NBA Amnesty Clause: Northwest Division

Continuing the analysis of the Amnesty Clause on NBA contracts, which contracts in the Northwest Division are most fitting for elimination?

NBA Amnesty Clause

The current Collective Bargaining Agreement (CBA) between the NBA and the NBA Players' Union is set to expire this year. There has been talk of a new agreement including an Amnesty Clause like the last CBA did. The last amnesty provision allowed teams to eliminate one contract. The teams still had to pay the entire amount on the contract and the contract still counted against the salary cap. The benefit to the team is that the salary no longer counted towards the luxury tax. The luxury tax in the NBA is a penalty for team salaries that are too high. If the team salary is above the luxury tax line, the team has to pay a $1 tax for each $1 it is above the tax line. Using the Amnesty Clause a team could eliminate a $20m contract from their luxury tax calculations and save $20m. If the NBA brings back the Amnesty Clause, which player contracts are the likeliest targets?

More Memory Game

This post is an attempt to answer the question I posed in a prior post about the Memory Game. If you are not familiar with the Memory Game, you can read that post to get familiar with the rules and terminology. The question:

With the second part of your turn, if you do not have a 100% chance of getting a pair is it better to flip an already known tile or try to flip an unknown tile?

As I explained in my prior post on Memory, there are two ways to score. The first method of scoring is to flip over your first tile and already know the position of its match on the board. The second method of scoring is to flip over your first tile, not know the position of its match, and then randomly guess and find its match. My question asks should you forgo the second method of scoring pairs? 

Memory Game

In the seventh episode of this season (22nd) of Survivor, two contestants played the Memory Game to see who would remain on the show. In the Memory Game you score points by flipping over pairs of the same card. Whoever identifies the most pairs wins. The Survivor version had 20 tiles (10 unique pairs) laid face down. The contestants took turns flipping over two tiles per turn. If you flipped over identical tiles (a pair) you received a point and those two tiles were removed from the game. If the contestant flipped over non-identical tiles, the tiles were returned to their face down position. The players alternated turns regardless of whether they scored a pair or not. First to get five pairs won the game. Watching the game, I had two questions:

1. Is it better to go first or second?
2. With the second part of your turn, if you do not have a 100% chance of getting a pair is it better to flip an already known tile or try to flip an unknown tile?

NBA Salary Commitments

As I sit around killing time until I can play some pick up basketball at the park, I'm taking a look at the salary data available at HoopsHype.com.  NBA salaries amuse.  Every year we get to see the winner's curse in action.  They gave how much to Joe Johnson?  Why on earth would you sign Hedo Turkoglu to a five year deal (and how the heck was he traded twice within the first 18 months of his contract)?  I took a look at each team and made some tables and graphs of each team's salary commitment.

More Fangraphs.com Org Rankings

To see the data in spreadsheet form, click here. You can see how teams changed in versus last years ranking and where they scored in each of the four component categories. Toronto, San Fransisco, Cincinatti, and the White Sox moved up 10 or more places while Milwaukee, Seattle, Cleveland, and Arizona were the big downgrades. I didn't like how Future Talent was compiled and have some reservations about Financial Resources  (perhaps a topic for another post).

Fangraphs.com Organization Rankings -- Star Plots

Fangraphs.com has an annual series of posts where they rank each Major League Baseball organization on the following criteria: Present Talent (30%), Financial Resources (30%), Baseball Operations (25%), and Future Talent (15%). The writers grade each team in each of the categories probably on a scale of 1-100 (I believe; no ranking is below 62 or above 95). I took the rankings for each category and made some star plots.

The Challenge: Cutthroat

After two episodes the MTV reality show The Challenge: Cutthroat has not had much to analyze strategically. The only major choices faced so far have been picking the teams and choosing who gets sent into the elimination round.

