and the field, while still competitive, does not sport the usual glut that the Western Conference playoff races had in the past few years.

The Western Conference playoff picture breaks down into three distinct sections:

The Untouchables

The San Antonio Spurs and the Oklahoma City Thunders, 2 teams that have such a wide lead over the rest of the field that they may have the playoff home court locked up in March.

The Middle

The Los Angeles Clippers, the Denver Nuggets, the Memphis Grizzlies, and the Golden State Warriors are pretty much locked into the playoffs already, but will compete against each other for playoff seeding until the bitter end.

The Hopefuls

The Utah Jazz, the Houston Rockets, the Portland Trail Blazers, and for argument's sake, the Los Angeles Lakers. These teams are not good enough to have control of their own destiny, so they have to rely on hope. For the Lakers, a lot of hope.

Unlike the past few seasons where spots 5-8 remained attainable to the bitter end of the year, this season seems to have more teams already have playoff spots locked up, leaving only the 7th and 8th playoff spots within striking distance for those on the outside looking in.

I decided to take a look at the rest of the schedules for the four teams currently in the race using a couple different metrics to evaluate who has the easiest path to the playoffs. All the metrics are based on how well each team has done up to this point, so I cannot take into account teams that have improved or worsened due to returning players, injuries or general player movement. Take this with a grain of salt, these metrics are prone to change day to day, so the exact numbers will not be the same in a week or even tomorrow. The idea is that we're looking at a snapshot of all the teams' records so far and use that as a basis for evaluating each team's schedule down the road.

Let's start with how well they've done with the schedule they had so far

The two metrics here are average winning percentages and average point differential of the opponents. ESPN uses wining percentage, and Basketball Reference uses point differential or margin of victory. Point differential has proven to more closely correspond to future success than actual winning percentage, and so Basketball-Reference uses it to determine strength of schedule.

	SoS by winning%	SoS by point differential	Winning %	Average Point differential	Expected Winning %
Utah Jazz	0.496 (20th)	0.05 (14th)	0.549 (13th)	-0.53 (16th)	0.481 (16th)
Houston Rockets	0.515 (3rd)	0.63 (2nd)	0.538 (14th)	3.13 (8th)	0.602 (8th)
Portland Trail Blazers	0.495 (21st)	0.03 (16th)	0.500 (17th)	-2.08 (21th)	0.427 (21th)
LA Laker	0.509 (5th)	0.36 (7th)	0.471 (18th)	1.31 (11th)	0.544 (11th)

In the first two columns are the strengths of schedules determined by the two different metrics. The numbers themselves probably mean very little, but in parenthesis are the relative ranks compared to the rest of the league that probably tell a better story. While the two metrics don't agree on the specifics, they both clearly show that Houston has played by far the toughest schedule up to this point between the 4 teams. Utah and Portland may have compiled similar records, but their schedules have been average to weak up to this point.

All things considered, the Rockets have performed well up to this point. Compiling an over .500 record, managing 8th best point differential in the league while playing the 2nd or 3rd hardest schedule in the league is pretty good, right? The thing is if you believe in the predictive power of the statistics, using Daryl Morey's own modified Pythagorean theorem, the Rockets should really have won more games. The way the Rockets are playing, they have actually under-performed in terms of win-loss. To a certain degree, the Rockets game the system. Notice the rankings are identical with point differential and expected winning percentage. That's because they are essentially derived from the same idea. The more points you score and the less points you give up, the better chance you have of winning. Rockets blow out teams when they win, exemplified by the near 50 point thrashing of the Jazz, so instead of beating 4 teams by 10, we beat a team by 40 to achieve the same point differential.

The same cannot be said of the Lakers, who do not really employ the same strategy yet seemingly under-perform more than we do. Due to a sudden rise in good divisional opponents with Warriors and Clippers the past 2 seasons, their strength of schedule is stronger than it has been in the past, which may contribute to their poor performance on the win loss column. Their point differential actually says they are playing just fine as they are the only team with a positive point different but a sub .500 record.

The Blazers and the Jazz are different stories, so far they've played a softer schedule than most and have been overachieving. They've been winning close games against opponents on a schedule that has more sub .500 teams than over .500 teams. It's true that good teams win close games, but good teams usually don't let games get close in the first place. Having more close wins than blow out wins is often of an indication of good luck, where you have to scrap and fight every night for a win. Both of them also sport negative point differentials, which historically does not bode well for Western Conference teams. In the past 10 years, only the Lakers and Warriors have made it to the playoffs with a negative margin of victory, and it was the only year where 42 wins were enough to make the playoffs. The Jazz may still be able to turn it around, but the Trail Blazers are so far below average on point differential that it is difficult to imagine them turning it around.

Looking into the remaining schedule

Why did I start with the strength of schedule up to this point? Because despite what we say about the NBA and David Stern, the NBA attempts to have its schedules be as equitable as possible. Every team in the league plays each other at least twice, and there's an equal amount of home games and road games for everyone. Of course there are logistics like back to backs, long road trips, conference and divisional strength and other factors, but overall, you get to play strong and weak opponents alike. What goes around comes around, and it all evens out at the end. Typically, the harder your schedule was before, the easier it will get, and vice versa.

