User Guide for Real Player Rating Reports, June 2009

REAL PLAYER RATINGS BY TEAM USER GUIDE
Updated June 8, 2009

==========INTRODUCTION SECTION==========

INTRODUCTION TO THE CONCEPT OF REAL PLAYER RATINGS
The Real Player Rating (RPR) is a very carefully constructed all inclusive performance measure. Most things of value that a basketball player can do are carefully recorded by official NBA scorekeepers who sit right along the edge of the court, mid-court, and who are trained to observe and record everything that happens in a game.

Since these days all of these counts are immediately input into continually updated public data bases online, such as at ESPN, it is possible to in real time combine everything together into an overall performance measure for each player that is intended to evaluate how valuable each player is toward winning games. This is what the RPR does.

Real Player Rating or RPR is everything tracked by scorekeepers that a player does, good and bad, added and subtracted (with negative things such as turnovers and missed shots being subtracted). Very carefully calibrated factors, or weights, are applied to the different elements.

The calibration, as you would expect, is done to reflect the different value toward winning games that different actions on the court have. These factors are subject to very small annual adjustments as knowledge about how games are won and lost is fine tuned.

Then, all of the good and bad combined together is divided by minutes, yielding RPR, which is really the rate per unit of time of the good minus the rate per unit of time of the bad. This is what we need to determine the overall quality or value of the player toward the objective of winning basketball games.

QUALITY (RPR) AND QUANTITY (RPP} SUMMARIZED
RPR reports show for each player the RPR (Real Player Rating) which tells you how good a player did (all the good things minus all the bad things) out on the court per unit of time. The RPP (Real Player Production) report tells you how much in total (the sum of the of the good things minus the sum of the bad things) a player did out on the court, without regard to playing time.

Many and maybe most sports watchers and an unknown but probably disturbingly large number of sports managers make the mistakes of exaggerating the importance of quantity and overlooking to some extent quality. These reports allow you to expand your horizons. These reports put quantity and quality side by side, which is extremely valuable, because both are roughly equally important in explaining accurately why and how the team is playing the way it is.

SIMPLICITY, RELIABILITY, TRANSPARENCY, AND FOCUS ONLY ON "WINNING POWER"
Like everything statistical we do at Quest, we have kept this process as simple and reliable as possible, while at the same time spending as much time as necessary on design, quality control and performance evaluation. Unlike some other practitioners, we avoid what you might call layered complexity, which leads to formulas which can not be understood without studying them and which high traffic sites will not show on any of their web pages for fear that the public will rebel against the statistic. At Quest, we think that our rating systems can be understood and evaluated by most high school graduates, and we keep everything out in the open through User Guides such as this one.

Basketball statistical gurus frequently forget that no matter how intricate their formulas are, they are very heavily manipulating process items such as assists and rebounds while most likely spending very little time on how these things fit together to produce wins and losses. We think that they are making the mistake, whether or not they are aware, of injecting value adjustments regarding how they think the game should be played and value adjustments about which playing styles are better than others.

Whereas, the primary objectives of the relative simplicity (small number of formulas, to be more precise) of the Quest RPR is to avoid all how the game should be played and how players should play value judgments. We don't care about the styles, only about the results. The RPR is concerned first and in fact exclusively with the impact each player has on the potential for winning games.

Quest thinks it makes more sense to minimize the manipulation of process items, and to focus much more on coming up with the best possible estimation of how the process items impact points for and points against in games, which in turn of course determines wins. Whereas other "advanced statistics" might give you more depth and flavor regarding how a particular player plays (his style) the Quest RPR is a way for the reader to, in a very quick and easy way, determine what the overall value of the player is with respect to producing wins or losses.

In other words, the foundation of RPR is and will always be measurement of a player's power to help win basketball games, whereas the foundation of other, more complicated statistics may include preferences about how the game should be played and about the style of players, with winning power measured less accurately as a result of those focuses.

IMPORTANCE OF PER UNIT OF TIME
Because it is per time, RPR is immediately in the running to be the best possible measure of the net quality of a basketball player, or simply "how good" the player is (on average) for each minute of playing time. All per game statistics are inferior to any reasonably good per unit of playing time measure. For example, points per minute (or per 40 minutes or any number of minutes) is a much better thing to look at than points per game.

