Analyzing Advanced Statistics and True Shooting Percentage in the NBA
Evan Boyd
May 10, 2016
Introduction
The intertwining of sports and statistics has now affected how each game is played. Basketball is in the midst of adding more numbers to define success. In baseball, there are more and more metrics being used to calculate how efficient a player and a team can be. Baseball is by far the most set in terms of advanced metrics. Basketball, on the other hand, is starting to emerge with more and more metrics to alter how the game is played. This is especially important when a game like basketball is constantly changing; the game played today is already much different from how it was played in the 1990’s. In today’s era, it is all about how well the team can shoot the ball, create open shots, and rely on the three pointer.
I am confident that in today’s era of basketball, the advanced metrics are driving team’s successes, and that one statistic, True-Shooting Percentage (TS%), should now be used to value a player and their team over regular statistics. TS% is a measure of shooting efficiency that takes into account field goals, 3-point field goals, and free throws. Basketball-Reference.com, where I collected the TS% data, has True-Shooting Attempts defined as FGA + 0.44*FTA. FGA is Field Goal Attempts, and FTA is Free Throw attempts.
Advanced statistics have been quite controversial in sports. Should we rely on numbers to measure talent, or should we look more at their athleticism and passion to win a game? Such arguments have gotten scouts and sports analysts fired because the GM wants to take a more analytical route. One such team that has started to take a more analytical approach to basketball is the Golden State Warriors. They are the 2014-2015 NBA Champions, and in 2015-16, set the record for the most amount of wins in a single season with a 73-9 record.
What’s notable about the Warriors is that they rely on shooting and creating open shots, something that TS% can measure better than other statistics because it weighs shot percentages and free throws. Golden State led the league with a .593 TS%. The second highest? The Oklahoma City Thunder, at .565, a huge difference. This year, among players who have taken more than 500 field goal attempts, the third best player in terms of TS% is Stephen Curry, the leader of the Warriors. Not far behind him is Klay Thompson, who averages 22 points for Golden State.
If I can prove that TS% is very significant in estimating the number of wins a team gets and how good a player can be, then it should start replacing regular statistics in basketball, and should be the biggest tool for NBA scouts and analysts in trying to find the best types of players. After proving that it is significant in estimating wins for teams, given other variables, and by examining TS% on specific teams, I can determine that it is the most valuable tool. Hence, TS% has the potential to become the way to monitor the future of basketball.
Methods
This report will focus on analyzing significant advanced and basic statistics in basketball, and using them to estimate the number of wins per team in a season. This will be done two ways - the first will be using a linear model approach, and the other will be through a tree-based model. I used a tree-based model to simplify the data and evaluate using only a few variables. Futhermore, I will evaluate TS% on its own in predicting how well it values a player’s performance per team.
I used basketballreference.com (advanced statistics) and nba.com (basic statistics) to sort out my various statistics. The number of wins was made into a separate list, and can be found anywhere online. Please see the appendix at the end of this sheet to find more information about each statistic given in the various models.
To analyze the data, I first tried to find a linear model that would fit my data, the used it to predict the number of wins each team would get. Another way I did this using team statistics is by a tree-based model, and using that to find out what model can be made. Lastly, I took statistics from individual players (n>300) to measure each TS% number, and used that to estimate the number of win shares each player contributed to the team. Win shares estimates how many wins each player contributes to his/her team. I summed up the players’ predictions based on what team they were on, and used that to estimate the wins.
Graphically, I used the plot_ly command to create interactive graphs, as well as make a little more comfortable. I also used the tree package, as well as the ISLR package.
setwd("C:/Users/Evan Boyd/Desktop/College/Spring 2016/Stat 479/Individual Project/Files/CSV")
basic = read.csv("basic.csv", header = T)
advanced = read.csv("advanced.csv", header = T)
advanced = advanced[,-22]
wins = c(60,40,38,33,50,53,50,30,32,67,56,38,56,21,55,37,41,16,45,17,45,25,18,39,51,29,55,49,38,46)
basic$wins = wins
advanced$wins = winsBelow are the first few lines of the “basic” NBA statistics table. Please see the references for a description of each statistic.
head(basic)## TEAM OWN OPP DIFF FG.OWN FG.OPP X3P.OWN X3P.OPP FT. OFF.REB.
## 1 Atlanta 102.5 97.1 5.4 0.466 0.439 0.380 0.341 0.778 0.214
## 2 Boston 101.4 101.2 0.2 0.443 0.450 0.327 0.336 0.754 0.247
## 3 Brooklyn 98.0 100.9 -2.9 0.451 0.456 0.331 0.358 0.748 0.239
## 4 Charlotte 94.2 97.3 -3.1 0.420 0.440 0.318 0.357 0.748 0.221
## 5 Chicago 100.8 97.8 3.0 0.442 0.435 0.353 0.335 0.783 0.270
## 6 Cleveland 103.1 98.7 4.4 0.458 0.456 0.367 0.343 0.751 0.268
## DEF.REB. TOT.REB.. OWN.TO OPP.TO wins
## 1 0.734 0.482 13.5 15.4 60
## 2 0.750 0.495 13.3 14.6 40
## 3 0.737 0.489 13.4 13.0 38
## 4 0.793 0.500 11.2 12.0 33
## 5 0.744 0.513 13.2 11.7 50
## 6 0.747 0.511 13.6 12.7 53Next are the first few lines of the “advanced” NBA statistics table. Please see the references for a description of each statistic.
