PBA Power Rankings: San Miguel duo leads the pack

PBA Power Rankings: San Miguel duo leads the pack

(games played up to 15 Jan 2014)

With only six games remaining in the elimination rounds of the 2013-2014 PBA Philippine Cup, the final playoff picture is slowly coming into full form, with the top teams cementing their holds on the precious twice-to-beat spots while the middling teams battle for that final spot to complete the cast of eight. After playing roughly thirteen games each, the PBA teams have established their identity going into the playoffs, and the true contenders have clearly risen above the rest.

The duo of Barangay Ginebra and San Mig Coffee headline this week's power rankings: the Gin Kings have been dominant the entire season, blitzing every opponent standing in their path, while the Coffee Mixers have peaked at just the right time, hauling in three impressive victories in a row, despite a slow start to the campaign. In this first ever edition of the PBA Power Rankings, compiled by yours truly, we examine how each team fares against the rest of the competition and separate the contenders from the pretenders.

ANR stands for adjusted net rating based on the whole season to date, ANR-L3 stands for adjusted net rating based on the last 3 games, PANR stands for predictive adjusted net rating which takes into account a team's current form together with its total season performance to date. Other stats provided are based on the whole season to date. League rank for advanced stats are provided in parentheses.
Rank Team Record

1 Barangay Ginebra San Miguel Kings (10-2)
ORtg: 101.6 (2), DRtg: 95.5 (3), NRtg: 6.1 (1), Pace: 88.9 (6)
ANR: +4.9 (1), ANR-L3: +8.3 (2), PANR: +6.6 (1)
 
2 San Mig Coffee Mixers (6-7)
ORtg: 92.6 (10), DRtg: 96.0 (4), NRtg: -3.4 (8), Pace: 86.0 (10)
ANR: -2.6 (8), ANR-L3: +12.2 (1), PANR: +4.8 (2)

3 Rain or Shine Elasto Painters (10-3)
ORtg: 101.3 (3), DRtg: 96.3 (5), NRtg: 5.0 (2), Pace: 89.9 (3)
ANR: +4.3 (2), ANR-L3: +1.3 (4), PANR: +2.8 (3)

4 Meralco Bolts (5-8)
ORtg: 96.9 (7), DRtg: 95.2 (2), NRtg: 1.6 (4), Pace: 88.0 (7)
ANR: +1.4 (4), ANR-L3: +0.8 (5), PANR: +1.1 (4)

5 Barako Bull Energy Cola (5-8)
ORtg: 100.5 (5), DRtg: 101.2 (7), NRtg: -0.7 (6), Pace: 88.0 (8)
ANR: -0.1 (6), ANR-L3: +1.5 (3), PANR: +0.7 (5)

6 Petron Blaze Boosters (9-4)
ORtg: 96.6 (8), DRtg: 93.6 (1), NRtg: 3.0 (3), Pace: 92.9 (1)
ANR: +2.4 (3), ANR-L3: -2.3 (7), PANR: +0.1 (6)

7 Talk 'N Text Tropang Texters (7-5)
ORtg: 102.3 (1), DRtg: 101.4 (8), NRtg: 0.9 (5), Pace: 89.9 (4)
ANR: +0.9 (5), ANR-L3: -2.6 (8), PANR: -0.9 (7)

8 Air21 Express (3-9)
ORtg: 92.7 (9), DRtg: 99.2 (6), NRtg: -6.6 (10), Pace: 89.2 (5)
APM: -6.3 (10), ANR-L3: +0.5 (6), PANR: -2.9 (8)

9 Alaska Aces (4-7)
ORtg: 100.4 (6), DRtg: 102.2 (9), NRtg: -1.9 (7), Pace: 86.6 (9)
ANR: -1.7 (7), ANR-L3: -9.4 (9), PANR: -5.6 (9)

10 Globalport Batang Pier (5-8)
ORtg: 100.8 (4), DRtg: 104.2 (10), NRtg: -3.4 (9), Pace: 91.3 (2)
APM: -3.1 (9), ANR-L3: -10.4 (10), PANR: -6.8 (10)

Thanks for reading and hit the comments section below for any questions, comments and suggestions!

A Quick Discussion about Adjusted Net Rating

A Quick Discussion about Adjusted Net Rating

　
　

"Any time Detroit scores more than a hundred points and holds the other team below a hundred points, they almost always win." -- Doug Collins

　
Ultimately, a game of basketball is decided by having one team score more points than the other team. It is on this simple and obvious (not to Doug Collins, it seems) principle that adjusted net rating (ANR) is based on. This rating system is what I use on this site for team power rankings and evaluations. Since I'm currently working on my first ever installment of the Philippine Basketball Association (PBA) Power Rankings and I'll be basing most of my conclusions on adjusted net rating, I figured I might as well discuss the metric prior to releasing the material I've been working on.