REAL PLAYER RATING REPORTS CAN BE FOR THE WHOLE NBA, FOR A TEAM, FOR A GAME, OR FOR A CAREER
With a Real Player Ratings Report for the entire NBA, you can see very rapidly who the best players in the NBA have been during the course of the season.

With a Real Player Ratings Report for a Team for the Regular Season, you can see very rapidly who the best players on the team have been during the course of the season. You can use this information to investigate the possibility that the coach is not perfect. Well, we know that no coach is perfect. So really, with the benefit of 20/20 hindsight, we can investigate and determine what mistakes the coach has apparently made with regard to rotations and playing times. Furthermore, by using the Ratings, basketball knowledge, a little creativity, and logical deduction, we can also investigate and perhaps determine whether the coach has made incorrect decisions regarding which strategies and plays are best for his team's offense and defense.

Real Player Ratings for games are a major part of Reports called Ultimate Game Breakdowns.

Real Player Ratings for a player's career, year by year and in total, are obviously very valuable looks at how the player changed over the years. Of course, most players get better from how they started in their rookie years.

[End of Introduction Section.]
============================================
CAUTIONS SECTION
To be completely honest and clear, although it is the best possible overall real life measure, RPR is still not a perfect or absolute, "final word" measure on any player. In general, you must remember that all performance measures including this one for the NBA are relative rather than absolute measures. The ratings are relative to the team context. Players do not exist in a vacuum, especially in basketball.

Several specific cautions will now be described.

RPRs ARE RELATIVE TO TEAMS, AND ARE SUBJECT TO THE CROWDING OUT EFFECT
Because basketball is a team game, and more so than most other sports, players who are on really good teams might have their own performances "crowded out" to some extent by just as good players and especially by even better players. So paradoxically, ratings of players of all ratings levels who are on better teams will generally have slightly lower ratings than they would have if they were on a not as good team. Conversely, players (at all ratings levels) who are on bad teams will have slightly higher ratings than they would have if they were on a better team. Numerically, a player on the best NBA team could easily have a RPR that is 15-20% less than what it would be if he was a player on the worst NBA team.

Always remember this important point, which we restate for emphasis. If a good player is on a good team where there are a number of players as good and even better than he is, than his RPR will likely be lower than it would be if he were on a not as good team.

Position in the team context can impact RPR as well. If a good player plays a certain position for which his team has an even better player, then it's probable that the better player will crowd out the lesser player to one extent or another, so that the lesser player's RPR will be lower than what it would be if he were the best player at the position on the team. Conversely, the best player at a position on a bad team can have a RPR which is higher than what it would be on many other teams.

ACTUAL RPR DIFFERENCES BETWEEN TEAMS ARE GREATER THAN APPARENT DIFFERENCES
An important implication of crowding out and relativity is that the average RPR among the best five, six, or seven players of the best teams in most cases will understate the real "potential RPR" of those players, where potential RPR is RPR with the least possible crowding out. In other words, the potential RPRs of players on the best teams is higher than their actual RPRs. Conversely, the long-run, true potential RPRs of the apparently better players on bad teams is actually lower than their actual RPRs.

This plays out at the team level in a very important way. Always remember this: the actual underlying gap in the real quality of the players between good and bad teams is greater than the actual RPRs are indicating. The true RPR differential between the best and the worst NBA team could easily be 20-30% greater than the apparent differential. In other words, team RPR averages understate real quality differences between teams.

PLAYERS NEED THE BALL FOR HIGHER RPRs
Players need not only playing time but possession of the ball in order to produce many of the things that count in the rating. So if, for whatever reason, a player does not get the ball as often as he would on a different team, or with a different coach, or with whatever other circumstances you can dream of, then his RPR will be lower than what it could or would be.

DO NOT FORGET WHAT THE RATINGS YOU ARE LOOKING AT ARE MEASURING
Many ratings that you see on Quest are only for the current season. It has recently been discovered that many player's ratings often change up or down by 10% from year to year, and can change by about 15% up or down without too much trouble from one year to the next. Moreover, over the course of a player's entire career, RPR ratings by year can and often do vary by 50% or even more when you compare the highest year or two to the lowest year or two. Although there are a fairly good number of exceptions, many NBA players have much lower RPRs in their first year or two in the NBA than they will eventually average out to.

