Fantasy Basketball Finding Correlation
1. Find the following statistics for all the students’ players in class and record them in the table:
______
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2. Next, Make up your own statistic you think would predict players’ fantasy basketball points. Four commonly used statistics in calculating other statistics are shooting percentage; getting to the free-throw line (FTM/FGA); turnover percentage (per possession); and offensive or defensive rebounding percentage. You must be able to justify, using mathematical reasoning, why the statistic you created will accurately predict the fantasy basketball points a player will produce.
For example one statistic commonly used is the efficiency rating calculated by the following:
Efficiency = (PTS + REB + AST + STL + BLK - FG missed - FT missed - TO)
a. Write the formula for the statistic you produced:
b. Justify why this statistic should predict the fantasy basketball points. Complete Stentences. ______
c. Calculate and record the statistics in the table below:
Total Fantasy Points Earned / Your Statistic3.
a. Make a scatterplot using a statistics package of the one stat in number 1 vs Points Gained in Fantasy Basketball.
b. Make a line of best fit on the graph.
c. Put the Correlation Coefficient on the graph.
4.
a. Make a scatterplot using a statistics package of the one stat in number 2 vs Points Gained in Fantasy Basketball.
b. Make a line of best fit on the graph.
c. Put the Correlation Coefficient on the graph.
5.
a. Make a scatterplot using a statistics package of the stat you made up how to calculate vs Points Gained in Fantasy Basketball.
b. Make a line of best fit on the graph.
c. Put the Correlation Coefficient on the graph.
6. Print off and save all graphs.
7. Which statistic best predicted players fantasy basketball points? Why? Complete Sentences.
______
8. How well did your statistic you made predict the fantasy basketball points of the players? Complete Sentences.
______
Fantasy Basketball Final
Your final for this class is a project involving the fantasy basketball statistics you have been working on all year. You will be doing an analysis to determine if certain statistics are a strong or weak prediction of how a player will perform on your fantasy basketball team.
This project will be graded for ____points of your final grade.
Your report for your fantasy basketball team needs to include the following:
-Title Page with Name, Date, Hour, and Name of team.
-List of Players on your team and their cost.
-Stacked graph showing each week, and the amount of points gotten by each player.
-Pie chart of two players
-3 Scatterplots showing correlation between statistics, and fantasy points earned
-Line graph showing all players on your team’s performance.
- A 600 or more word summery double spaced report in 12 pt. font including:
· What your statistical analysis revealed as the biggest statistical weakness of your team. What statistic earned you the least points?
· What your statistical analysis revealed as the biggest statistical strength of your team. What statistic earned you the most points?
· Justification, using mathematical reasoning, why the statistic you created will accurately predict the fantasy basketball points a player will produce.
· Who your top performing player was and how strong the correlation was for predicting his performance.
· Who was the best deal of a player was by their cost and performance?
· The player did not live up to their value that you paid for them at the beginning of the year.
· Using the statistical data, re-pick a team that is under the $60,000,000 salary cap.
· Conclusion on what part of the analysis helped you to pick a better team for next semester, and what other type of analysis you could have done to better predict your team.
- Record data collected.
- Report is neat and presented in a clear and
TS%: True Shooting Percentage - what a player's shooting percentage would be if we accounted for free throws and 3-pointers. True Shooting Percentage = (Total points x 50) divided by [(FGA + (FTA x 0.44)]
AST: Assist Ratio - the percentage of a player's possessions that ends in an assist. Assist Ratio = (Assists x 100) divided by [(FGA + (FTA x 0.44) + Assists + Turnovers]
TO: Turnover Ratio - the percentage of a player's possessions that end in a turnover. Turnover Ratio = (Turnover x 100) divided by [(FGA + (FTA x 0.44) + Assists + Turnovers]
USG: Usage Rate - the number of possessions a player uses per 40 minutes. Usage Rate = {[FGA + (FT Att. x 0.44) + (Ast x 0.33) + TO] x 40 x League Pace} divided by (Minutes x Team Pace)
ORR: Offensive rebound rate
DRR: Defensive rebound rate
REBR: Rebound Rate - the percentage of missed shots that a player rebounds. Rebound Rate = (100 x (Rebounds x Team Minutes)) divided by [Player Minutes x (Team Rebounds + Opponent Rebounds)]
PER: Player Efficiency Rating is the overall rating of a player's per-minute statistical production. The league average is 15.00 every season.