Before we get to the more extensive computational discussion, allow me to give a brief description of ANR and how I came up with the idea. Basically, a team's ANR is an indication of the team's relative strength with regards to the rest of the teams in its league. It is very similar to point differential, which is simply points per game minus opponent points per game, or efficiency differential (better known as net rating), which is offensive rating minus defensive rating; however, adjusted net rating is "adjusted" in the sense that it accounts for the strength of opposing teams and hence provides a more stable value in assessing a team. For lack of a better name, I decided to just use "adjusted net rating." Not very creative, I know, so I'd be glad to receive any suggestions on what to name the metric through the comments section below.

Why use an adjustment?
　
The problem with simple point differential or net rating lies in the fact that it accounts for each point margin equally. In other words, a 10-point win over a great team is worth the same as a 10-point win over a bad team: well, 10 points. However, it is clearly much harder to win by 10 points against an NBA team than against your neighborhood pickup team, therefore simple point differential or net rating does a lousy job of accounting for the strength of opposition in giving credit to a team's value. Because the goal of adjusted net rating is to compute a team's true strength regardless of opposition, an adjustment is necessary to "level the playing field." This is especially necessary for team evaluation in leagues and tournaments where the format does not give equivalent schedules to teams. Such is the case in the NBA's 82-game season, with more games among division opponents and less inter-conference match ups, as well as in the PBA's three conferences, where teams are pooled into two groups which determine the match ups and scheduling.

A Simple Example

Let's take a look at a hypothetical example. Consider a four team league consisting of teams A, B, C and D. Now suppose the first four games of the season resulted in the following:

A 90 B 86: A wins and is +4, B is -4.
C 85 D 92: D wins and is +7, C is -7.
B 80 D 78: B wins and is +2, D is -2.
C 81 A 99: A wins and is +18, C is -18.

Their simple point differential ratings are:

A +11.0
B -1.0
C -12.5
D +2.5

Note that for simplicity, I use point differential derived from raw game results rather than computing the offensive and defensive ratings for each game. Using point differential, one may say that A is the best team in this league, while C is the worst team. By focusing solely on this point differential data, one may also say that D is 3.5 points better than B on a per game basis. However, if we examine closely, D's differential was significantly padded by its 7 point win over C, which is a much weaker team considering it also lost to A by 18 points. On the other hand, B's first game was against A, considerably better than team C. Hence, it is an inappropriate conclusion to state that D is 3.5 points better than B because D has faced a much easier opponent than B. Adjusted net rating takes this disparity in opposition into account, diminishing the value of D's 7-point win over C as an inferior opponent against the value of D's 2-point loss to B. The same goes for A's 18-point win over C (sorry, Team C, one team had to be horribly bad for the example to be clearer) as compared against its 4-point win over B.

So, how would these teams fare using adjusted net rating? Here are the results:

A +7.6
B +2.4
C -9.1
D -0.9

These numbers can be interpreted as follows: A is 7.6 points better than an average team, B is 2.4 points better than an average team, and so on. Hence, based on these results, if A plays a large number of games against B, we expect A to win by an average of 5.2 points (or 7.6 - 2.4) per game, which is pretty close to the four-point margin from the actual result in their first game.

As we can see, adjusted net rating places B above D, at +2.4 instead of -1.0 from using simple point differential, while D is at -0.9 instead of +2.5 from using simple point differential. Clearly, these ratings paint a clearer picture of the team's true strengths as compared to using simple point differential models because it credits the difficulty of winning or losing to better teams. Of course, we were only talking extensively about B and D in the example, but the same could be said for A and C.
　
Computing Adjusted Net Rating

In this section, we'll be discussing about the method used in computing for the adjusted net ratings based on the observed game results, using terms like linear regression and coefficient of determination. If you're not that into math and statistics, just bear with me, I'll try to make this as quick and painless as possible, or you can skip this part if you like.

So how are the basic point differentials adjusted to arrive at adjusted net rating?