INJURIES AND RECOVERIES FROM INJURIES
Players often play with minor injuries. They also often start playing again before they are 100% recovered from an injury. They sometimes even postpone surgery that has become necessary due to injury until the off-season, and play with some type of impairment in the meantime. In all of these situations, RPR will be lower than it would be were the player not dealing with any injury.

MAGNITUDE OF THE ADJUSTMENT FOR HIDDEN DEFENDING
Those who think defense in basketball is much more important than offense will consider the magnitude of the defensive adjustment to be inadequate. They will contend that defensive specialists who are poor offensive players should have a higher rating. While we realized that we needed to adjust the ratings for defending not tracked by NBA scorekeepers, and while we put in a huge effort to come up with a valid adjustment system, we continue to believe that players who are great defensive specialists but poor or undeveloped offensive players should in most cases rank no higher than the Major Role Player/Good Enough to Start level, which is the level just below the Solid Starter level.

AVOID BEING CONFUSED BETWEEN RPR AND RPP AND DO NOT MINIMIZE THE IMPORTANCE OF RPP
Do not forget that RPR is a per time measure. RPP and not RPR measures total impact of a player. RPR measures how valuable a player has been toward winning basketball games, per unit of time.

Do not make the mistake of ignoring the importance of RPP, now improved to TRPP. Players with the highest TRPP are showing they have the stamina, knowledge, and trust of the coaching staff to be able to get all the playing time needed to produce that. So even if their RPRs are a little lower than you might expect, players with the highest TRPPs should still be considered as extremely important and valuable players.

Having said that, one of the most important objectives for any top Coach must be to make sure that his highest RPR players are also found at or close to the top of the TRPP list.

THE CLASSIFICATION SCHEME IS RELATIVE TOO
The classification scheme, like the ratings, is relative. A role player on a really good team might be a solid starter on a bad team. A star on a bad team might be just a major role player on a really good team. And so on and so forth. A player is a star, a role player, or whatever only in the contexts of the particular season and the particular team involved. If he was on a different team, or if it was a different year, his classification could easily be different.

So to conclude the Cautions section of this guide, don't think of RPR as the ultimate gospel or bible on how good players are. But do think of it as an extremely accurate and reliable summary of how good the players actually have been in real life in the specific time (season or playoffs) and place (team) involved.

[end of cautions section]

===========STRATEGICALLY USING RPR SECTION============

RELATIVITY ADJUSTMENT FOR PROJECTED RPR FOR PLAYERS CHANGING TEAMS
When you are trying to judge how good a player might be if he were on another team, you need to, due to the relativity factor discussed previously, adjust the expected RPR upwards if the player is moving to a lower quality team and to adjust the expected RPR downwards if the player is moving to a higher quality team. The maximum such adjustment necessary is believed to be about 15%, with that full amount applied only when the player is moving from one of the worst teams to one of the very best teams, or vice versa.

GREAT VARIABILITY OF PLAYER RPRs FOR INDIVIDUAL GAMES
Not as many breakdowns of individual game ratings are going to closely track the overall average for the roster as you might think. This is because one of the interesting things about basketball that makes it different from most other sports is that "how good" a player is from game to game varies radically. The best players sometimes have terrible games where they do almost nothing, while players who normally do not do much can every once in a while have outstanding games, at least if you measure it per minute on the court anyway. If you just looked at actual production, and never at a reserve player's Real Player Rating, you would hardly notice any of his unusually outstanding games, since players who normally do not do much will normally not have much playing time.

INTERACTIONS BETWEEN PLAYING TIMES, RPRs, TRPPs, AND THE NEEDS OF TEAMS
There are certain things that only certain players can do very well, and if those things are crucial for the team, than those players will have to play more minutes than they might otherwise play. The extra minutes might tend to reduce the player's Real Player Rating, while his total production will rise with the additional minutes. So to fairly and completely evaluate any player, you must always look at both the Real Player Rating (RPR) and the Real Player Production (RPP).

Furthermore, it is strongly suspected that, in order to compete in the playoffs, a team must have as many players of as high a quality (RPR) as possible, while at the same time having at least one or two players whose actual production is among the highest in the NBA regardless of exactly how high the RPRs happen to be. (All high RPP players will be relatively high RPR players; some will be higher than others.) Specifically for example, LeBron James' actual massive amount of production is most likely just as important to the Cleveland Cavaliers as is his RPR or, in other words, as is his rate of production. Similarly, Kobe Bryant's quantity is probably at least as important to the Lakers as is his quality.