VA: Value Added - the estimated number of points a player adds to a team’s season total above what a 'replacement player' (for instance, the 12th man on the roster) would produce. Value Added = ([Minutes * (PER - PRL)] / 67). PRL (Position Replacement Level) = 11.5 for power forwards, 11.0 for point guards, 10.6 for centers, 10.5 for shooting guards and small forwards
EWA: Estimated Wins Added - Value Added divided by 30, giving the estimated number of wins a player adds to a team’s season total above what a 'replacement player' would produce.
Dean Oliver a famous Basketball Statitician has developed four statistical team factors that summarize most of what matters in terms of winning or losing: effective field goal percentage, offensive rebounding percentage, turnovers per possession, and free throws made per field goal attempted.
GLOSSARYAssisted field goal - Simply, a field goal on which a player received an assist. This matters because credit must be split between the assisting player and the scoring player. Play-by-play data like that used by 82games.com can be used to find each player's exact percentage of assisted field goals, but it is usually estimated.
Defensive Rating - Points allowed per 100 possessions (see Offensive Rating).
Effective Field-Goal Percentage - An adjusted form of field-goal percentage that takes into account the added value of three-pointers by weighting them as 1.5 times as valuable as two-pointers. This is a popular statistic with the general public that is available at ESPN.com. It was popularized by Rick Barry's Pro Basketball Bible in the 90s, which was where I first saw it as a kid (see True Shooting Percentage).
Statistically: (FGM + .5*3PM)/FGA
Floor Percentage - The percentage of a team's possessions that end in scoring possessions.
Four Factors - Oliver evaluates teams and players with four factors on offense and defense -- shooting (effective field goal percentage); getting to the free-throw line (FTM/FGA); turnover percentage (per possession); and offensive or defensive rebounding percentage.
Free-throw modifier - Because basketball analysts usually express statistics in terms of possessions, an adjustment needs to be made for the fact that two free throws do not always constitute a possession. Three-point plays, three-shot fouls, and technicals all increase the number of free throws per possession. Thus, we need to use something less than 0.5 when multiplying by free throws to calculate possessions. Analysis has revealed that the appropriate multiplier is 0.44 (see Possessions).
Linear weights formulas - Rating systems that assign a value to each major statistical event on the court (PTS, FGA, FTA, OR, DR, AST, STL, BLK, TO, PF) and sum these. The most common form of rating system; TENDEX and Manley Credits (in both cases, all weights are 1 or -1) are both examples.
Offensive Rating - Points scored per 100 possessions (see Defensive Rating).
Plays - See Possessions.
Play Percentage - The percentage of a team's plays that end in a score.
Points per shot - This is something you'll see those who are not statistical analysts use to evaluate scoring efficiency. Usually, it simply means points per field goal attempt, which means that tight ends are essentially free points for the player. Players like Shaquille O'Neal, who attempt a high number of free throws, are overrated by this method. (See True shooting percentage.)
Statistically: Pts/FGA
Possessions - Here is one place where defining a term becomes tricky, because there are two different definitions of possessions used by various analysts. (Baseball analysts, alas, are lucky enough not to have this problem. An out is an out is an out.) The most commonly-held view is that a possession is all the time a team holds the ball before the other team gets it. The defining characteristic of this definition is that an offensive rebound does not start a new possession. There are also those who view the offensive rebound as starting a new offensive possession. These people define possessions as time before an attempt to score is made or a turnover is recorded. Analysts operating on the first definition call these plays instead of possessions.