Bill Simmons and the NFC West

In his weekly football column, Bill Simmons of ESPN.com harshly criticizes the NFC West. His main point of evidence is the NFC's west record since 2002 (go-go arbitrary end points). He posts this table in his article:

Aging Curves in Basketball

The NBA offseason raised a few questions. In order to answer these questions I need to do a little research and figure out a few things. One of these things is an aging curve for basketball players. What is their prime? What rate do they decline after that prime? Luckily this question has been asked and answered in baseball so I can use their methodology and apply it to basketball.

For data, I went to www.basketball-reference.com and pulled the advanced data for players from the 2000-2001 season through the 2009-2010 season (the seasons from the last collective bargaining agreement). My methodology follows the work of TangoTiger and MGL, particularly this article written by MGL. I will try to briefly summarize the methodology. MGL offers a much clearer explanation so I recommend reading that article first.

The World Cup Approaches...

Another World Cup tradition: players complaining about the new ball. The Adidas Jabulani replaces the much maligned 2006 Teamgeist and the hated 2002 Fevernova. Goalkeepers complained about the 1994 Questra ball and I'm sure soccer players wished many unkind things towards the 1998 Tricolore ball but I can't find a link. I'm not sure why but I find the sky-is-falling stories about the new balls amusing.

Fresh Meat II: Episode 7

Continuing my strange fascination with the MTV show Fresh Meat II, here's a post about the latest episode. Wes's coalition officially reached its end as the two remaining teams in it where forced into the elimination challenge. Wes's team lost and left the game. We are left with 6 teams. 4 eams are in Kenny's alliance and 2 are on the outskirts. The last 4 teams go to the finals where they compete for cash money. 1st place in the final challenge wins $200k, 2nd place $60k, 3rd place $40k, and 4th place receives nothing. The goal is to not only make it to the finals, but to maximize your expected winnings in the finals. Strategically, how should the six remaining teams behave to optimize their expected payout?

The Challenge: Fresh Meat II Episode 6

A few weeks ago I wrote a post saying that Kenny's alliance had basically no chance to retake the majority (0.2%). The Kenny's alliance was down 7 teams to 3. The alliance would have to win 4 reward challenges and 3 elimination challenges in order to take back the majority. 3 reward challenge victories and 3 elimination challenge victories later, Kenny's alliance has seized control of the game and is in a dominant position. What happened? Why was I so wrong in underestimating the chances of Kenny's alliance?

Fresh Meat II: The Challenge Episode #4

My earlier posts on the MTV reality show Fresh Meat II: The Challenge recommended two strategies for the competing factions in the show: one side should tighten the bounds in its group and keep loyalty strong while the other side should use the threat throwing a team into the elimination challenge as a way to get teams to defect to their faction. However the factions got the strategies backwards. I recommended Kenny's alliance use the threat of being sent into the elimination challenge to get someone to defect to his alliance. Wes's coalition had the superior numbers. It was in Wes's coalition's best interests to keep loyalty strong within the group. Instead Kenny let someone in his alliance choose who was going into the elimination challenge, thus trying to boost loyalty withing the group while Wes's coalition used the threat of being thrown into the elimination round to get a team to defect to his coalition.

NBA #1 Seeds that Struggle in the First Round

A post on Hoops Analyst talks about the Los Angeles Lakers - Oklahoma Thunder NBA playoff first round series. The Lakers are the highly rated #1 seed and the Thunder are the lowest rated #8 seed. The two teams are playing a best-of-seven series. The author asks if a #1 seed that is struggling against a #8 seed is "a bad indicator for their success in the playoffs"? The post then looks at each of the #1 seeds that struggled against #8 seeds and concludes "I would venture that there is little correlation between a round one struggle and overall team weakness." What does the data say?