Whereas, teams such as the Denver Nuggets, who have instructed a possible huge producer, Carmelo Anthony, to "not worry about scoring," may have made a fatal mistake relative to the playoffs, because teams with no extremely high rate producers may be generally doomed to lose quickly in the playoffs even if they have an unusually large number of high quality players as shown by RPR. This is because extremely high RPP players can by themselves "dominate a game" to some extent, meaning they can by themselves possibly win the game for their team, without worrying about complications that come in to play if you need to coordinate several high RPR but ultimately and theoretically limited RPP players.

Players who over the course of a season appear to rank higher in RPR (quality) but lower in RPP (quantity) may not be getting enough playing time. Players who over the course of a season appear to rank lower in RPR (quality) but higher in RPP (quantity) may be getting too much playing time. But as alluded to earlier, you must not automatically conclude this, because some skills are needed out on the court most of the time, but yet may be available only from a small number players on the roster. Such players may have to get more playing time due to that critical skill in short supply, even if their overall quality does not seem to justify all of that playing time.

A relatively common reason for unusual playing time will be players who are either truly outstanding defenders (who get extra playing time) or truly bad defenders (who get their playing time reduced).

Another common reason for extra playing time will be if a team has a point guard who has many more turnovers than the average point guard has. Because the point guard is so important, a good coach has to play his best guard who can make plays at the position for a full set of minutes every game, and he or she must do so almost regardless of how many turnovers that player makes. If you take out your designated point guard due to "too many turnovers," it may end up sort of like cutting your foot off because you have a bad case of athletes foot!

EVALUATION OF REAL PLAYER RATINGS

EVALUATION SCALE FOR A REGULAR SEASON
Remember: Meaningful regular season ratings are not possible until about Jan. 20 of each year. Ratings become truly valuable after the all star break.

Perfect for all Practical Purposes / Major Historic Super Star 1.100 and more
Historic Super Star 1.000 1.099
Super Star 0.900 0.999
A Star Player / A Well Above Normal Starter 0.800 0.899
Outstanding Player: A Solid Starter 0.750 0.799
Major Role Player / Good Enough to Start 0.700 0.749
Good Role Player / Often a Good 6th Man 0.640 0.699
Satisfactory Role Player 0.580 0.639
Marginal Role Player 0.520 0.579
Poor Player 0.460 0.519
Very Poor Player 0.400 0.459
Extremely Poor Player and less 0.399

NOTE ABOUT LOW REGULAR SEASON RATINGS
Players rated below about .550 often get playing time based largely on factors outside of RPR, but valued by coaches and other players, such as:
--Great energy and hustle
--Toughness, such as diving after loose balls and taking charges
--Leadership and/or knowledge, especially in the case of veterans
--Perceived potential for future improvement in terms of real basketball production, especially in the case of young players
--See also the User Guide section called "Cautions"

EVALUATION SCALE FOR SINGLE GAMES
Remember: Single game ratings do NOT include any adjustment for hidden defending

Perfect for all Practical Purposes / Major Historic Super Star 1.210 and more
Historic Super Star 1.050 1.209
Super Star 0.890 1.049
A Star Player / A Well Above Normal Starter 0.730 0.889
A Very Good Player: A Solid Starter 0.650 0.729
Major Role Player / Good Enough to Start 0.570 0.649
Good Role Player / Often a Good 6th Man 0.490 0.569
Satisfactory Role Player 0.410 0.489
Marginal Role Player 0.330 0.409
Poor Player 0.250 0.329
Very Poor Player 0.170 0.249
Extremely Poor Player 0.169 and Less

NOTE ABOUT LOW SINGLE GAME RATINGS
Players rated below about .400 often get playing time based largely on factors outside of RPR, but valued by coaches and other players, such as:
--Great energy and hustle
--Toughness, such as diving after loose balls and taking charges
--Leadership and/or knowledge, especially in the case of veterans
--Perceived potential for future improvement in terms of real basketball production, especially in the case of young players
--See also the User Guide section called "Cautions"

EVALUATION SCALE FOR A CAREER (OF A PLAYER)
Remember: Many players have lower ratings in their first one to three years than they will have ultimately.

