[Historical and Non-Current] User Guide for the Defending Components or Sub Ratings of Real Player Ratings, January 2009

THE DEFENDING COMPONENTS OR SUB RATINGS OF REAL PLAYER RATINGS--NEW AS OF JANUARY 2009
As of January 8, 2009, The Quest is proud to announce to you that the second major improvement to Real Player Ratings (RPR) in less than half a year is now fully up and running. The first major improvement were some needed changes in the factors used for RPR. The second major improvement (series of improvements, actually) is so far as I am aware the first ever effort to rate the defensive efforts of players that are hidden unless you watch all that player's games, because they are not scored or tracked by scorekeepers.

I have been talking about and working for and expecting the breakthrough in evaluation of defending for almost two years. Now that the breakthrough has come, I am now even more certain that RPR is the best overall rating system in existence, and that it is now roughly as good as it will ever or can ever be.

I recently developed a statistically valid way to rate the defending of players, that is, what they do to prevent scores other than rebounding, blocks, steals, and fouls, which were always included in RPR. This would include man to man defending, zone defending, pick and roll defending, defensive recognition, and defensive rotation.

Although the technique used had to be indirect and inexact, it validly awards the better defenders with bigger RPR bonuses. It has been validated by comparing results obtained with the defensive ratings shown on three different "advanced basketball statistics" web sites. Our results were shown to be extremely highly correlated with the results shown on the other sites. Where there are small differences, I believe mine are better, if only because mine uses simple, bedrock statistical theory rather than involved formulas.

HIDDEN DEFENDING
Before revealing what we do to reveal it, let's define "hidden defending." Exactly what is hidden defending? It's every action that helps to prevent the other team from scoring other than rebounding, stealing, and blocking. So it would include man to man defending, zone defending, rotating in general, defensive recognition, and quick defensive response to various offensive tactics, such as pick and rolls. Obviously, if a defender is good at these things, the other team doesn't score as many points than if the defender is lousy at these things.

HOW TO REVEAL HIDDEN DEFENDING IN FIVE STEPS
STEP ONE: CALCUATION OF RAW HIDDEN DEFENDING RATINGS
Unlike most "advanced statistics" that are published on the internet or in print, we give you all the details about how we do ours, so that you can evaluate the evaluations, so to speak. The following is specifically what we are doing to be able to accurately and fairly compare players' defending:

Where do we start to discover what is hidden? We keep it as simple and yet as accurate as possible. We use the most official and therefore presumably the most reliable data as the building blocks for rating the defense of NBA players. We start with the player minutes and points scored by the other team while the player was on the court that are shown in the plus/minus statistical section at NBA.com.

After simply dividing points allowed by minutes on the court, we adjust that rate for the pace of the team and for the quality of the team's defense. The two adjustments are needed so that the ratings of players who are on different teams can be fairly compared.

Players who are on teams with faster paces give up more points per minute through no fault of their own. Similarly, players who are on teams with less efficient defenses give up more points per minute, everything else held constant. You could not fairly compare players on two or more teams with different paces and different team defense qualities unless you standardized, or in other words controlled for those differences for all NBA players.

USE OF BASIC STATISTICAL SAMPLING THEORY
What we are doing is using an indirect and inexact yet accurate and statistically valid way to discover who the better defenders are. No two players are out on the court for all the exact same minutes. So although for every player, what the other players out on the court do defensively while they are out on the court is a very large factor determining what that player's points per minute allowed will be, when you look at many, many hundreds of minutes, what the individual player does, or does not do defensively, as the case may be, will eventually show up in that particular player's points allowed per minute statistic.

In other words, what any individual player does defensively has to sooner or later show itself in the points allowed per minute. As the number of minutes rise above 500, and then 1,000 and then, for many players, above 2,000 and even 3,000 for a regular season, what a particular player does or does not do defensively becomes more and more exactly shown by the points allowed per minute number. This is very basic statistical sampling theory in operation. Statistical sampling theory is the easy to understand bedrock theory of statistics.

Due to the necessity of a large sample of minutes, we will not do defending estimates for any player who has played for fewer than 300 minutes. Quality of defending estimates will be slightly less accurate for players who have only played between 301 and about 600 minutes than they will be for players who have played for more than 600 minutes. We believe that the estimates are going to be extremely accurate for all players who have played 750 minutes or more. The idea is relatively simple: as the number of hundreds of minutes played goes up, the accuracy of this system improves, to the point where it gives you the same information you would have if you knew exactly how many possessions of the other team each player ruined with his defending.