The Challenge: Fresh Meat II Wes's Coalition

With Wes's coalition in such a dominate position, the 7 teams in it have to start moving beyond the threat of Kenny's alliance (3 teams) and strategizing  for the end game. In particular two things: avoiding the elimination round and being one of the final four teams that gets to compete for the cash prize. As long as Kenny's alliance remains, Wes's coalition will keep choosing them to go into the elimination challenge. Wes's coalition could be left with 7 teams or it could lose a couple elimination challenges and be left with 5 teams when Kenny's alliance is down to one team. At that point Wes's coalition will have to turn on itself.

Fresh Meat II: The Future for Kenny's Alliance

In the last episode of The Challenge: Fresh Meat II, Kenny's alliance lost the elimination challenge. It also became clear that one of the teams in Kenny's alliance was a mole. That puts Wes's coalition at 7 teams and Kenny's alliance at 3 teams. Kenny's alliance is pretty much doomed. They would have to win four reward challenges and three elimination challenges in a row to get back to equal footing. A loss in any of those challenges would lead to one of the teams in Kenny's alliance going home. If every elimination challenge is a 50-50 proposition and all teams are equally likely to win a reward challenge, the probability of Kenny's alliance winning three reward challenges and two elimination challenges in a row is 0.2% (30%*50%*33%*50%*38%*50%*43%= 00.2%). There is basically no chance of Kenny's alliance seizing the majority unless Kenny's alliance gets a team from Wes's coalition to defect.

Fresh Meat II

A couple of strategic decisions came up in the MTV show The Challenge: Fresh Meat II. For those who don't watch reality TV here's a quick run down. Thirteen teams of two compete to win prizes in a reward challenge. The winner gets a prize and is safe from the elimination round. At the end of the show, two teams are picked to go to an elimination round where the losing team goes home. One of the two teams that goes to the elimination round is picked by the winner of the reward challenge, the other is picked by majority vote. After nine teams have been eliminated, the final four teams get to compete in the final challenge with the top three teams winning money.

Quick Response to Fangraphs War Article

A response to this article on Fangraphs.

WAR has an R^2 of .83, but what does that really mean? Some context (all stats from ESPN.com):

ALwins ALera ALba ALops ALrbi

ALwins 1.000 -0.642 0.588 0.704 0.672

That is how American League wins correlates (little "r" not R^2) with ERA, Batting Average, OPS, and RBI. And the NL:

NLwins NLera NLba NLops NLrbi

NLwins 1.000 -0.751 0.369 0.503 0.572

I made three linear models for each league to find the R^2 of wins versus ERA and BA, ERA and RBI, and ERA and RBI. The R^2 values are .84, .86, and .87 respectively for the AL. For the NL .61, .82, and .81. Below are the print outs from R.

Call:

lm(formula = ALwins ~ ALera + ALba)

Residuals:

Min 1Q Median 3Q Max

-7.6862 -2.7943 -0.7403 1.9202 9.0998

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -49.532 46.485 -1.066 0.309461

ALera -24.762 4.224 -5.862 0.000109 ***

ALba 907.270 166.522 5.448 0.000201 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.265 on 11 degrees of freedom

Multiple R-squared: 0.8414, Adjusted R-squared: 0.8126

F-statistic: 29.18 on 2 and 11 DF, p-value: 3.995e-05

> summary(al2)

Call:

lm(formula = ALwins ~ ALera + ALrbi)

Residuals:

Min 1Q Median 3Q Max

-8.888 -2.575 1.766 3.284 5.192

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 96.20702 22.96652 4.189 0.001513 **

ALera -22.33402 3.96918 -5.627 0.000154 ***

ALrbi 0.11425 0.01941 5.885 0.000105 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.971 on 11 degrees of freedom

Multiple R-squared: 0.8586, Adjusted R-squared: 0.8329

F-statistic: 33.4 on 2 and 11 DF, p-value: 2.124e-05

> summary(al3)

Call:

lm(formula = ALwins ~ ALera + ALops)

Residuals:

Min 1Q Median 3Q Max

-8.8988 -2.1200 0.6058 2.9829 8.0973

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -6.139 34.441 -0.178 0.861764

