User Guide for Real Player Rating Reports, May 2010

REAL PLAYER RATINGS BY TEAM USER GUIDE
SECTIONS UPDATED WITH THIS UPDATE
--Strategically Using RPR (Most of the Evaluation scales were slightly improved.)
--Defensive and Offensive Sub Ratings Section (The procedure for determining accurate and unbiased Hidden Defending Ratings has been extensively improved.)

SECTIONS
This guide has the following main sections, with sub sections as highlighted within each section.

Introduction Section
Cautions Section
Strategically Using RPR Section
Mechanics of Real Player Ratings and Real Player Production Section
Defensive and Offensive Sub Ratings Section
Summary of Primary Formulas Section

========== 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 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 ratings. 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 even on the same team, and ratings can change by about 15% up or down without too much trouble from one year to the next even on the same team. 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. In a few relatively rare cases, defensive specialists who have decent offensive games will be ranked as Solid Starters.

None of this is to say that having a "defensive specialist" is a disqualifier to winning the Quest. It is merely a caution that coaches often make the mistake of giving them too much playing time.

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 absolute maximum such adjustment necessary is believed to be about 20%, with that full amount applied only when the player is moving from one of the very worst one or two teams to one of the very best one or two teams, or vice versa.

For players changing teams, RPR chamges in the 5-15% range will be much more common than changes of about 20% simply because most teams are neither among the very worst nor among the very best teams.

On top of RPR changes due to different teams, remember that RPRs often change by 10-15% from year to the next regardless of team. The combined RPR change for a player changing teams could therefore be as much as about 35%. This would be true if a player in the same year was intrinsically 15% better, and he moved from one of the very best teams to one of the very worst teams.

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 REGULAR SEASONS
--Meaningful regular season ratings with high statistical validity are not possible until about Jan. 20 of each year.
--The following scale assumes that the Hidden Defending Adjustments have been correctly done and included

Major Historic Super Star / "Perfect Player" 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 0.820 0.899
Very Good Player / A Solid Starter 0.760 0.819
Major Role Player / Good Enough to Start 0.700 0.759
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

SHOULD PLAYERS WITH LOW RATINGS BE PLAYING IN THE PLAYOFFS?
For the two teams that play in the Championship, players rated below about .560 are almost always a drag on the Championship run. However, such players sometimes get playing time based largely on factors outside of RPR, but valued by coaches and other players, such as:

--Great energy, effort, 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

But keep in mind also that the value of these qualities may be and often are overestimated, particularly with respect to playoff games. In general we see that players below .560 are often getting too much playing time in playoff games.

Many playoff teams are forced to play players with ratings below .560, especially shooting guards and small forwards, simply because they would not have anyone at the position or because they would not have at least eight players available to play if they didn't play any players with ratings below .560. The fewer players below .560 a team has to play the better. One of the worst playff mistakes a coach can make is to play a player whose rating is lower than .560 for more minutes at a postion than another player at that position whose rating is above .560.

The advice regarding players rated even lower is simple and clear. Players rated below .500 should not be playing at all in the playoffs (except in garbage time) for teams that are serious about winning the Quest for the Ring. Coaches who play players with ratings lower than .500 in the playoffs when any player was available at the position whose rating was higher than .500 should in most cases be fired.

EVALUATION SCALE FOR SINGLE GAMES
There are two scales for a single game, one for if no hidden defending adjustment is included and one if the new as of June 2010 hidden defending adjustment for a playoff game is included.

EVALUATION SCALE FOR BASIC REAL PLAYER RATINGS FOR A SINGLE GAME WITH NO HIDDEN DEFENDING ADJUSTMENT
Major Historic Super Star / "Perfect Player" 1.060 and more
Historic Super Star 0.940 0.979
Super Star 0.820 0.939
A Star Player / A Well Above Normal Starter 0.720 0.819
Very Good Player / A Solid Starter 0.640 0.719
Major Role Player / Good Enough to Start 0.560 0.639
Good Role Player / Often a Good 6th Man 0.480 0.559
Satisfactory Role Player 0.400 0.479
Marginal Role Player 0.320 0.399
Poor Player 0.240 0.319
Very Poor Player 0.160 0.239
Extremely Poor Player and less 0.159

