Player Ratings

Below is an explanation of the different player ratings used on this site. They are intended only as a means of highlighting the accomplishments of great players from the past.

Standard Tendex

The Tendex rating was developed by Dave Heeran over the course of 30 years as a way to differentiate players by using statistics found in boxscores. The formula has been developed over the years and currently stands as

Standard Tendex Rating = {[Points + Rebounds + Assists + Steals + Blocks - Turnovers - Missed Field Goals - Missed Free Throws] / Minutes / Game Pace}

In this system, the score is divided by minutes played and by a "Game Pace" factor which takes into account the fact that some teams play at a faster pace than others, and therefore individual statistics may be padded for players on those teams that do play at a faster pace. (Game Pace is calculated by simply measuring a 'ninedex' [Tendex without regard for game pace] of the team in question and adding the result to the 'ninedex' of its opponent). Dividing by the game pace serves to normalize players between different teams. It should be noted that Personal Fouls are not counted in the above formula as Heeran determined that they were neither detrimental nor beneficial to a team's success. It should be noted that for the purpose of the career lists, the game pace was determined as a weighted average of the appropriate game pace results from each season the player in question participated. (So that if a player only played in 5 games as a freshman but 30 as a senior, that fact is weighted accordingly in the overall game pace calculation).

The standard tendex is based on minutes as above, but for the fun of it, I also calculated a 'standard tendex' based on games played. When comparing ratings of UK players with published tendex results of other players, only the per minute rating is valid for comparison. Note that the Tendex based on games played but without a game pace factor is equivalent to the Efficiency formula championed by Martin Manley.

Modified Tendex

The Modified Tendex system is one I created after doing about 5 minutes of research on the internet about what the "Tendex" system was all about. Although it loosely follows the "system" Heeran took 30 years to develop, it has absolutely no theory behind it and does not claim to be better nor worse than any of the other systems. It simply uses coefficients which I believed at the time made more sense than using 1.0 for each measure as done by Heeran.

Modified Tendex Rating = {[Points + Rebounds + 1.25*Assists + 1.25*Steals + Blocks - 1.25*Turnovers - Missed Field Goals - (Missed Free Throws/2) - PersonalFouls/2] / Minutes / Game Pace }

The above rating I calculate based both on a "per minute" basis and a "per game" basis. The per game basis weighs more heavily toward players who play more substantial minutes and therefore reflect their worth to the team (from the fact that the coach chose to play them the majority of the minutes). The "per minute" basis better highlights players who may come in for short times, but who are extremely productive while in the game.

Non-Scoring Modified Tendex

A second rating used was one which I believe is useful in highlighting players who may not be great scorers for their team, but who do many of the little things on the court which are extremely important for team success. Simply being on the court and collecting rebounds, making assists, etc. while minimizing turnovers and missed shots etc. is very important, however can often be overlooked unless the player also scores a bunch of points.

The Non-Scoring Modified Tendex is the same as above Modified Tendex, with the exception that points scored is completely removed. Many players who are high-scorers on their team, but who do little else but shoot often fare poorly in this measure as missed shots goes against them while points scored is not considered. Other players, who in addition to score also do the little things like collect rebounds, shoot a high percentage etc. do well in this rating.

Non-Scoring Modified Tendex Rating = {[Rebounds + 1.25*Assists + 1.25*Steals + Blocks - 1.25*Turnovers - Missed Field Goals - (Missed Free Throws/2) - PersonalFouls/2] / Minutes / Game Pace }

Prouty

The Prouty rating is a simple, yet effective, method of rating players developed by John Prouty. It is based on averaging four areas: Offensive Efficiency, Total Offense, Possessions Gained and Win Rating. The various individual parts are based on a per minute basis. I also calculated a career prouty rating and as with the game pace above, the rating determined as a weighted average of the appropriate Prouty results (on a per minute basis this time) from each season the player in question participated. (So that if a player only played 200 minutes as a freshman but 1500 as a senior, that fact is weighted accordingly in the overall Prouty calculation.)

Prouty Rating = [{Points / (Field Goals Attempted*2 + FTA)} + {(Points + Assists*2 - Turnovers) / Minutes} + {(Rebounds + Steals + (Blocks/2) - Personal Fouls) / Minutes} + {(Minutes / (TEAM TOTAL Minutes / 5)) * Team Winning Pct} ] / 4

Player Efficiency Rating (PER)

The Player Efficiency Rating is a formula developed by John Hollinger, primarily for NBA players.