Perfect for all Practical Purposes / Major Historic Super Star 1.000 and more
Historic Super Star 0.930 0.999
Super Star 0.860 0.939
A Star Player / A Well Above Normal Starter 0.780 0.859
A Very Good Player: A Solid Starter 0.740 0.779
Major Role Player / Good Enough to Start 0.700 0.739
Good Role Player / Often a Good 6th Man 0.652 0.699
Satisfactory Role Player 0.604 0.651
Marginal Role Player 0.556 0.603
Poor Player 0.508 0.555
Very Poor Player 0.460 0.507
Extremely Poor Player 0.459 and Less

NOTE ABOUT LOW CAREER RATINGS
Players rated below about .580 often get playing time based largely on factors outside of RPR, but valued by coaches and other players, such as:
--Great energy and hustle
--Toughness, such as diving after loose balls and taking charges
--Leadership and/or knowledge, especially in the case of veterans
--Perceived potential for future improvement in terms of real basketball production, especially in the case of young players
--See also the User Guide section called "Cautions"

[End of the Strategic Use of Ratings Section]

==========MECHANICS OF REAL PLAYER RATINGS AND REAL PLAYER PRODUCTION==========

MINIMUM PLAYING TIME RULES
Due to the minimum sample size requirement for the adjustment for hidden defending, regular season ratings for NBA players can not be meaningfully done until at least mid January. Generally, we need at least 3 players to have played 1,500 minutes or more before we can or will rate that team's players.

Also, only players who played at least 10% of the minutes of whoever has played the most minutes on the team are included in intra-regular-season team RPR reports. Any player who has played for less than 10% of the minutes of the player who has played the most minutes is not included, since he didn't play for long enough to be fairly or reasonably compared with the other players. However, in the interests of completeness, all players who have played at least 300 minutes are included in the end of season team RPR report, even though a small number of players will have played for less than 10% of the time of the highest minutes player.

Furthermore, as described extensively in the adjustment for defending section of this Guide, only players who have played at least 300 minutes can have a defensive rating, or an overall RPR given to him. Both the 10% and the 300 minutes minimums must be met for a player to be rated.

REAL PLAYER PRODUCTION
Of course, looking at actual production (everything positive added together and everything negative subtracted out) is something that is extremely important too. The total production (everything good and everything bad combined together) is simply called Real Player Production or RPP.

BASIC VERSUS TOTAL REAL PLAYER PRODUCTION
Basic RPP does not include any estimate of how much value from hidden defending was done by the player. Starting from June 2009, there is an estimate made for the value of hidden defending of each player, calculated from the following formula:

Hidden Defending Production = Total Scored Defensive Production * (Hidden Defending Rating / Total Scored Defensive Rating)

The validity of this adjustment is somewhat less than the high validity of the defending adjustments for RPR in general. Therefore, the user is advised to not go overboard in using the results.

Then of course Total Real Player Production is Basic Real Player Production plus Hidden Defending Production. Note: At this time, RPP still refers to basic RPP, and so TRPP is the adjusted version.

SOURCE OF TRACKED BASKETBALL COUNTS
The sources for the raw counts of scores, rebounds, steals, turnovers, and so forth are ESPN.com and NBA.com.

NOTES ON SOME OF THE TECHNOLOGIES USED
Microsoft Excel is extensively used to accurately produce RPR report. The internet has been very extensively used both in the development and in the continuing production of RPR and related reports.

THE BASIC FORMULA
For 2008-09, the RPR formula has been very carefully and accurately tweaked again and is set to be as follows:

POSITIVE FACTORS
Points 1.00 (at par)
Number of 3-Pt FGs Made 1.00
Number of 2-Pt FGs Made 0.60
Number of FTs Made 0.10

Assists 1.75

Offensive Rebounds 1.25
Defensive Rebounds 1.20
Blocks 1.60
Steals 2.20

NEGATIVE FACTORS
3-Pt FGs Missed -1.00
2-Pt FGs Missed -0.85
FTs Missed -0.90

Turnovers -2.00
Personal Fouls -0.90

ACTUAL COMBINED AWARD OR PENALTY BY TYPE OF SHOT
3-Pointer Made 4.00
2-Pointer Made 2.60
Free Throw Made 1.00
3-Pointer Missed -1.00
2-Pointer Missed -0.85
Free Throw Missed -0.90

ZERO POINTS: PERCENTAGES BELOW WHICH THERE IS A NEGATIVE NET RESULT
3-Pointer 0 score % 0.200
2-Pointer 0 score % 0.246
1-Pointer 0 score % 0.459

This means that if a player has a lower percentage than any of the three above, then his RPR would be lower rather than higher as a result of his shooting that type of shot.