head(advanced)## Team Age PW PL MOV SOS SRS ORtg DRtg Pace FTr
## 1 Atlanta Hawks* 27.8 56 26 5.43 -0.68 4.75 108.9 103.1 93.9 0.259
## 2 Boston Celtics* 25.0 41 41 0.16 -0.56 -0.40 104.7 104.5 95.8 0.233
## 3 Brooklyn Nets* 28.6 33 49 -2.88 -0.25 -3.13 104.4 107.4 92.7 0.267
## 4 Charlotte Hornets 26.0 32 50 -3.17 -0.27 -3.44 100.1 103.5 93.0 0.269
## 5 Chicago Bulls* 28.8 50 32 3.00 -0.46 2.54 107.5 104.3 92.8 0.304
## 6 Cleveland Cavaliers* 26.9 53 29 4.48 -0.40 4.08 111.1 106.3 92.3 0.287
## X3PAr TS. eFG. TOV. ORB. FT.FGA eFG..1 TOV..1 DRB. FT.FGA.1
## 1 0.321 0.563 0.527 13.5 21.4 0.201 0.492 14.9 73.4 0.185
## 2 0.280 0.523 0.489 12.5 24.7 0.176 0.494 13.7 75.0 0.208
## 3 0.240 0.529 0.491 13.0 23.9 0.200 0.506 12.9 73.7 0.185
## 4 0.226 0.498 0.456 11.2 22.1 0.202 0.487 12.0 79.3 0.188
## 5 0.269 0.536 0.489 12.9 27.0 0.238 0.473 11.3 74.4 0.182
## 6 0.334 0.557 0.520 13.4 26.8 0.216 0.502 12.6 74.7 0.177
## Attendance wins
## 1 713909 60
## 2 721350 40
## 3 698529 38
## 4 704886 33
## 5 886612 50
## 6 843042 53plot(basic$OPP, wins, main = "Wins by Opponents Points Per Game", xlab = "Opponent PPG", ylab = "Wins",col=ifelse(basic$OPP==basic[10,3], "red", "blue"),
pch=ifelse(basic$OPP==basic[10,3], 19, 1), cex=ifelse(basic$OPP==basic[10,3], 1, 1))
legend(101.0909,65.20229,
c("Golden State"),
lty = c(1,1),
col = "red")
Notice that, though they had the most wins in the 2014-15 season, Golden State did not hold their opponents to the fewest points on average.The correlation between wins and opponent points per game is -.51; there is a medium-level negative correlation between the two variables.
Linear-based model
out.basic = lm(wins~.-TEAM-DIFF+X3P.OWN:FG.OWN+FG.OPP:X3P.OPP+TOT.REB..:OWN.TO,data=basic)
out.basic.AIC = step(out.basic, trace = FALSE)
out.basic2 = update(out.basic.AIC, .~. -OFF.REB.)
out.basic3 = update(out.basic2, .~. -FG.OPP)
out.basic4 = update(out.basic3, .~. -OPP.TO)
out.basic5 = update(out.basic4, .~. -X3P.OWN)
summary(out.basic5)##
## Call:
## lm(formula = wins ~ OWN + OPP + FG.OWN + X3P.OPP + TOT.REB..,
## data = basic)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4541 -1.0268 -0.1471 1.4232 4.1071
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 144.6642 37.3273 3.876 0.000721 ***
## OWN 2.2902 0.2089 10.964 7.91e-11 ***
## OPP -2.7084 0.2074 -13.060 2.13e-12 ***
## FG.OWN 87.5261 49.1573 1.781 0.087654 .
## X3P.OPP -132.0821 51.2540 -2.577 0.016541 *
## TOT.REB.. -109.8973 37.5014 -2.930 0.007316 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.434 on 24 degrees of freedom
## Multiple R-squared: 0.9729, Adjusted R-squared: 0.9673
## F-statistic: 172.5 on 5 and 24 DF, p-value: < 2.2e-16plot(out.basic5)
Our summary finds that of the basic stats, there are five variables that are significant in predicting wins at the .1 significance level. First, the amount of points per game scored and opponents points per game are significant in the model. This makes perfect sense - the more points you score and the more you limit your opponents, the more likely you win. The other significant variables are field goal percentage, Opponent 3-point field goal percentage, and total rebound percentage. I took a look at logical interaction terms, but none of them appear to be significant in the model. Our diagnostics are reasonable, so there is nothing skewed about the model and it is appropriate to use.
Now, I’ll take a look at the significant variables in the advanced data, computing using the standard p-value approach. This method will check to see what variables are significnant and calculate a linear model, using wins as the dependent variable.
setwd("C:/Users/Evan Boyd/Desktop/College/Spring 2016/Stat 479/Individual Project/Files/CSV")
advanced = read.csv("advanced.csv", header = T)
advanced = advanced[,-22]
advanced$wins = wins
head(advanced)## Team Age PW PL MOV SOS SRS ORtg DRtg Pace FTr
## 1 Atlanta Hawks* 27.8 56 26 5.43 -0.68 4.75 108.9 103.1 93.9 0.259
## 2 Boston Celtics* 25.0 41 41 0.16 -0.56 -0.40 104.7 104.5 95.8 0.233
## 3 Brooklyn Nets* 28.6 33 49 -2.88 -0.25 -3.13 104.4 107.4 92.7 0.267
## 4 Charlotte Hornets 26.0 32 50 -3.17 -0.27 -3.44 100.1 103.5 93.0 0.269
## 5 Chicago Bulls* 28.8 50 32 3.00 -0.46 2.54 107.5 104.3 92.8 0.304
## 6 Cleveland Cavaliers* 26.9 53 29 4.48 -0.40 4.08 111.1 106.3 92.3 0.287
## X3PAr TS. eFG. TOV. ORB. FT.FGA eFG..1 TOV..1 DRB. FT.FGA.1
## 1 0.321 0.563 0.527 13.5 21.4 0.201 0.492 14.9 73.4 0.185
## 2 0.280 0.523 0.489 12.5 24.7 0.176 0.494 13.7 75.0 0.208
## 3 0.240 0.529 0.491 13.0 23.9 0.200 0.506 12.9 73.7 0.185
## 4 0.226 0.498 0.456 11.2 22.1 0.202 0.487 12.0 79.3 0.188
## 5 0.269 0.536 0.489 12.9 27.0 0.238 0.473 11.3 74.4 0.182
## 6 0.334 0.557 0.520 13.4 26.8 0.216 0.502 12.6 74.7 0.177
## Attendance wins
## 1 713909 60
## 2 721350 40
## 3 698529 38
## 4 704886 33
## 5 886612 50
## 6 843042 53out.adv = lm(wins~.-Team-PL-PW+Pace:ORtg+TS.:X3PAr+eFG.:TS.+eFG.:X3PAr+Pace:FTr+ORtg:DRtg,data = advanced)
out.adv.AIC = step(out.adv, trace = FALSE)
out.adv1= update(out.adv.AIC, .~. -X3PAr:eFG.)