For your information, all players allow between 1.87 and 2.16 points per minute; most allow between 1.94 and 2.11. The overall NBA average is about 2.03 points per minute allowed.

STEP TWO: CONVERSION OF RAW HIDDEN DEFENDING POINTS ALLOWED PER MINUTE TO FILTERED HIDDEN DEFENDING POINTS ALLOWED PER MINUTE
Since different players have different breakdowns between how much of their defending shows up in tracked statistics such as defensive rebounding and how much of it does not, in order to improve accuracy we need to have a method to filter, or in other words, separate, the two categories of defending. If we didn't do this, we would still have a useful statistic, but it would be biased in favor of players whose defending is counted in tracked statistics more so than other players. There would be in effect some double counting of defending for players who have most of their quality defending tracked by scored statistics.

The filter used is to multiply the raw hidden defending ratings by the percentage of the real player production that is offensive. In other words we take the inverse of the percentage of a player's real player production that is defensive and multiply the raw hidden defending ratings by that. The rationale to do this is that although the exact relation is unknowable, we know that for a given raw hidden defending performance level, there will be an inverse relation between scored defending and hidden defending. The more defensive rebounds, steals, and blocks a player is making for any raw level, the less he is relying on hidden defending to achieve the raw level. And vice versa. So multilying by the inverse of the percentage of all contributions that are defensive (in other words, multiplying by offensive contributions) filters out much of the bias that is in the raw hidden defending rating.

To be even more specific, we first extract out defensive rebounding, steals, blocks, and personal fouls, the sum total of which is called "Scored Defensive Contribution". All of the other components combined constitute "Scored Offensive Contribution". Now we can determine the percentages of the RPP that are offensive and defensive, and then we can use the offensive percentages to convert the raw hidden defending ratings to filtered hidden defending ratings.

STEP THREE: CONVERSION OF FILTERED ALLOWED POINTS PER MINUTE TO FILTERED HIDDEN DEFENDING RATING
We need to translate the adjusted or filtered points allowed per minute into numerical terms that are the most useful with respect to RPR. So with a very carefully designed translation scale, we amplify the very small differences in different player's points allowed per minute numbers into much larger different hidden defending ratings for each player. Then we simply add the hidden defending rating to the Base RPR to yield RPR.

STEP FOUR: USE OF HIDDEN DEFENDING RATING
We now have added in a reasonably good estimate of the value of actions of players that are not even kept track of by scorekeepers! The filtered hidden defending ratings are added to the "Base or Scored RPR" to give RPP. The range of possible defending adjustments to the base RPR is from 0 to about .230. In most cases, however, the adjustment will be between 0.030 and .150.

STEP FIVE: OVERALL EVALUATION OF DEFENDING
Aside from the Hidden Defending Rating we can find out how well each player does in terms of unhidden or scored defending, can't we? Of course se can.

Aside from the hidden there is of course unhidden defending, which would be rebounding plus steals plus blocks minus personal fouls. If we extract the combination of those four out of the same counts that underlie the RPR as a whole, we get what we are going to call the Scored Defending Contribution. This could also be thought of as Tracked Defending Contribution if you prefer. Then if we divide this by minutes, we can have a Scored (or Tracked) Defending Rating.

Finally, if we combine Hidden Defending Rating (HDR) with Scored Defending Rating (SDR) we can have an Overall Defending Rating (ODR). I am for now going to simply multiply the HDR by two and add that to the SDR to yield the ODR. To combine them this way is more arbitrary than my usual standards allow; I am doing this because there is as of yet no non-arbitrary way of doing it. The formula of two times HDR plus SDR brings HDR almost up to par with SDR in terms of the actual numbers and the averages of those numbers involved.

In other words, I am saying for now that hidden defending is almost as important as scored defending. There appear to be many coaches and not a few hardcore basketball fans who believe that hidden defending is actually more important than scored defending, but I am very likely never going to agree with that. I think that although hidden defending is important, and plausibly almost as important as tracked defending, that it is like a quicksand in that there seems to be a tendency for a substantial minority of basketball people to get carried away with estimating the importance of it and then become more and more trapped by their error in terms of how they look at basketball or in terms of how they coach their team if they are coaching.