ASSISTS VERSUS TURNOVERS ZERO POINT
Assist/Turnover Ratio That Yields 0 Net Points: 1.143

This means that any player who has an assist/turnover ration of less than 1.143 is losing RPR rating when assists and turnovers are considered. He would have to either increase assisting or reduce turnovers to turn the combined effect from assists and turnovers positive.

DEFENDING RATING
A quality of defending rating of between 0 and .268 is added to base or unadjusted RPR. In most cases, the defending rating is between 0.050 and .200. See the Hidden Defending Adjustment to Real Player Ratings below below for a very detailed explanation of how we determine player defensive ratings and how we combine them with base RPR.

[End of Mechanics of Real Player Ratings and Real Player Production.]
======== DEFENSIVE AND OFFENSIVE SUB RATINGS ======================

DEFENDING SUB RATING

THE HIDDEN DEFENDING ADJUSTMENT (HDA) TO REAL PLAYER RATINGS
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.

As of June 8, 2009, the mechanics of the HDA were slightly changed to increase accuracy; see the outlier adjsutment below for details.

Obviously, some valuable things that basketball players do are never counted by scorekeepers. Many of these uncounted things are defensive, insofar as they prevent scores, or reduce the scoring opportunities of the opponent. These things would include chasing down loose balls, taking charges, and good or great man to man defending. Man to man defending that is good enough to prevent what would have been a score from actually being a score is the most common and important basketball action which can not be and is not tracked by NBA scorekeepers.

Man to man defending however, although the most important, is not by any means the only defensive element that can not be tracked or scored. Broadly, what is missed or hidden is all the things that the player does to make the possessions of the opposing teams worthless other than what is already counted, which would be rebounds, steals, blocks, and personal fouls. These untracked or hidden actions would include:

SOME BASKETBALL FACTORS ESTIMATED BY THE HIDDEN DEFENDING ADJUSTMENT TO RPR
--effective man to man defending
--effective rotation / switching on defense, especially off screens and picks
--effective pick and roll defense
--effective defensive recognition
--quickness of defensive reaction
--energy and hustle on defense
--effective taking of charges (causing a driving offensive player to be called for an offensive foul)
--effective hustling after loose balls

These things would be counted by scorekeepers if it were possible. But, for example, there is no way to know exactly how many shots a good (or any kind of) defender has changed from being a score to a miss.

Quest for the Ring has developed a statistically valid way to accurately estimate the untracked or hidden aspects of defending. This is described in complete detail in the latter sections of this Guide.

HDA IS AN UPGRADE TO DEFENSIVE EFFICIENCY RATINGS OF PLAYERS SEEN ON OTHER SITES
There are a small number of sites that show you each player's "defensive efficiency," which is number of points allowed per 100 possessions. This sounds nice, but it actaully is not all that valuable. The Hidden Defending Adjustment of RPR is an upgrade for this.

Probably the most important improvement is that in HDA, players' defending is standardized for team defending. With the defensive efficiency on certain other sites, players who are on good defensive teams have elevated ratings simply because they are on those teams. But obviously, many of the players on a good defensive team are producing that good defense, not just any one of them. The Hidden Defensive Adjustment corrects for this quality of team defense bias, which enables players on different teams to be fairly compared with respect to hidden defending.

THE HIDDEN DEFENDING ADJUSTMENT EXPLAINED
It took almost two years of hoping, searching for things, planning, and then developing, but finally the breakthrough was achieved in the objective of correct evaluation of defending. Now that the breakthrough has come, I am now more certain than ever 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.

HDA is a statistically valid way to rate the hidden 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 subject to a very small amount of statistical error, it validly awards the better defenders with bigger RPR bonuses. It has been validated by comparing results obtained with the player defensive efficiency ratings shown on three different "advanced basketball statistics" web sites. HDA results were shown to be highly correlated with those efficiency ratings.

Where there are small differences, HDA is better, because of the correction for team defense bias, because HDA uses simple, bedrock statistical theory rather than involved formulas involving assumptions, and for other lessor reasons.