EVALUATION SCALE FOR REAL PLAYER RATINGS FOR A SINGLE GAME WITH THE SINGLE GAME HIDDEN DEFENDING ADJUSTMENT INCLUDED
Major Historic Super Star / "Perfect Player" 1.200 and more
Historic Super Star 1.080 1.119
Super Star 0.960 1.079
A Star Player / A Well Above Normal Starter 0.860 0.959
Very Good Player / A Solid Starter 0.780 0.859
Major Role Player / Good Enough to Start 0.700 0.779
Good Role Player / Often a Good 6th Man 0.620 0.699
Satisfactory Role Player 0.540 0.619
Marginal Role Player 0.460 0.539
Poor Player 0.380 0.459
Very Poor Player 0.300 0.379
Extremely Poor Player and less 0.299

EVALUATION SCALE FOR A CAREER (OF A PLAYER)
Remember that many players have lower ratings in their first one to three years than they will have ultimately. Remember also that players in their last season or two before they retire will generally have lower ratings than their career average.

All Career Real Player Ratings require a Hidden Defending Adjustment (HDA). For active players, the adjustment will be the average of the two HDA adjustments from the most recent two seasons. For retired players, the adjustment will be the average adjustment for the third to last and the fourth to last season (in other words, the final two years of the players' career are skipped and the two years prior to those years are considered).

EVALUATION SCALE FOR A CAREER (OF A PLAYER)
Perfect for all Practical Purposes / Major Historic Super Star 1.000 and more
Historic Super Star 0.940 0.999
Super Star 0.870 0.939
A Star Player / A Well Above Normal Starter 0.800 0.869
A Very Good 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 0.650 0.699
Satisfactory Role Player 0.600 0.649
Marginal Role Player 0.540 0.599
Poor Player 0.480 0.539
Very Poor Player 0.420 0.479
Extremely Poor Player 0.419 and Less

NOTE ABOUT LOW CAREER RATINGS
Players rated below about .600 in their careers 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
As explained further in the adjustment for defending section of this Guide, only players who have played at least 300 minutes can have a hidden defending rating and an overall RPR given to them. 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.

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. Other sites used as important data sources are Basketball-reference.com, Knickerblogger.net, and USAToday.com.

NOTES ON SOME OF THE TECHNOLOGIES USED
Microsoft Excel is extensively used to accurately produce RPR reports. Hundreds of Internet sites have been used to one extent or another in the development and in the continuing production of RPR and related reports. A very small number of sites, however, are relied on for the raw data, especially ESPN.com and NBA.com.

THE BASIC FORMULA
For 2009-10, 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 0.40
Number of FTs Made 0 (no "bonus for a made free throw; just the point itself goes into RPR)

Assists 2.15

Offensive Rebounds 1.43
Defensive Rebounds 1.31
Blocks 1.80
Steals 2.30

NEGATIVE FACTORS
3-Pt FGs Missed -1.00
2-Pt FGs Missed -1.03
FTs Missed -1.3256

Turnovers -1.95
Personal Fouls -1.00

ACTUAL COMBINED AWARD OR PENALTY BY TYPE OF SHOT
3-Pointer Made 4.00
2-Pointer Made 2.40
Free Throw Made 1.00
3-Pointer Missed -1.00
2-Pointer Missed -1.03
Free Throw Missed -1.3256

ZERO POINTS: PERCENTAGES BELOW WHICH THERE IS A NEGATIVE NET RESULT
3-Pointer 0 score % 0.200
2-Pointer 0 score % 0.300
1-Pointer 0 score % 0.570

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: 0.908

Asset/turnover rations greater than .908 are positive with respect to RPR. This also means that any player who has an assist/turnover ration of less than .908 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.

HIDDEN DEFENDING RATINGS
A quality of defending rating of between 0 and .324 is added to base or unadjusted RPR. In most cases, the hidden defending rating is between 0.050 and .230. See the Hidden Defending Adjustment to Real Player Ratings sub section that follows just below below here for a very detailed explanation of how we determine player hidden defensive ratings and how we combine them with base RPR.

[End of Mechanics of Real Player Ratings and Real Player Production Section.]