out.adv2= update(out.adv1, .~. -ORtg:DRtg)
out.adv3= update(out.adv2, .~. -ORtg:Pace)
out.adv4= update(out.adv3, .~. -ORtg)
out.adv5= update(out.adv4, .~. -Attendance)
out.adv6= update(out.adv5, .~. -SOS)
out.adv7= update(out.adv6, .~. -SRS)
summary(out.adv7)##
## Call:
## lm(formula = wins ~ Age + MOV + DRtg + Pace + FTr + X3PAr + TS. +
## eFG. + TOV. + ORB. + FT.FGA + eFG..1 + TOV..1 + DRB. + FT.FGA.1 +
## TS.:eFG. + Pace:FTr, data = advanced)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9961 -1.2007 0.1919 0.7763 2.4821
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2534.7292 668.0572 3.794 0.00256 **
## Age 0.7875 0.3495 2.253 0.04373 *
## MOV -9.7722 3.1751 -3.078 0.00958 **
## DRtg -17.7768 4.6622 -3.813 0.00247 **
## Pace -5.7064 2.4711 -2.309 0.03953 *
## FTr -3087.2407 995.1980 -3.102 0.00915 **
## X3PAr 48.6919 20.2582 2.404 0.03330 *
## TS. -4441.8665 1395.8790 -3.182 0.00789 **
## eFG. 2332.7848 1088.0784 2.144 0.05321 .
## TOV. -15.4753 4.0611 -3.811 0.00248 **
## ORB. 6.4102 1.7898 3.581 0.00377 **
## FT.FGA 2262.8943 634.1885 3.568 0.00387 **
## eFG..1 898.4616 364.7875 2.463 0.02988 *
## TOV..1 -7.9169 3.3131 -2.390 0.03416 *
## DRB. -4.1530 1.3748 -3.021 0.01065 *
## FT.FGA.1 154.9870 77.2950 2.005 0.06804 .
## TS.:eFG. 3510.7995 1420.3594 2.472 0.02940 *
## Pace:FTr 20.7749 8.8546 2.346 0.03697 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.985 on 12 degrees of freedom
## Multiple R-squared: 0.991, Adjusted R-squared: 0.9782
## F-statistic: 77.66 on 17 and 12 DF, p-value: 1.152e-09plot(out.adv7)
In the advanced set, there are many more variables that are significant in fitting the model. We even have two significant interaction terms: True Shooting Percentage with Effective Field Goal Percentage, as well as Pace of Play with Free Throw Attempt Rate. The Adjusted R-Squared is still high at 0.9782.
Now, I will combine the two data sets of significant variables and predict a stronger model.
out = lm(wins~advanced$Age+advanced$MOV+advanced$DRtg+advanced$Pace+advanced$FTr+advanced$X3PAr+advanced$TS.
+advanced$eFG.+advanced$TOV.+advanced$ORB.+advanced$FT.FGA+advanced$eFG..1+advanced$TOV..1+advanced$DRB.
+basic$OWN+basic$OPP+basic$FG.OWN+basic$X3P.OPP+basic$TOT.REB..+advanced$FT.FGA.1
+advanced$TS.:advanced$eFG. + advanced$Pace:advanced$FTr
+basic$OWN:advanced$TS.+basic$FG.OWN:advanced$TS.
+basic$FG.OWN:advanced$X3PAr+basic$OWN:advanced$FTr+basic$X3P.OPP:advanced$X3PAr
+basic$TOT.REB..:advanced$ORB.)
out.AIC = step(out, trace = FALSE)Using backwards elimination at the .025 level, I ended up with this model:
out2 = glm(wins~advanced$Pace+advanced$FTr+advanced$X3PAr+advanced$TS.
+advanced$eFG.+advanced$ORB.+advanced$FT.FGA+advanced$eFG..1+advanced$TOV..1
+basic$OWN+basic$FG.OWN+basic$TOT.REB..
+advanced$TS.:advanced$eFG.
+basic$FG.OWN:advanced$TS.
+basic$FG.OWN:advanced$X3PAr
+basic$TOT.REB..:advanced$ORB.)
summary(out2)##
## Call:
## glm(formula = wins ~ advanced$Pace + advanced$FTr + advanced$X3PAr +
## advanced$TS. + advanced$eFG. + advanced$ORB. + advanced$FT.FGA +
## advanced$eFG..1 + advanced$TOV..1 + basic$OWN + basic$FG.OWN +
## basic$TOT.REB.. + advanced$TS.:advanced$eFG. + basic$FG.OWN:advanced$TS. +
## basic$FG.OWN:advanced$X3PAr + basic$TOT.REB..:advanced$ORB.)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.74936 -0.50681 0.03013 0.47220 1.52704
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.603e+02 2.559e+02 2.580 0.02287 *
## advanced$Pace -3.929e+00 2.634e-01 -14.915 1.48e-09 ***
## advanced$FTr -4.700e+02 1.743e+02 -2.697 0.01831 *
## advanced$X3PAr 3.727e+03 3.693e+02 10.092 1.62e-07 ***
## advanced$TS. -3.143e+03 9.489e+02 -3.312 0.00561 **
## advanced$eFG. -1.591e+04 2.420e+03 -6.573 1.79e-05 ***
## advanced$ORB. -2.199e+01 5.270e+00 -4.173 0.00109 **
## advanced$FT.FGA 9.350e+02 3.593e+02 2.602 0.02191 *
## advanced$eFG..1 -4.176e+02 3.366e+01 -12.406 1.40e-08 ***
## advanced$TOV..1 1.726e+00 4.994e-01 3.457 0.00425 **
## basic$OWN 2.988e+00 2.310e-01 12.937 8.44e-09 ***
## basic$FG.OWN 2.001e+04 2.290e+03 8.738 8.40e-07 ***
## basic$TOT.REB.. -1.071e+03 2.784e+02 -3.848 0.00201 **
## advanced$TS.:advanced$eFG. 3.166e+04 3.618e+03 8.751 8.26e-07 ***
## advanced$TS.:basic$FG.OWN -3.211e+04 3.819e+03 -8.409 1.29e-06 ***
## advanced$X3PAr:basic$FG.OWN -8.081e+03 8.131e+02 -9.939 1.93e-07 ***
## advanced$ORB.:basic$TOT.REB.. 4.193e+01 1.040e+01 4.032 0.00142 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 1.476056)
##
## Null deviance: 5250.000 on 29 degrees of freedom
## Residual deviance: 19.189 on 13 degrees of freedom
## AIC: 107.73
##
## Number of Fisher Scoring iterations: 2plot(out2)
lm.predict = predict(out2)It is clear that advanced statistics seem to be more valuable than basic statistics, but there are some important interaction terms with the two datasets. The variables with a strong significance are PPG, Pace of Play, and TS%. We will come back to this model later when looking at specific players and the 2015-16 season numbers. Once again, our diagnostics are appropriate.