Statistically: .96 * (FGA + 0.44*FTA + TO - OR) or
FGA + 0.4 * FTA - 1.07 * (OReb/(OReb + OppDReb)) + TO Plays: FGA + 0.44*FTA + TO
Possession usage - The percentage of a team's possessions used by an individual player, also known as simply usage. On average, naturally, a player uses 20% of his team's possessions.
Pythagorean winning percentage - A Bill James invention in baseball, Pythagorean records are based on the knowledge that team winning percentages are generally closely related to points scored and points allowed (and, in cases where they differ, the reason is usually temporary luck). This relationship can be approximated by PF^x/((PF^x) + (PA^x), where x depends on the total points scored. In baseball, over the course of a season, x is close enough to be approximated by two. In basketball, x is a little more difficult to calculate. When Oliver did it a decade and a half ago, it was about 16.5. Now, because point totals are lower, the exponent is believed to be closer to 13 or 14. It is also possible to calculate Pythagorean percentages in different ways, like a multiplier (2.7) by the team's point differential (for an 82-game season). This is slightly less accurate, but much easier. A third, more complicated method is employed by Oliver, which takes into account the variability in a team's points scored or points allowed and is thus more accurate.
Statistically: PF^13.5/((PF^13.5)+(PA^13.5))
Expected wins = 2.7*(PF/G-PA/G) + 41
Rate - This is usually used to denote that a statistic is being calculated on a per-minute basis. "Rebound rate", for example, generally means rebounds per 48 minutes (it may be expressed in per-minute form as well).
Rebound percentage - The percentage of all available rebounds that a player or team grabs, often broken down into offensive rebound percentage and defensive rebound percentage. This is a better measure of rebounding prowess than rebound rate because it adjusts for game pace, although total rebound percentage is skewed by the ratio of offensive and defensive rebound opportunities. (In other words, a team with a really great defense will have its total rebound rate artificially inflated because defensive rebounds are much easier to grab.) Usually, rebound opportunities are estimated for players based on the team's rebound opportunities per minute, but play-by-play data -- like that used by 82games.com -- can identify a player's exact opportunities.
Statistically: for teams, Reb/(Reb+OPPReb)
for players, (Reb*Min)/((TMReb+OPPReb)/(TMMin/5))
Replacement level - A valuable concept borrowed by some NBA analysts from their baseball counterparts, replacement level estimates numerically the performance of players who can be aquired at little or no cost to the team. This generally means either players signed as free agents during the season or those who make teams as training-camp invitees. I studied replacement level for Hoopsworld.com. (See Value Over Replacement Player.
Scoring possession - Any possession on which the offense scores at least one point. (See possessions.)
Similarity scores - A measure of how statistically similar two players are. There are several such ratings floating around. Oliver and BR.com use methods that are rather literally trying to compare statistics -- on a pure stat basis (i.e. 350 rebounds vs. 400). Hollinger, B-R.com and I have ratings that are skill-based, looking at the differences in secondary statistics like shooting percentages, rate stats, and our overall ratings. (Actually, Oliver uses something more like this, but it's proprietary.) These are generally complicated formulas.
Two-point percentage - The percentage of a player's two-point attempts he makes. Though field-goal percentage and three-point percentage are often used together to determine approximately how effective players are inside the arc, this is a more accurate measure.
Statistically: (FGM - 3PM)/(FGA - 3PA)
True shooting percentage - One of the trickiest things about creating a glossary for NBA statistics is that so many terms are used differently by different people. Even I use at least two different terms for what I've chosen to call true shooting percentage. Other terms used are scoring efficiency, adjusted shooting percentage, effective percentage, and points per shot attempted (Hollinger used to use this term and did not express the concept as a percentage, but has since converted). What these all are getting at is that this is the truest measure of a player's efficiency in terms of shooting, how many points he scores divided by how many shooting possessions he uses. (True shooting percentage can also be used to mean effective field-goal percentage.)
Statistically: Pts/(2 * (FGA + (0.44 * FTA)))