======== DEFENSIVE AND OFFENSIVE SUB RATINGS ======================

DEFENDING SUB RATINGS
DEFENSIVE AND OFFENSIVE SPECIALISTS
Defensive specialists will have a much higher percentage of their overall RPR determined by the defensive sub rating than the League average of 45%. At the extreme, defensive specialists who are power forwards or centers will have defensive sub ratings that constitute as much as about 75% of their overall ratings. Due to the team nature of basketball, it is not an automatic disqualifier for winning the Quest to have a player unbalanced in this way, provided that the unbalanced player is truly outstanding defensively.

Offensive specialists will have a much higher percentage of their overall RPR determined by the offensive sub rating than the League average of 55%. At the extreme, offensive specialists who are guards will have offensive sub ratings that constitute as much as about 85% of their overall ratings. Due to the team nature of basketball, it is not an automatic disqualifier for wining the Quest to have a player unbalanced in this way, provided that the unbalanced player is truly outstanding offensively.

THE HIDDEN DEFENDING ADJUSTMENT (HDA) TO REAL PLAYER RATINGS
The hidden defending adjustment is on average 20.25% of overall RPR. Players will range widely though: as little as virtually 0% and as much as about 45% of a players' full RPR will be the hidden defending component.

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
--effective calling of time-outs, for example, to avoid a jump ball being called

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 basic 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.

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 an 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, all players allow between 1.87 and 2.26 points per minute; most allow between 1.96 and 2.17. The overall NBA average is about 2.06 points per minute allowed.

A REMINDER: NOTHING IS HIDDEN HERE
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.

HOW TO REVEAL HIDDEN DEFENDING IN FOUR STEPS
STEP ONE: CALCUATION OF RAW POINTS GIVEN UP PER MINUTE
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, for that matter, regarding a team's defending style. We don't care about style. Using points allowed per minute is looking at results, nothing more and nothing less.

STEP TWO: THE PACE ADJUSTMENT
After simply dividing points allowed by minutes on the court, we adjust (or standardize, or correct) that rate for the relative pace of the team. Pace is the average number of possessions per game. The faster the pace, the greater the number of possessions per game. Relative pace is average League pace divided by the team's pace. For your information, the average League pace in 2009-10 was 92.7 possessions per game. Fast paced teams will have pace adjustments of slightly less than 1 and slow pace teams will have pace adjustments of slightly greater than 1.

Then we simply multiply each player's raw points allowed per minute played by his team's pace adjustment.

It would be grossly unfair to compare the rate of points allowed by a player on a fast paced team to a player on a slow paced team. The player on the fast paced team automatically gives up more points per minute defensively because there are more possessions in a fast paced teams' games and, therefore, more points scored by the opponents. In other words 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. The correction for pace has just been described. The correction for team defensive efficiency turned out to be a big problem that was not largely solved until May 2010. See below for how the correction is made for team defensive efficiency.

STEPS THREE AND FOUR: CONVERSION OF PACE ADJUSTED POINTS GIVEN UP PER MINUTE TO A SCALE APPROPRIATE FOR REAL PLAYER RATINGS WHILE SIMULTANEOUSLY CORRECTING FOR TEAM DEFENSE BIAS
We need to translate the pace-adjusted points allowed per minute into numerical terms that are the most useful with respect to RPR. We also need to as well as we can correct or standardize for very different team defense qualities. Before we describe how we accomplish both of these objectives at the same time, let's back track a little for a brief history...

A BRIEF HISTORY OF THE HIDDEN DEFENDING ADJUSTMENT
Beginning in January 2009 the Hidden Defending Adjustment (HDA) was included in Real Player Ratings after extensive research and development. However, the early versions of HDA did not correctly and/or did not completely solve the comparability of ratings among players on different teams problem so earlier versions of HDA were replaced in May 2010 by a version that appears to be accurate enough to be the permanent version, subject in the future to only relatively minor tweaking.

HDA was apparently 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. The basic problem of course is that much of what players do defensively can not and is not tracked by scorekeepers and box scores.

As of June 8, 2009, the mechanics of the HDA were slightly changed to increase accuracy.

As of November 14, 2009, the HDA was upgraded, on the average, from about 40% of the overall defensive sub rating of players to about 45%. Furthermore, as of November 14, 2009, the overall defensive sub rating was recalibrated so that it would now be about 45% of the overall RPR, versus about 42% in 2008-09. The offensive sub rating was recalibrated so that it would now on average constitute about 55% of the overall RPR, versus about 58% in 2008-09.