The method I use is a linear regression model used to compute values for each team's rating to fit the values of their expected results into the actual results. Basically, the objective is to obtain a set of ratings which closely mirror what actually transpired on the basis of the data observed. The reasoning is simple: the margin of victory or result of a game is determined by the difference in the underlying or "true" strength of the two teams involved. Using a linear regression model, I can estimate this "true" strength by minimizing the deviations or differences of the expected game results from the actual game results. In statistical terms, the model is maximizing the R-squared or coefficient of determination, a measure of the goodness of fit of the adjusted net ratings to the observed data, and minimizing the root mean squared error.
　
For a more concrete illustration, let's look back at our four-team league from earlier. We'll plot the teams' ratings and the expected results from each game based on these ratings and compare these with the actual results. As previously explained, given two teams with ratings X and Y, the expected result or margin of victory is [X - Y]. Each expected result is then compared with the actual result to obtain the squared deviation for each game, which is simply [expected result - actual result] squared. Root mean squared error (RMSE) is computed by getting the average of all squared deviations, and then getting the square root of this average; this final value can be crudely interpreted as the average amount by which the expected value overstates or understates the actual value. The goal of our model is to minimize RMSE because a lower value to RMSE indicates a better fit of the derived rating values to the actual or "true" strength values. At the same time, the model looks to maximize the correlation between expected and actual results through R-squared, to measure goodness of fit.
　
First, we look at how simple point differential fits as a measure of true team strength.

Team1	Team2	Team1 Rtg	Team2 Rtg	ExpRes	ActRes	SqDev
A	B	+11.0	-1.0	+12.0	+4.0	64.0
C	D	-12.5	+2.5	-15.0	-7.0	64.0
B	D	-1.0	+2.5	-3.5	+2.0	30.3
C	A	-12.5	+11.0	-23.5	-18.0	30.3
					RMSE	6.9

　
As you can see, simple point differential as a measure of team strength isn't doing very well to estimate the actual results, being off by an average of 6.9 points per estimate. Now, we compare these results with using adjusted net rating.

Team1	Team2	Team1 Rtg	Team2 Rtg	ExpRes	ActRes	SqDev
A	B	+7.6	+2.4	+5.3	+4.0	1.6
C	D	-9.1	-0.9	-8.2	-7.0	1.5
B	D	+2.4	-0.9	+3.3	+2.0	1.6
C	A	-9.1	+7.6	-16.8	-18.0	1.5
					RMSE	1.3

　
With adjusted net ratings, our predicted results are only off by an average of 1.3 points per estimate. This minimization of RMSE is the basis for the goodness of fit of the model with actual game results, allowing for a more accurate evaluation of a team's performance.
　
See, quick and painless, right?
　
Limitations and Areas for Improvement

Despite the fact that the linear regression model allows for the minimization of deviations, a 100% exact fit to observed data is very difficult to achieve due to the randomness of nature itself. This randomness can be minimized by the inclusion of more data in the observation set; simply put, the larger the sample, the better (sort of). As with most models derived from observed data, the accuracy and reliability of the derived results are greatly dependent on the quality and quantity of the source used. Hence, adjusted net ratings derived from a sample of four games only (as in our example) is much less reliable than adjusted net ratings derived from a sample of say, forty or fifty games, because smaller samples are prone to higher variances. Also, the model is susceptible to extreme data points or outliers, such as margins of victory of 40 or more points on extremely rare cases, which may severely distort the results of the model. Again, quality and quantity of data is important. These limitations are something which I hope to look into in the future to improve the quality of ANR as a team evaluation metric.

In addition, I wish to look into the reliability of the adjusted net ratings for predicting the results of future games. As of the moment, the ANR numbers are primarily designed to be "descriptive," meaning they give us an idea of how good a team is based on what they've done in the past through observed results, rather than "predictive," meaning they allow us to have an idea of how a team will do in the future given a different set of circumstances. Expect a future post regarding a study on how ANR fares as a predictive tool for basketball games.

How Adjusted Net Rating was Developed

As previously stated, adjusted net rating is based on a linear regression model. The idea of using linear regression to derive ratings for basketball is not an original idea of mine. In fact, it's been around for quite some time, however, it is primarily used as a player evaluation metric in the form of adjusted plus-minus (APM) developed by Wayne Winston, now an analyst for the Dallas Mavericks. Because the use of the linear regression model as a team evaluation metric is not as widespread, I decided to create my own variation of a linear regression model using a similar logic to APM, but applied to teams instead. Moreover, because of the lack of advanced statistical resources relating to the PBA as opposed to the global favorite NBA, I've decided to dedicate a considerable amount of time towards developing my ANR metric as well as other future metrics for application to the PBA.

Thanks for reading and hit the comments section below for any questions, comments and suggestions!