	SoRS by winning %	SoRS by point differential	# of over .500 opponents at home	# of over .500 opponents on the road	# of under .500 opponents at home	# of under .500 opponents on the road	Games against competition	Moe formula
Utah Jazz	0.529 (2)	0.712	10	10	6	5	3	3
Houston Rockets	0.485 (22)	-0.792	8	7	7	8	3	2
Portland Trail Blazer	0.539 (1)	1.033	10	11	6	5	5	0
LA Lakers	0.500 (17)	-0.168	9	9	7	6	3	-1

Portland's schedule is much harder for the rest of the season. Their opponents' average winning percentage is .539 and the average point differential of their remaining opponents is a whopping 1.033. In stark contrast, The Rocket's remaining schedule has an average winning % of .485, near the bottom of the league, and the average point differential of their remaining opponents is -0.792. This means they play a lot of weak opponents rest of the way. The Rockets are also helped out by having the least road games against over .500 opponents, and tie with the Lakers with most home games against sub .500 teams. Blazers have 11 of their 16 road games against over .500 opponents, and the Jazz also has 10 of their 15 road games against over .500 teams.

The Moe formula is a quick and dirty way to evaluate how good a team is at stealing wins on the road and protecting home court, by looking at differences between road wins and home losses. Utah and Houston have the edge on stealing wins on the road. Typically, road games against sub .500 teams are your best opportunity for road wins, and home games against over .500 teams are your most likely chance for home losses. The Rockets hold an advantage here because the have equal amount of both, so even if they lose all the home games against over .500 team, they have just as many chances to steal it back on the road against sub .500 teams. The other 3 teams all have more home games against over .500 teams than they do road games against sub .500 teams.

Portland also has the most games against the other 3 teams in the race. Blazers have 1 more game against the Rockets and 2 more games each against Utah Jazz and LA Lakers, so they have the most games that will have direct impact in the standings. The Rockets are fortunate because they only have one more game left with each of them, so the best each of them can do is gain one game on the Rockets directly.

Looking at Extremes

After looking over the general strength of the remaining schedule, I decided to look for as many sure things as possible. Here I'm basically looking for games either against teams so good it's unlikely to win against them, or teams so bad that anyone can win against them.

	RPI	# Opponents with better RPI	# of top SRS opponents games	# of bottom SRS opponents games	# against top Moe system teams on the road	# against bottom Moe system teams at home
Utah Jazz	.509	14	8	2	4	2
Houston Rockets	.521	12	5	9	3	1
Portland Trail Blazers	.497	23	8	2	5	1
LA Lakers	.485	17	6	4	4	1

For the people that follows college basketball, RPI is not a foreign concept. It's called the relative percent index, and it's a number that takes into account both strength of schedule and how well teams did against the schedule. The basic formula is 25% of a team's winning percentage, 50% of the team's opponents' winning percentage, and 25% the opponents' opponents' winning percentage. The Rockets rank 9th in the league while the Jazz, Lakers, and Blazers rank 13th, 17th, and 18th, respectively. Games against better RPI opponents are likely to be a loss. The Rockets and Jazz have each only won around 25% of their games against opponents with better RPI, while the Blazers are Lakers have beaten more. This is a biased concept, however, because the Rockets have just 8 teams higher than them in RPI while the Lakers and Blazers have far more.

SRS stands for simple rating system, and it's the point differential equivalent of RPI, taking both margin of victory and strength of schedule into account to get a number that rates the team. The calculation is simply average point differential + average opponents' point differential. I define the top SRS team to be a standard deviation above the average, and the SRS bottom team a standard deviation under the average. The top teams are the Miami Heat, the New York Knicks, the Oklahoma City Thunder, the San Antonio Spurs, the Los Angeles Clippers and the Denver Nuggets, and the rest of the league is a combined 67 and 186 against the 6 of them. The bottom teams are the Cleveland Cavaliers, the Orlando Magic, the Charlotte Bobcats, the Phoenix Suns and the Sacramento Kings, and the rest of the league is 157 and 57 against them. Basically any team has a 73% chance of losing to the top SRS teams, and 73% chance of beating the bottom SRS teams. These are essentially guaranteed wins and losses.

Use the Moe formula and to factor in the road and home advantages and the same idea as above to determine the best and worst opponents, and we get highly likely home wins and road losses.

Once again, Houston schedule looks exceptionally soft with 9 games against the dead bottom SRS teams, only 5 games against the top SRS teams, and only 3 games on the road are against the very best Moe teams.

Non-opponent related factors

	# of Back to back	Longest road trip	Longest home stand
Utah Jazz	4 (1 Road, 3 Split)	4 games	4 games
Houston Rockets	6 (4 Road, 1 Home, 1 Split)	3 games	7 games
Portland Trail Blazers	5 (3 Road, 2 Split)	4 games	4 games
LA Lakers	6 (4 Road, 2 Split)	4 games	4 games

Here is where Rockets have a bit of the disadvantage. Rockets and the Lakers have 6 back to backs left, and most of them on the road. However, the Rockets have the benefit of a nice 7 game home stretch in the middle of March where the Rockets stay home for 2 and a half weeks, and no visible stretches without reasonable breaks after the All-star game. March is not friendly the other 3 teams. Utah has a grueling 5 game, 7 day trip book-ended by back to backs at the end of March that may make or break their season. Portland also has a similar stretch in the middle of March. Lakers too have an early March schedule that's not unlike our current February schedule.

No matter how you look at the remaining schedule, the Rockets seem to have the easiest path to the playoffs compared to the rest of their competitors, and the team currently right on their tails for the 8th place, the Blazers seem to have to most difficult schedule from this point on. Both are very encouraging signs point toward a long awaited playoff berth. These are indeed exciting times to be Houston Rockets fan.