Tree Based Model
Tree-based modeling is a simple way to interpret what variables are used in evaluating (NOT predicting) an observed variable. A regression tree can predict the number of wins, based on what values our specific stats are. Here I found a basic tree to help examine wins:
library(tree)## Warning: package 'tree' was built under R version 3.4.2library(ISLR)## Warning: package 'ISLR' was built under R version 3.4.2tree.basic=tree(wins~Pace+FTr+X3PAr+TS.
+eFG.+ORB.+FT.FGA+eFG..1+TOV..1
+basic$OWN+basic$FG.OWN+basic$TOT.REB..
,advanced
)
summary(tree.basic)##
## Regression tree:
## tree(formula = wins ~ Pace + FTr + X3PAr + TS. + eFG. + ORB. +
## FT.FGA + eFG..1 + TOV..1 + basic$OWN + basic$FG.OWN + basic$TOT.REB..,
## data = advanced)
## Variables actually used in tree construction:
## [1] "TS." "eFG." "eFG..1"
## Number of terminal nodes: 5
## Residual mean deviance: 36.46 = 911.6 / 25
## Distribution of residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -8.6000 -4.1670 -0.4111 0.0000 3.4750 12.0000plot(tree.basic, main = "Tree-Based Model: After Significant Model")
text(tree.basic,pretty=0)
cv.advanced=cv.tree(tree.basic)
plot(cv.advanced$size,cv.advanced$dev,type='b',xlab="Size",ylab="Deviations",main="Tree-Based Plot")
yhat=predict(tree.basic)
out = lm(wins~yhat)
cor(yhat,wins)## [1] 0.9090457Our tree indicates that TS%, effective field goal percentage (eFG), and opponent effective field goal percentage, create an accurate tree model with a correlation of .90 with wins. Effective field goal percentage adjusts for the fact that a 3-pointer is worth more than a two-pointer. Hence, it would make sense for a team like the Golden State Warriors to have such a high percentage, and thus it makes sense for the two variables to be correlated with wins.
When TS% is less than .5265 (below the 2015 average, which is .5341), then a team will get about 21 wins with an eFG less than .476 and about 33 with an eFG above .476. When TS% is greater than .5265 but less than .543, a team will get about 38 wins (3 games under .500) with an eFG greater than .494, but 46 wins if it is less than .494. It appears as though having too low of an eFG percentage will hurt, but if it is too high, then teams are not taking as many two-point shots or free throws, and thus are losing a few extra games.
Note: Interaction factors do not work with tree-based models. Also, none of the “basic” statistics that we found were significant were needed in predicting this model.
True Shooting Percentage Analysis
Next, I will take a look at TS% on its own, by looking at each individual player’s percentage from the 2014-15 season. To avoid skewness, I took out any player that did not play more than 500 minutes on the season. Instead of wins, my y-variable will be win shares.
## Warning: package 'plotly' was built under R version 3.4.2## Loading required package: ggplot2##
## Attaching package: 'plotly'## The following object is masked from 'package:ggplot2':
##
## last_plot## The following object is masked from 'package:stats':
##
## filter## The following object is masked from 'package:graphics':
##
## layoutTS_FRAME = data.frame(shooting,teams,wins_frame,WS,Player)
names(TS_FRAME) = c("TS","Team","# of Wins", "Win_Shares","Player")
head(TS_FRAME, n =20)## TS Team # of Wins Win_Shares Player
## 1 0.699 ATL 60 7.5 Kyle Korver
## 2 0.565 ATL 60 8.3 Paul Millsap
## 3 0.563 ATL 60 8.7 Al Horford
## 4 0.566 ATL 60 7.7 Jeff Teague
## 5 0.603 ATL 60 7.0 DeMarre Carroll
## 6 0.516 ATL 60 2.5 Dennis Schroder
## 7 0.520 ATL 60 1.6 Kent Bazemore
## 8 0.543 ATL 60 2.7 Mike Scott
## 9 0.508 ATL 60 1.5 Pero Antic
## 10 0.506 ATL 60 2.5 Thabo Sefolosha
## 11 0.489 ATL 60 1.3 Shelvin Mack
## 12 0.608 ATL 60 1.9 Mike Muscala
## 13 0.507 BOS 40 2.5 Avery Bradley
## 14 0.482 BOS 40 2.5 Evan Turner
## 15 0.557 BOS 40 5.3 Brandon Bass
## 16 0.491 BOS 40 2.9 Marcus Smart
## 17 0.594 BOS 40 6.5 Tyler Zeller
## 18 0.503 BOS 40 4.0 Jared Sullinger
## 19 0.558 BOS 40 3.6 Kelly Olynyk
## 20 0.512 BOS 40 3.3 Jae Crowderplotbox <- plot_ly(TS_FRAME, x = shooting, color = teams,
type = "box",xlab = "True Shooting Percentage",
main = "True Shooting Percentages by Team")
plotbox## Warning in RColorBrewer::brewer.pal(N, "Set2"): n too large, allowed maximum for palette Set2 is 8
## Returning the palette you asked for with that many colors## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'
## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'
## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'
## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
## Valid attributes include:
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
## Valid attributes include:
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## Warning: 'box' objects don't have these attributes: 'xlab', 'main'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'The graph above gives boxplots for each team based on each player’s TS%. It appears that Golden State, Toronto, Los Angeles (Clippers), Cleveland, and Atlanta all have an average TS% greater than the rest of the NBA teams. All of these teams made it to the playoffs in 2015.
