Sprocket Points is a methodology for measuring the productivity of players and teams by weighting and combining a set of commonly used basketball statistics. The unique aspect of Sprocket Points is that the computation values different statistical categories in terms of how each produces or precludes points to be scored. The method values positive contributions (e.g., scoring, blocking a shot) while penalizing negative contributions (e.g., missing shot, turning the ball over).

Example

Made Two Point Field Goal – A two point field goal produces two points. (A lot of this is pretty obvious.) In Sprocket Points a made two point field goal is valued at two points.

Missed Two Point Field Goal – But what is the point production value of a missed two point field goal? Sprocket Points define missed field goals as an opportunity cost accessed to a player. Rather than taking and missing a two point shot, the player could have passed the ball to a teammate who could have taken a shot. That teammate might make the shot and he might miss it, but by factoring in NBA league average shooting percentages we can access a value for a two point field goal attempt - the league average shooting percentage times the value of a field goal. So, if the average NBA player shoots 48% from two, then the expected value of a two point shot is two times 0.48 or 0.96 points. When a player takes and misses a two point shot we penalize him by subtracting 0.96 from his Sprocket Point total.

Methods

Sprocket points include the following basic basketball statistics. These statistics are readily available for analysis from a variety of public sources.

• Field goals made
• Field goals missed
• Three point shots made
• Three point shots missed
• Free throws made
• Free throws missed
• Offensive rebounds
• Defensive rebounds
• Assists
• Steals
• Turnovers
• Blocks
• Personal fouls
• Technical fouls

Within the method a value is placed on each of these events that measures the points either directly or potentially produced, or taken away from the opponent. Bear in mind that any event that takes place on the floor will generally have two consequences. For example, making a steal both takes a possession away from the opponent and provides an incremental possession for the stealing team. The steal gives the stealing team incremental in-control time within the game they may use as they wish.

Some other things to keep in mind

• Points win games, but only if the other team doesn’t score more so it is important to look at many other statistical categories other than just scoring the access the true value of players.
• Some events have measurable consequences and immeasurable ones. For example, having enough shots blocked can both demoralize a team and change the kinds of shots it takes, generally from less to more difficult since most blocks are close in and therefore higher percentage shots. Good shot blockers can take a team out of its offense.
• Missing shots can be as detrimental to a team’s performance as making them is beneficial. As with blocks, missed shots can have a long term demoralizing impact so penalties must be assessed for missing shots.

Scoring

Following are point or penalty values assigned to each of the statistics used in the creation of Sprocket Points. League average values are based on the last complete season available. The average values are updated at the end of each season to produce a new version of the model for the upcoming season. In order to make the model comparable over the entire season no changes are made to the weights during the course of the season.

Two point shots made
Weight: 2.0
Rationale – Seems logical.

Two point shots missed
Weight: -0.9559
Rationale – For each two point shot missed, two points times the league average shooting percentage for a two point shot (0.4779) is subtracted. Basically this says that rather than taking and missing the shot the player could have given the ball up to an average teammate who would have taken a shot valued at 0.9559 points. A player’s scoring is devalued if he shoots more poorly than the average NBA player and prized if he shoots at a higher percentage. Sprocket Points will penalize players who take thirty shots to make ten.

Three point shots made
Weight: 3.0
Rationale – Seems logical.

Three point shots missed
Weight: -1.0749
Rationale – For each three point shot missed, three points times the league average shooting percentage for a three point shot (0.3583) is subtracted. Basically this says that rather than taking and missing the shot the player could have given the ball up to an average teammate who would have taken a shot valued at 1.0749 points. Again, a player’s scoring is devalued if he shoots more poorly than the average NBA player and prized if he shoots at a higher percentage. If a player misses 75% of three pointers taken, he will actually lose points in the scoring regardless of how many shots he makes.

Free throws made
Weight: 1.0
Rationale – Seems logical.

Free throws missed
Weight: -0.7453
Rationale – Again, the league average free throw shooting percentage is used to penalize players who miss free throws. In effect the method says that every NBA player ought to be able to hit free throws at the average league rate.

Offensive rebounds
Weight: 2.2922
Rationale – An offensive board results in the rebounding team scoring 50.5% of the time. 2.203 is the average value of a made shot in the NBA (weighting shooting percentages by the share of shots that are twos and the share that are threes). First part of weight = .5048 * 2.203 = 1.1121. However, an offensive board also takes away an opponent’s possession. Assuming the opponent gets off an attempt (with the average NBA FGA value of 0.9801), then 1.1121 + 0.9801 = 2.0922. A 0.2 kicker is added for the emotional value of an offensive rebound for a total weights 2.2922.

Defensive rebounds
Weight: 2.0922
Rationale – Same rationale as for offensive board, just in the opposite order, except you’re supposed to get defensive boards so there is no kicker.