MAY 2010 REFORMULATION OF THE HIDDEN DEFENDING ADJUSTMENT
A fairly major problem was discovered in March 2010: the HDA was substantially (but not overwhelmingly, though) biased against players playing for the best defensive teams and it was similarly biased in favor of the players playing for the worst defensive teams. The problem was that the method at that time was to standardize for both pace and the relative team defensive efficiency by blunt multiplication of the raw points allowed per minute by those factors for teams. Team defensive efficiency is number of points surrendered per 100 possessions and relative team defensive efficiency is League average defensive efficiency divided by a team's defensive efficiency.

What we used to do is multiply the relative defensive efficiency by the raw points scored by opponents when a player is on the court (which is the raw starting point for HDA). The objective of standardizing or correcting for team defense was to prevent poor defenders on good defensive teams from getting a too high rating and to prevent good defenders on bad defensive teams from getting a too low rating.

When you do this full standarization for relative team defensive efficiency however, it turns out that you "overshoot the mark" and you unfairly and excesssively shrink HDAs of the better defenders on the better defending teams. And vice versa, you unfairly and excessively magnify HDAs of the lesser defenders on the poor defending teams. So in solving one set of problems we created another set of problems.

The solution was to modify the use of the (relative) team defensive efficiencies and to split the difference between the biases. In other words we are compromising between not adjusting for team defense at all and over adjusting. Very small biases remain for which there is no solution:

--The best defenders on the best defensive teams have slightly lower HDAs than they deserve.

--The worst defenders on the best defensive teams have slightly higher HDAs than they deserve.

--The worst defenders on the worst defensive teams have slightly higher HDAs than they deserve.

--The best defenders on the worst defensive teams have slightly lower HDAs than they deserve.

The HDA as redesigned in Spring 2010 is considered rock solid because the biases that remain are very small, at the very most .025 in terms of Real Player Rating. In the vast majority of cases, the remaining bias is less than .010 in terms of RPR. For example, a player who has a RPR of .720 might really deserve only a .710 or as much as a .730 if a perfect HDA was possible.

Instead of using the relative team defensive efficiencies "in full force" by directly multiplying the raw points per minute by the relative defensive efficiencies, we created a huge evaluation grid (chart) with team relative defensive efficiency on one axis, with Hidden Defending Ratings on the other axis, and with points per minute scored by opponents when the player is on the court (adjusted for team pace) arrayed throughout the interior of the chart. By doing this we can compromise between too much standardization for relative team defensive efficiency and no standardization at all.

In effect we grade every player's hidden defending "on the curve". The better a player's team is defensively, the lower the points per minute the opponents score while the player is on the court for any given Hidden Defending Rating. For example, let's say a player gives up 2.01 points per minute (adjusted for team pace) while he is on the court. If that player is on one of the best defensive teams, the chart shows that his Hidden Defending Rating shall be .174. But if that player is on one of the worst defensive teams, the chart shows that his Hidden Defending Rating shall be .258. The player deserves and gets a higher HDA for the same points given up per minute if he is on a lousy defensive team.

But as previously noted the overshooting the mark problem is avoided through the use of the chart as opposed to bluntly multiplying by team relative defensive efficiencies.

Remember that the chart simultaneously achieves two objectives. First, the very small differences in different players' points allowed per minute are translated into numerical terms that correlate to the role that HDA needs to play within overall RPR. Second, we adjust for the differences between teams' defenses without over adjusting, and we compromise as described above.

STEP FIVE: 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 (Real Player Rating).

GUARD AND FORWARD OUTLIER RULES ARE REPEALED
With the May 2010 revamping, outlier rules are unnecessary and are repealed.

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 .325. In most cases, however, the adjustment will be between 0.075 and .250.

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 about 45% of ODR while SDR constitutes the other 55%. In other words, the value of hidden defending is perceived to be about 45% of the overall value of defending, while the value of scored (unhidden) defending is perceived to be about 55% 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

Step One for Hidden Defending Adjustment:
Points Scored by Opponents While Player was on the Court / Minutes Played by Player

Step Two for Hidden Defending Adjustment:
Result of Step One * Relative Pace Adjustment (Team's Pace Relative to League Average)