plot_ly(TS_FRAME, x = TS., y = Win_Shares, text = paste("Player: ", TS_FRAME$Player),
mode = "markers", color = TS., size = TS., opacity = TS.)## No trace type specified:
## Based on info supplied, a 'scatter' trace seems appropriate.
## Read more about this trace type -> https://plot.ly/r/reference/#scatter#plot(TS_FRAME$TS, TS_FRAME$Win_Shares, xlab = "True Shooting Percentage",ylab="Win Shares",main = #"True Shooting Percentage versus Win Shares")
cor(TS_FRAME$TS, TS_FRAME$Win_Shares)## [1] 0.580575out_shares = lm(Win_Shares ~ TS, data = TS_FRAME)
summary(out_shares)##
## Call:
## lm(formula = Win_Shares ~ TS, data = TS_FRAME)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.0250 -1.4046 -0.3676 0.8578 10.7471
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -14.653 1.268 -11.56 <2e-16 ***
## TS 33.567 2.384 14.08 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.275 on 390 degrees of freedom
## Multiple R-squared: 0.3371, Adjusted R-squared: 0.3354
## F-statistic: 198.3 on 1 and 390 DF, p-value: < 2.2e-16predictions = predict(out_shares)
TS_FRAME$predictions = predictions
TS_FRAME$diff = TS_FRAME$Win_Shares - predictions
head(TS_FRAME, n = 15)## TS Team # of Wins Win_Shares Player predictions diff
## 1 0.699 ATL 60 7.5 Kyle Korver 8.810322 -1.3103217
## 2 0.565 ATL 60 8.3 Paul Millsap 4.312345 3.9876551
## 3 0.563 ATL 60 8.7 Al Horford 4.245211 4.4547891
## 4 0.566 ATL 60 7.7 Jeff Teague 4.345912 3.3540881
## 5 0.603 ATL 60 7.0 DeMarre Carroll 5.587891 1.4121095
## 6 0.516 ATL 60 2.5 Dennis Schroder 2.667562 -0.1675623
## 7 0.520 ATL 60 1.6 Kent Bazemore 2.801830 -1.2018303
## 8 0.543 ATL 60 2.7 Mike Scott 3.573871 -0.8738711
## 9 0.508 ATL 60 1.5 Pero Antic 2.399026 -0.8990264
## 10 0.506 ATL 60 2.5 Thabo Sefolosha 2.331892 0.1681076
## 11 0.489 ATL 60 1.3 Shelvin Mack 1.761254 -0.4612536
## 12 0.608 ATL 60 1.9 Mike Muscala 5.755726 -3.8557255
## 13 0.507 BOS 40 2.5 Avery Bradley 2.365459 0.1345406
## 14 0.482 BOS 40 2.5 Evan Turner 1.526285 0.9737154
## 15 0.557 BOS 40 5.3 Brandon Bass 4.043809 1.2561910TS% only gives us a correlation of about .58. Some players that stand out in this graph are Stephen Curry, James Harden, and Chris Paul. Curry won the 2015 MVP race, while Harden finished in 2nd place and Paul in 6th place. All of them are excellent shooters, and Curry and Harden especially are notable 3-point shooters. Anthony Davis, Kyle Korver, Jimmy Butler, DeAndre Jordan, and LeBron James also stand out. All of these players were all-stars that year.
Looking at the first 20 rows of the data frame, some of the differences are minute, while others are very inaccurate, which can lead to a lot of problems. Summing up the total number of “wins” from the predictions column by team, I added it back to the advanced dataset.
advanced$Predictions = team.predictions
write.csv(advanced,'advanced_with_predictions.csv',row.names=F)Based on our results, we find that true shooting percentage can be very accurate in estimating some teams wins, but at other times it comes nowhere close. This may be due to too much noise in the data, or the fact that there needs to be more variables implemented into the model. After all, basketball is not just about shooting (thought that is a big factor).
What’s interesting to see how accurate it is for some teams (eg. Dallas Mavericks, Indiana Pacers, Milwaukee Bucks), but really poor on others (Chicago Bulls, Memphis Grizzlies,Miami Heat). Chicago and Memphis are known to be defensive-minded teams, while Dallas is a more offensive team. What is interesting, however, is that of the 16 teams that made it to the playoffs, 13 of them would have made it to the playoffs in 2015.