HOW TO REVEAL HIDDEN DEFENDING IN FOUR STEPS
STEP ONE: CALCUATION OF RAW HIDDEN DEFENDING ADJUSTMENTS
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.

There are no value judgments made regarding a player's defending style, or regarding a team's defending style for that matter. We don't care about style. Using points allowed per minute is looking at results, nothing more and nothing less.

After simply dividing points allowed by minutes on the court, we adjust (we standardize, to be more precise) 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. For example, it would be grossly unfair to compare the rate of points allowed of a player on a fast paced, poor defense quality team to a player on a slow paced, high defense quality team.

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, regardless of how well they defend, everything else held constant. You can not fairly compare players on two or more teams with different paces and different team defense qualities unless you standardize, or in other words control 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 a differentiation from other players of his 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, after adjustments for pace and team defense quality, all players allow between 1.88 and 2.28 points per minute; most allow between 1.98 and 2.18. The overall NBA average is about 2.08 points per minute allowed.

STEP TWO: CONVERSION OF RAW HIDDEN DEFENDING ADJUSTMENT TO UNADJUSTED 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. The scale is approximately symmetrically (two sided) inverse logarithmic with respect to the average point.

STEP THREE: APPLICATION OF OUTLIER RULES IN VERY LIMITED NUMBER OF EXTREME CASES
An outlier rule is not the best way to produce a valid and useful measure. However, if it is the only technique available to correct for bias, using it is certainly better than not using it.

Although the HDRs emerging from Step 2 are valid and valuable, there are apparently two kinds of players whose HDRs are biased upwards. These players are relatively rare; we are only talking about fewer than two dozen of the close to 400 NBA players who play for 300 minutes or more during a season.

In general the problem is that a tiny number of forwards / centers make most of their defensive efforts in the tracked actions, such as defensive rebounding, and a very small number of guards, at the opposite extreme, make most of their defensive efforts in the hidden defending actions.

The problem is that the HDA scaling presupposes that there is some correlation between hidden defending and scored or tracked defending. For at least 90% of the players, there is a strong correlation. But where a player's defending is mostly tracked and very little hidden, or vice versa, the HDR rating is biased upward slightly. In both cases, the player would be given a higher HDA than he in real life deserves were it not for the outlier rules.

So the following are the two outliers that require minor adjustments. Of the two kinds of players who have been flagged for adjustment, the first one below, the guards, are much more common in real life.

1. Guards who do not rebound, steal, or block much, but who are great at hidden defending actions, sometimes end up with excessive HDR ratings, ones that they can not possibly be due.

An outlier rule is applied to prevent this bias from showing up in the final RPR of such guards. No player can have an HDR rating higher than double what his Scored Defensive Rating (SDR). The SDR is defensive rebounds, steals, and blocks minus personal fouls factored according to RPR. However, no player's HDR rating will be adjusted downward by more than .100 under this rule, so as to prevent excessive downward adjustment for a handful of guards who are truly good man to man defenders but who are not at all good at rebounding, stealing, and blocking.

2. At the opposite extreme, you have forwards and centers who produce an extreme number of defensive rebounds, steals, and blocks. Obviously, these players will tend to have high raw HDRs by virtue of those things alone. It is both logical and observable in games that such players can not get a very large number of rebounds/steals/blocks, and defensive stops via great man to man defending, at the same time. Technically, a great man to man defend on a possession is essentially an uncalled block. And forwards and centers who get a very large number of rebounds can not do that and get in a lot of good or great man to man defending in the same game.

Therefore, for such players, HDR would be biased upward; there would be some double counting involved.

An outlier rule is applied to prevent most of this bias from showing up in the final RPR. No player can have an HDA rating and a Scored Defensive Rating (SDR) combined higher than .600, which in turn is approximately 1.5 times the average Scored Offensive Rating for NBA players. (The average scored offensive rating is roughly .400.) For example, if an outstanding rebounder has a SDR of .400, his HDR must be reduced to .200 if it exceeds .200.

Remember, less than two dozen NBA players are subject to either of the outlier rules. The huge majority of NBA players are within the scaling parameters for HDR and so there is very low bias for them.

STEP FOUR: CALCULATION OF REAL PLAYER RATING (ADJUSTED FOR HIDDEN DEFENDING)
The final step is to simply add the hidden defending rating to the Base RPR to yield RPR.