Detailed calculations are available at Basketball Reference. An unadjusted and adjusted PER is calculated for the individual player

For calculations for NCAA players, Pace was calculated on a 40-minute basis, rather than 48-minutes. The uPER for the 'league' is based on NCAA averages provided by the NCAA trends, which are published annually and generally available in the NCAA Record Book. Unfortunately, the NCAA does not provide Offensive or Defensive rebounds, only Total Rebounds. Since uPER calculations heavily rely on the defensive and offensive rebounding percentages, these numbers are required.

Since I don't subscribe to any commercial statistical sources, these numbers are estimated. Fortunately, based on analysis of UK's historical statistical trends, typically the NCAA average is close to the average of UK and their opponent's statistics, so these averages are utilized for the purpose of estimating typical offensive and defensive percentages for a given year. Because these numbers are estimated, this likely is the difference seen between these ratings and other published values.

These calculations only go back to the 1992-93 season. This is primarily due to the fact that the NCAA does not provide Division I average rebounds, assists, blocked shots, steals or turnovers prior to this season.

Offensive and Defensive Efficiency Ratings

Offensive and Defensive Ratings were developed by Dean Oliver in his book Basketball on Paper (Brassey's, 2004). The rating is on the basis of one hundred individual possessions, so a high offensive rating is desired, while a low defensive rating is desired.

Detailed calculations are available at Basketball Reference.

Note that these ratings do appear to provide some potentially surprising results, in that it can highlight role players who are efficient on the offensive or defensive ends. For this reason I am including the "Usage" statistic which is a measure of how much of the overall team statistics are contributed by the player in question.

While the individual Offensive and Defensive Efficiency Ratings are interesting, the overall measure which best considers the player's positive contribution on both sides the court is the "Net" rating which is simply the difference between the Offensive and Defensive Efficiency.

The data set for these ratings doesn't require knowing the 'league' statistics, as in PER, but does rely heavily on offensive rebounds along with defensive rebounds, turnovers, assists, steals and blocked shots. So while it's possible to go a bit further back in time with this measure (back to the 1991-92 season), offensive and defensive rebounds will likely need to be estimated to include players from earlier eras.

Points per Field Goal Attempt

Points per Field Goal Attempt is a very simple, yet deceptively powerful measure of offensive efficiency. In some ways, this measure is slightly different than the other models. Instead of trying to determine which player is the 'best,' this measure can be used as a tool by coaches who need points (such as at the end of the game) to determine who to get the ball to.

The fact that points, and not shots made, are utilized help to remove biases of other models which punish players who play in the era of the 3-point shot. It is well known that what is considered a 'good' 3-point shooting percentage is far less than a 'good' 2-point shooting percentage. By counting points in this model, a 3 point shot is weighted higher than a 2-point shot, thus helping to offset the generally lower shooting %. This measure also accounts for free throws, so the ability of a player to get fouled and making shots at the line is a huge bonus in this model, especially since most free throws generally don't come with a FGA penalty.

One very good attribute of this model is that it requires very little statistical information. So while some models can only be calculated back to 1979, this model can be used back to at least 1947. Unfortunately for the early players, shooting percentages were far worse than more modern times, so they tend to fare very poorly in this measure.

Versatility Index

One interesting measure I ran across is the versatility index, which aims to highlight well-rounded players. This is done by considering the points per game, assists per game and rebounds per game a player averages. The higher these numbers (especially if all three measures are substantial), the higher the versatility index and more well-rounded the player is considered.

Versatility Index = Cubed Root {Points per game * Rebounds per game * Assists per game}

Modified Versatility Index

After condering the versatility index, I thought that the index could use some improvement. For one thing, there are certainly other criteria which are valid when considering how well-rounded a player is. Secondly, the scoring average is generally a much higher level than the assists per game or rebounds per game etc. In order to even things out a little, I devised a modification to the index which takes some of these things into account. The rebounds per game is boosted by including blocks, which is a complementary type of statistics. In addition, the assists per game is boosted by steals, which is also complementary. Boosting each of these categories put them closer (although still not quite on the same order of magnitude) as points per game, and thus makes a cubed root of the product a more meaningful number.

It should be noted that for early players, blocks and often steals were not collected in the boxscores, so their modified versatility index score is often their standard versatility index score.

Modified Versatility Index = Cubed Root {Points per game * (Rebounds + Blocks) per game * (Assists + Steals) per game}

Note that there is also available a rating (modified tendex per minute) of the most recent game played by Kentucky, with included grades.