Assists
Weight: 2.2031
Rationale – An assist provides a made basket. 2.2031 is the average value for a made field goal, (not a field goal attempt) properly weighted by the shares of twos and threes.

Steals
Weight: 1.9602
Rationale – A steal takes away an opponent FGA and provides an FGA for the stealing team - 2 times 0.9801 (average value of an field goal attempt) = 1.9602.

Turnovers
Weight: -1.9602
Rationale – A turnover functions in the same way as a steal, except in the opposite order.

Blocks
Weight: 1.9987
Rationale – Shots that are blocked tend to be closer in and a study by 82games says that a blocked shot on average had a 62% chance of going in. Therefore a block takes away 0.62 * 2 = 1.24 points from the opponent. (Lacking source for counts of blocked two and three point shots, the method assumes that all blocked shots are two point attempts.) 82games also reports that 57% of the time the blocking team gets possession (often the block goes out of bounds or is picked up by the offense). So, 57% of the time a block provides an FGA and 0.57 * 0.9801 (average value of FGA) = 0.5587. Summing, the total value of a block is 1.7987. A value of 0.2 is added for residual intimidation for a total of 1.9987.

Personal fouls
Weight: -0.6921
Rationale – Some guesswork here. There are not data to tell what percent of fouls result in zero, one, or two free throws so the model makes some assumptions based on the average team committing about 28 fouls per game. Assumptions - 12 of 28 are not shooting fouls, leaving 16 fouls that resulted in free throws - 10 of those are two shot fouls and 6 one shot fouls Putting all that together with the average free throw shooting percentage, the average points given up for a foul are 0.6921.

Technical fouls
Old weight: -1.000
New weight: -1.000
Rationale – Technicals are generally shot by the other teams best shooter so the model assesses a one point penalty for every technical.

Common statistics not directly used in Sprocket Points

Field goals made - Better to separate out two and three point shots.

Field goals missed - Better to separate out two and three point shots.

Field goals attempted - Better to separate out two and three point shots.

Two point shots attempted – Already handled by weighting both shots made and missed.

Three point shots attempted – Already handled by weighting both shots made and missed.

Free throws attempted – Already handled by weighting both shots made and missed.

Total rebounds – Already handled with the weighting of offensive and defensive boards.

Disqualifications – The player obviously doesn’t produce after being ejected, so no additional penalty is added.

Games played – There is more flexibility in the measure if it does not include games played, but is used to create a second measure - Sprocket Points per game when needed.

Games started – In general starters are the most productive players on a team so there is no need to bump their production further by including a positive weight for starts. Such a bump would also penalize a non-starter who plays starter type minutes – McHale in the old days for Boston, Stackhouse for Dallas last year, etc.

Minutes played – As with games played, leaving minutes out provides more flexibility by allowing a points per minute measure to be computed from the basic Sprocket Points. This is useful for comparing players who play varying numbers of minutes.

Points scored – Already handled in the scoring of field goals and free throws.

Validating the Method

Although Sprocket Points are a method to evaluate individual players, they can also be used to evaluate teams. When evaluating teams, there is a clear performance standard and that is how many times the team wins. If Sprocket Points are compared to team winning percentages the predictive power of Sprocket Points can be determined. Any change to the weights/values should increase the predictive relationship between Sprocket Points and team winning percentage. That is the standard used in development.

The current 2006/2007 version of Sprocket Points aggregated to the team level strongly correlated with winning percentage (r = 0.743, r squared = 0.552).

Note that lots of other things influence winning, so no player/event based measure can predict it all. For example, teams have different schedule strength, different numbers of back to backs, different distances to travel for road games, etc. And remember, that Sprocket Points are built to measure players and not team performance. However, the strong relationship with winning at the team level should provide confidence that the value Sprocket Points measures is quite important in evaluating players and team.

Using Sprocket Points

Different kinds of analysis use Sprocket Points in different ways. There are three common forms in which Sprocket Points are presented.

Count of Sprocket Points – This provides an objective measure of total player production and value to their team.

Player Share of Team Sprocket Points – Different teams have different playing styles and will therefore produce more or less on the court. Currently the highest scoring team in the league scores about eighteen more points per game than the lowest scoring team. They generate more possessions and more opportunities for the components of Sprocket Points. By looking at a player’s Sprocket Points not as a count, but as a percentage of total team Sprocket Points the effect of different styles of play is removed and players can be compared on apples to apples basis.

Sprocket Points per Ten Minutes – Different players play differing numbers of minutes. Sometimes it is useful to equalize the minutes in order to compare them on an equal footing. To do this the count of Sprocket Points is divided by the number of minutes a player has played and then multiplied by 10 to create the average production over a ten minute stretch. This measure provides the means to play what if kinds of games with players – what if player x played the same minutes as player y?

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