overall.pred = data.frame(advanced$Team,lm.predict,yhat,team.predictions,wins)
names(overall.pred) = c("Team","LM Pred","Tree","TS Pred","Wins")
overall.pred## Team LM Pred Tree TS Pred Wins
## 1 Atlanta Hawks* 59.19007 55.22222 48.59284 60
## 2 Boston Celtics* 39.82644 33.00000 38.58785 40
## 3 Brooklyn Nets* 36.47296 37.60000 36.89373 38
## 4 Charlotte Hornets 32.59971 21.00000 30.97220 33
## 5 Chicago Bulls* 50.50716 45.83333 26.38726 50
## 6 Cleveland Cavaliers* 52.40175 55.22222 46.56103 53
## 7 Dallas Mavericks* 49.98080 55.22222 50.13692 50
## 8 Denver Nuggets 30.63676 33.00000 37.95008 30
## 9 Detroit Pistons 31.50735 33.00000 37.36367 32
## 10 Golden State Warriors* 67.17686 55.22222 49.46558 67
## 11 Houston Rockets* 55.58915 55.22222 37.36570 56
## 12 Indiana Pacers 37.60497 33.00000 38.26998 38
## 13 Los Angeles Clippers* 57.18031 55.22222 43.20635 56
## 14 Los Angeles Lakers 21.13945 21.00000 36.67453 21
## 15 Memphis Grizzlies* 55.69056 45.83333 33.10066 55
## 16 Miami Heat 36.80245 37.60000 53.12033 37
## 17 Milwaukee Bucks* 41.28591 45.83333 40.97313 41
## 18 Minnesota Timberwolves 15.19497 21.00000 35.21336 16
## 19 New Orleans Pelicans* 43.56867 37.60000 44.61414 45
## 20 New York Knicks 18.12086 21.00000 39.99361 17
## 21 Oklahoma City Thunder 44.95894 45.83333 43.48863 45
## 22 Orlando Magic 26.32363 33.00000 37.09513 25
## 23 Philadelphia 76ers 17.92769 21.00000 26.32013 18
## 24 Phoenix Suns 38.30892 37.60000 44.09486 39
## 25 Portland Trail Blazers* 51.70299 55.22222 47.09810 51
## 26 Sacramento Kings 29.18525 37.60000 40.04903 29
## 27 San Antonio Spurs* 53.50904 55.22222 58.80892 55
## 28 Toronto Raptors* 50.74936 55.22222 42.85491 49
## 29 Utah Jazz 38.35128 45.83333 32.53205 38
## 30 Washington Wizards* 46.50574 45.83333 43.50643 46mse.lm.2015 = (1/30)*sum((lm.predict-wins)^2)
mse.yhat.2015 = (1/30)*sum((yhat-wins)^2)
mse.TS.2015 = (1.30)*sum((team.predictions-wins)^2)
c(mse.lm.2015,mse.yhat.2015,mse.TS.2015)## [1] 0.6396242 30.3862963 5199.3585102Based on our mean-squared error analysis, the linear model by far predicts wins better than the tree-based method or by looking at TS% alone. Despite this, at some points the other models had a better prediction of the actual number of wins by a team than the full linear model.For example, the Tree-based model did better at estimating the number of wins for the Washington Wizards, and the TS% approach estimated the number of wins for the Dallas Mavericks with extreme accuracy. Though TS% might not be good alone in solely predicting wins, it might be better at predicting offensive performance than normal statistics like just 2-point field goal percentage. TS% can estimate the number of wins a team gets due to their offense, while others could be explained by defensive factors.
Results: Predicting 2016 Data
The 2015-16 NBA regular season, meaning that the new data is available to test on. Using the data from the 2014-15 season, I will predict the number of wins and win shares each player gets through three ways: Our linear model combining basic and advanced statistics, our TS% model, and our tree-based model.
setwd("C:/Users/Evan Boyd/Desktop/College/Spring 2016/Stat 479/Individual Project/Files/CSV/2016")
basic.2016 = read.csv("leagues_NBA_2016_team.csv", header = T)
TOT.REB.. = c(.475,.494,.494,.496,.502,.52,.485,.511,.521,.513,.491,.498,.474,.48,
.491,.517,.492,.498,.49,.501,.547,.494,.464,.506,.51,.496,.52,.516,.519,.486)
basic.2016$TOT.REB.. = TOT.REB..
advanced.2016 = read.csv("leagues_NBA_2016_misc.csv", header = T)
advanced.2016 = advanced.2016[,-23]
advanced.2016 = advanced.2016[,-24]
wins2 = c(48,48,21,48,42,57,42,33,44,73,41,45,53,17,42,48,33,29,30,
32,55,35,10,23,44,33,67,56,40,41)I will be taking the same approach as using the 2015 data, only I am using the variables expressed in the 2015 data in the linear model, as well as seeing what new variables fit a respectable tree diagram.
TS_FRAME_2016 = data.frame(shooting.2016,teams.2016,WS.2016,Player.2016)
names(TS_FRAME_2016) = c("TS","Team","Win_Shares","Player")
head(TS_FRAME_2016, n = 15)## TS Team Win_Shares Player
## 1 0.556 ATL 10.1 Paul Millsap
## 2 0.565 ATL 9.4 Al Horford
## 3 0.578 ATL 4.1 Kyle Korver
## 4 0.551 ATL 5.9 Jeff Teague
## 5 0.551 ATL 4.1 Kent Bazemore
## 6 0.578 ATL 4.5 Thabo Sefolosha
## 7 0.510 ATL 2.2 Dennis Schroder
## 8 0.575 ATL 3.2 Mike Scott
## 9 0.563 ATL 1.9 Tim Hardaway
## 10 0.571 ATL 1.7 Tiago Splitter
## 11 0.576 ATL 1.6 Mike Muscala
## 12 0.562 BOS 9.7 Isaiah Thomas
## 13 0.538 BOS 4.8 Avery Bradley
## 14 0.565 BOS 7.3 Jae Crowder
## 15 0.513 BOS 4.0 Evan Turnerplot_ly(TS_FRAME_2016, x = TS., y = Win.Shares,
text = paste("Name: ", TS_FRAME_2016$Player),
mode = "markers", color = TS., size = TS.,
opacity = TS.)## No trace type specified:
## Based on info supplied, a 'scatter' trace seems appropriate.
## Read more about this trace type -> https://plot.ly/r/reference/#scatter#plot(TS_FRAME_2016$TS, TS_FRAME_2016$Win_Shares,xlab="True Shooting Percentage",ylab="Win #Shares",main="True Shooting Percentage versus Win Shares: 2016")
cor(TS_FRAME_2016$TS, TS_FRAME_2016$Win_Shares)## [1] 0.5977635out.shares.2016 = lm(Win_Shares ~ TS, data = TS_FRAME_2016)
summary(out.shares.2016)##
## Call:
## lm(formula = Win_Shares ~ TS, data = TS_FRAME_2016)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.0252 -1.5121 -0.3207 1.0127 9.9134
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -18.169 1.548 -11.73 <2e-16 ***
## TS 40.172 2.872 13.99 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.339 on 352 degrees of freedom
## Multiple R-squared: 0.3573, Adjusted R-squared: 0.3555
## F-statistic: 195.7 on 1 and 352 DF, p-value: < 2.2e-16predictions.2016 = predict(out.shares.2016)
TS_FRAME_2016$predictions = predictions.2016
TS_FRAME_2016$diff = WS.2016 - predictions.2016
head(TS_FRAME_2016, n = 20)## TS Team Win_Shares Player predictions diff
## 1 0.556 ATL 10.1 Paul Millsap 4.1669193 5.9330807
## 2 0.565 ATL 9.4 Al Horford 4.5284714 4.8715286
## 3 0.578 ATL 4.1 Kyle Korver 5.0507133 -0.9507133
## 4 0.551 ATL 5.9 Jeff Teague 3.9660570 1.9339430
## 5 0.551 ATL 4.1 Kent Bazemore 3.9660570 0.1339430
## 6 0.578 ATL 4.5 Thabo Sefolosha 5.0507133 -0.5507133
## 7 0.510 ATL 2.2 Dennis Schroder 2.3189863 -0.1189863
## 8 0.575 ATL 3.2 Mike Scott 4.9301959 -1.7301959
## 9 0.563 ATL 1.9 Tim Hardaway 4.4481265 -2.5481265
## 10 0.571 ATL 1.7 Tiago Splitter 4.7695061 -3.0695061
## 11 0.576 ATL 1.6 Mike Muscala 4.9703684 -3.3703684
## 12 0.562 BOS 9.7 Isaiah Thomas 4.4079540 5.2920460
## 13 0.538 BOS 4.8 Avery Bradley 3.4438150 1.3561850
## 14 0.565 BOS 7.3 Jae Crowder 4.5284714 2.7715286
## 15 0.513 BOS 4.0 Evan Turner 2.4395036 1.5604964
## 16 0.476 BOS 4.8 Jared Sullinger 0.9531227 3.8468773
## 17 0.602 BOS 5.9 Amir Johnson 6.0148523 -0.1148523
## 18 0.463 BOS 2.9 Marcus Smart 0.4308808 2.4691192
## 19 0.561 BOS 4.1 Kelly Olynyk 4.3677815 -0.2677815
## 20 0.531 BOS 2.4 Jonas Jerebko 3.1626078 -0.7626078Notice that in our TS%/Win Shares graph, Steph Curry has the highest TS% and the highest number of win shares. Next to him Kevin Durant and Kawhi Leonard. Curry was named unanimous Most Valuable Player for the 2016 season, with Leonard coming in second place, and Durant in 4th place. Once again, TS% is significant when estimating win shares alone in the model, though the adjusted-R^2 is low, meaning that there could be other variables to make a more accurate prediction.
tree.2016=tree(wins2~Pace+FTr+X3PAr+TS.
+eFG.+ORB.+FT.FGA+eFG..1+TOV..1
+basic$OWN+basic$FG.OWN+basic$TOT.REB..
,advanced.2016
)
summary(tree.2016)##
## Regression tree:
## tree(formula = wins2 ~ Pace + FTr + X3PAr + TS. + eFG. + ORB. +
## FT.FGA + eFG..1 + TOV..1 + basic$OWN + basic$FG.OWN + basic$TOT.REB..,
## data = advanced.2016)
## Variables actually used in tree construction:
## [1] "eFG..1" "TS." "TOV..1"
## Number of terminal nodes: 4
## Residual mean deviance: 43.87 = 1141 / 26
## Distribution of residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -13.2900 -3.3960 -0.7929 0.0000 4.6500 14.5700plot(tree.2016,main = "Tree-Based Plot: 2016")
text(tree.2016,pretty=0)
tree.basic## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 30 5250.0 41.00
## 2) TS. < 0.5265 10 702.0 27.00
## 4) eFG. < 0.476 5 194.0 21.00 *
## 5) eFG. > 0.476 5 148.0 33.00 *
## 3) TS. > 0.5265 20 1608.0 48.00
## 6) TS. < 0.543 11 502.9 42.09
## 12) eFG..1 < 0.494 6 186.8 45.83 *
## 13) eFG..1 > 0.494 5 131.2 37.60 *
## 7) TS. > 0.543 9 251.6 55.22 *cv.2016=cv.tree(tree.2016)
plot(cv.2016$size,cv.2016$dev,type='b',xlab="Size",ylab="Deviations",main ="Tree-Based Plot: 2016")
yhat.2016=predict(tree.2016)
out.2016.tree = lm(wins~yhat)
cor(yhat.2016,wins2)## [1] 0.8921499There is still a strong correlation with the number of wins and the tree model. What is interesting, however, is that there are different variables being used to create this tree than the 2014-15 data, AND TS% is not the highest part in the tree. We will continue to evaluate the model by estimating the number of wins.
setwd("C:/Users/Evan Boyd/Desktop/College/Spring 2016/Stat 479/Individual Project/Files/CSV/2016")
overall.2016 = data.frame(advanced.2016$Team,predict.2016,yhat.2016,
team.predictions.2016,wins2)
names(overall.2016) = c("Team","LM Pred","Tree","TS Pred","Wins")
overall.2016## Team LM Pred Tree TS Pred Wins
## 1 Atlanta Hawks* 45.32603 58.42857 48.16611 48
## 2 Boston Celtics* 50.26584 43.30000 33.23298 48
## 3 Brooklyn Nets 19.17782 23.28571 35.40941 21
## 4 Charlotte Hornets* 48.77669 43.30000 36.64374 48
## 5 Chicago Bulls 39.17992 43.30000 36.91783 42
## 6 Cleveland Cavaliers* 54.87495 58.42857 40.90592 57
## 7 Dallas Mavericks* 42.31609 43.30000 37.35972 42
## 8 Denver Nuggets 34.04783 23.28571 36.74612 33
## 9 Detroit Pistons* 44.52795 43.30000 29.97901 44
## 10 Golden State Warriors* 75.00185 58.42857 58.96149 73
## 11 Houston Rockets* 39.61921 37.50000 36.95800 41
## 12 Indiana Pacers* 45.93655 43.30000 39.91974 45
## 13 Los Angeles Clippers* 52.49417 58.42857 49.18857 53
## 14 Los Angeles Lakers 14.56487 23.28571 25.45766 17
## 15 Memphis Grizzlies* 39.17754 37.50000 33.66386 42
## 16 Miami Heat* 45.95549 43.30000 48.30477 48
## 17 Milwaukee Bucks 32.39930 37.50000 34.93836 33
## 18 Minnesota Timberwolves 33.06054 23.28571 36.47593 29
## 19 New Orleans Pelicans 32.03207 23.28571 45.20048 30
## 20 New York Knicks 35.02824 43.30000 33.37163 32
## 21 Oklahoma City Thunder* 54.66215 58.42857 46.17563 55
## 22 Orlando Magic 38.20079 37.50000 43.20287 35
## 23 Philadelphia 76ers 12.91266 23.28571 36.22388 10
## 24 Phoenix Suns 20.62755 23.28571 37.26836 23
## 25 Portland Trail Blazers* 42.49434 43.30000 38.77678 44
## 26 Sacramento Kings 34.26589 37.50000 47.91406 33
## 27 San Antonio Spurs* 65.63326 58.42857 54.62286 67
## 28 Toronto Raptors* 53.35108 58.42857 41.45731 56
## 29 Utah Jazz 45.69640 43.30000 44.68925 40
## 30 Washington Wizards 38.39292 37.50000 43.86766 41mse.lm.2016 = (1/30)*sum((predict.2016-wins2)^2)
mse.yhat.2016 = (1/30)*sum((yhat.2016-wins2)^2)
mse.TS.2016 = (1.30)*sum((team.predictions.2016-wins2)^2)
c(mse.lm.2016,mse.yhat.2016,mse.TS.2016)## [1] 5.396527 38.024762 4472.239454Based on the MSE values, the tree-based model did slightly better in its accuracy, but the linear model was not too far behind. Similar to the 2015 data, there were still some teams that are estimated better by TS% or the linear model.