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! Technically, you could call the final result "Ajusted RPR," but we are trying to avoid that terminology because of how important we think it is to include the hidden defending in the performance measure.

SIZE OF THE DEFENDING ADJUSTMENTS
Base regular season RPR's for most NBA players range between .400 and 1.000. The total range of possible defending adjustments to the base RPRs is from 0 to .268. In most cases, however, the adjustment will be between 0.050 and .200.

THE DEFENDING SUB RATING: PUTTING THE HIDDEN AND THE UNHIDDEN TOGETHER
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 we can.

Unhidden or tracked defending, is defensive rebounding plus steals plus blocks minus personal fouls, calibrated according to the usual RPR factors. If we extract the combination of those four out of the same counts that underlie the RPR as a whole, and use the usual factors, we get what we are going to call the Scored Defending Production. This could also be thought of as Tracked Defending Production if you prefer. Then if we divide this by minutes, we 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).

Obviously, the HDR scaling is designed to coordinate correctly with both SDR and with RPR as a whole. All of the coordinations reflect the latest undertanding of how basketball games are won and lost. The HDR constitutes 40-43% of ODR while SDR constitutes the other 57-60%. In other words, the value of hidden defending is perceived to be slightly more than 40% of the overall value of defending, while the value of scored (unhidden) defending is perceived to be slightly less than 60% of the overall value of 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 never going to agree with that. I think that although hidden defending is important, and plausibly almost as important as tracked defending, that it can not be more than this. Hidden defending 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.

FORWARDS AND CENTERS WILL GENERALLY HAVE SUBSTANTIALLY HIGHER DEFENDING RATINGS
Due to having primary responsibility for defense of the paint and for rebounding, centers and forwards are going to inevitably have higher defensive ratings than will guards. Along with much greater opportunity for rebounds and blocks, centers and forwards also have more opportunity for such hidden defending actions as good man to man defending and correct rotations than do guards. Guards out on the perimeter generally should not and do not man to man defend as closely as do interior defenders, due to the well known guideline that it is quite foolish to foul a jump shooter outside of the paint.

THE OFFENSIVE SUB RATING
The Offensive Sub Rating is all tracked actions other than the defensive ones (defensive rebounding, steals, blocks, and personal fouls) combined together using the RPR weights, divided by minutes. In other words, it is Total Offensive Production divided by minutes. For the list of all tracked actions and the weight factors assigned to each, see the secion titled "The Formula" above.

THE BEST GUARDS WILL HAVE THE HIGHEST OFFENSIVE SUB RATINGS
The very best guards in basketball are ones who, although they are not afraid to drive to the hoop from time to time, are able to make outside shots at a good rate. Also, guards in general, and especially point guards, are usually primarily responsible for making assists. These two are among the several reasons why the better guards in pro basketball will have the highest offensive sub ratings in the League.

On the other hand, some of the most valuable players in the NBA are centers and forwards who are great defenders and efficient inside scorers at the same time. Even more unusual and probably for that reason more valuable is a forward who is (a) a great inside defender (b) a great inside scorer and (c) someone who can hit jump shots, perhaps even including threes, from outside the paint. Lamar Odom is an example of this kind of extremely valuable player.

Some of these big men will have offensive sub ratings that exceed those of the lessor skilled shooting guards and even those of some of the less skilled point guards.

[End of Defensive and Offensive Sub Ratings Section.]

======== SUMMARY OF PRIMARY FORMULAS SECTION =================
Real Player Production or RPR = (All tracked or scored actions weighted according to best available analysis of importance / minutes) + Hidden Defending Rating

Real Player Production or RPP = Total Offensive Production + Total Defensive Production. (All tracked or scored actions weighted according to best available analysis of importance.)

Offensive Sub Rating = Total Scored or Tracked Offensive Production / Minutes

Defensive Sub Rating = Total Scored or Tracked Defensive Production + Hidden Defending Rating

Hidden Defending Rating = Raw Hidden Defending Adjustment amplified via an approximtely reverse logarithmic scale symmetric as to the average. The objective of this is to correctly show value toward winning games via amplification of seemingly minute differences in points allowed per minute.

Raw Hidden Defending Adjustment = Points Allowed Per Minute * Pace Adjustment Factor * Team Defense Adjustment