Conclusion
Evaluating True-Shooting percentage to predict wins failed to solely provide an accurate prediction on wins compared to a linear model or a tree-based model, which incorporated potential confounding and/or lurking variables. Despite this, I was able to accurately predict wins based on a small number of basketball statistics. In an field where new statistics are being made every week, it is interesting to see what statistics actually generate team wins.
Obviously, TS% does not account for defensive performance, which I believe resulted in the over/underappreciation of many teams. Teams with high shooting percentages but low defensive statistics will have more wins on paper.
What is important is that advanced statistics seem to have a much larger impact on the models than basic statistics. Based on the number of variables in the linear model, the tree diagrams, and the correlation with TS% and wins, advanced statistics appear to have a profound impact. NBA teams should consider investing more in valuing these statistics in order to create shots, run the shot clock well, and rebound the ball successfully. Also, media outlets such as ESPN and 538 should consider analyzing various teams using advanced statistics to try and create better models, as well as draw more interest.
Many of the statistics I used were offensive-oriented, meaning that they focus on a team’s offensive performance instead of defensive. One limitation for that is the fact that there are not as many advanced statistics out there for defense than for offense. With more resources, like defensive numbers and data for over the past 10 years, I would like to look in more to see how important defense, and what type of defense, is to create wins.
I also will confirm the idea that creating the right shot is the new emphasis on the NBA. This is with more three pointers, sharing the ball, and generating on-and-off-ball screens. True Shooting Percentage measures exactly that, which is why it predicted teams like the Warriors, Spurs, and Mavericks so high, and why it valued the Bulls and Jazz less.
The playoffs are beginning in the NBA, with the frontrunners to win it all being the Golden State Warriors. If the advanced statistics do not lie, then Golden State, Oklahoma City, and the Cleveland Cavaliers will make deep runs in the playoffs. May the best numbers win!
Appendix: List of Variables and Descriptions
Basic Statistics:
OWN = The number of points scored per game by that team.
OPP = The number of points allowed per game that by team. In other words, the amount of points the opposing team scores on average.
DIFF = OWN = OPP
FG.OWN = The team’s field goal percentage. This calculates two-pointers and three-pointers, not free throws.
FG.OPP = The opponent’s field goal percentage, on average.
X3P.OWN = The team’s three-point field goal percentage.
X3P.OPP = The opponent’s three-point field goal percentage.
FT. = The team’s free throw percentage. A player can attempt a free throw by drawing any sort of foul from the opposing team.
OFF.REB. = The percentage of offensive rebounds a player obtains while on the court. This is averaged for each team.
DEF.REB. = The percentage of defensive rebounds a player obtains while on the court.
TOT.REB.. = The percentage of total rebounds a player obtains while on the court.
OWN.TO = The number of turnovers a team makes per game.
OPP.TO = The number of turnovers a team creates per game. In other words, the number of turnovers the opponent team makes per game.
Advanced statistics:
PW = Pythagorean wins, i.e., expected wins based on points scored and allowed
PL = Pythagorean losses, i.e., expected losses based on points scored and allowed
MOV = Margin of Victory
SOS = Strength of Schedule - A rating of strength of schedule. The rating is denominated in points above/below average, where zero is the average.
SRS = Simple Rating System; A team rating that takes into account average point differential and strength of schedule. The rating is denominated in points above/below average, where zero is average.
ORtg = Offensive Rating: An estimate of points produced (players) or scored (teams) per 100 possessions
DRtg = Defensive Rating: An estimate of points allowed per 100 possessions
Pace = Pace Factor: An estimate of possessions per 48 minutes
FTr = Free Throw Attempt Rate: Number of free throw attempts per field goal attempt
x3PAr = 3-Point Attempt Rate: Percentage of FG Attempts from 3-point range.
TS. = True Shooting Percentage: A measure of shooting efficiency that takes into account 2-point field goals, 3-point field goals, and free throws
Efg.=Effective Field Goal Percentage
Adjusts for the fact that a 3-point field goal is one more point than a 2-point field goal
TOV. = Turnover percentage: An estimate of turnovers committee per 100 plays
ORB. = Offensive Rebound Percentage: An estimate of the percentage of available offensive rebounds a player grabbed while he was on the floor
FT.FGA = Free Throws per Field Goal Attempt (might wanna delete)
Opp Efg = Opponent Effective Field Goal Percentage
OTOV = Opponent Turnover Percentage
DRB = Defensive Rebound Percentage: An estimate of the percentage of available defensive rebounds a player grabbed while he was on the floor
OFT/FGA = Opponent Free Throws Per Field Goal Attempt
Attendance = Total Attendance during home games
Wins = # of wins for each team in the 2014-15 (2015-16) season