ALera -21.489 3.783 -5.681 0.000142 ***

ALops 240.741 38.383 6.272 6.07e-05 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.734 on 11 degrees of freedom

Multiple R-squared: 0.8718, Adjusted R-squared: 0.8485

F-statistic: 37.41 on 2 and 11 DF, p-value: 1.239e-05

summary(nl1)

Call:

lm(formula = NLwins ~ NLera + NLba)

Residuals:

Min 1Q Median 3Q Max

-9.467 -4.923 -1.258 3.634 12.506

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 69.111 70.851 0.975 0.34714

NLera -16.635 4.173 -3.986 0.00155 **

NLba 312.338 251.322 1.243 0.23590

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 7.43 on 13 degrees of freedom

Multiple R-squared: 0.6113, Adjusted R-squared: 0.5515

F-statistic: 10.22 on 2 and 13 DF, p-value: 0.002150

> summary(nl2)

Call:

lm(formula = NLwins ~ NLera + NLrbi)

Residuals:

Min 1Q Median 3Q Max

-7.950 -3.843 1.426 3.937 5.915

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 85.42980 19.82645 4.309 0.000849 ***

NLera -16.63429 2.77925 -5.985 4.55e-05 ***

NLrbi 0.09444 0.02190 4.311 0.000845 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.042 on 13 degrees of freedom

Multiple R-squared: 0.821, Adjusted R-squared: 0.7935

F-statistic: 29.82 on 2 and 13 DF, p-value: 1.39e-05

> summary(nl3)

Call:

lm(formula = NLwins ~ NLera + NLops)

Residuals:

Min 1Q Median 3Q Max

-7.792 -3.753 1.456 4.205 5.731

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 2.526 39.070 0.065 0.94944

NLera -17.588 2.853 -6.164 3.41e-05 ***

NLops 204.851 50.095 4.089 0.00128 **

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.198 on 13 degrees of freedom

Multiple R-squared: 0.8098, Adjusted R-squared: 0.7805

F-statistic: 27.67 on 2 and 13 DF, p-value: 2.065e-05

Yet Another Way to Look at Free Throw Percentage

John Branch wrote an article in the New York Times noting that in the past 50 years, Free Throw Percentage (FT%) has not improved in the NBA. The Freakonomics blog posted a follow up to this article that suggested that free throw percentage among the best Free Throw (FT) shooters has improved during that period. Unfortunately, I read this post and wasted the best weather of the year fooling around on R rather than going outside and getting sunburnt.

Ashley Smart, the person who supplied the data and analysis the blog post is based on, seems intelligent and probably knows more about stats than I do. The data she has for her analysis is deeply flawed. The biggest mistake she made was getting the data from N.B.A. Encyclopedia. The place for NBA data is Basketball Reference. You can download several spreadsheets of NBA data stretching back to 1946. As several commentators noted, Ms. Smart's other mistake is not controlling for the number of players.

That said there are two major flaws in Ms. Smart's analysis:

1. The NBA Encyclopedia is arbitrary and inconsisent. The data collectors changed their standards on who qualified as a top 20 FT shooter 14 times between 1950 and 2007. The biggest supposed gain in FT% in Ms. Smart's study occurs between the 1972 and 1973 seasons when qualification standards go from 350 Free Throw Attempts (FTA) to 160 FTA. 
2. The study does not account for the number of players in the league. Of course the top 20 players in the league now are going to have a better FT% than those in 1950. In 1950 there were 135 players, in 2007 595 players. If I took a group of 100 random people and made them shoot a bunch of Free Throws and then took a group of 500 people and made them shoot a bunch of Free Throws which group do you think would have the best average among the top 20 Free Throw shooters? 

I corrected the first problem by getting my data from Basketball Reference. Anyone who had 100 FTA qualified for my analysis. Let us take a look at the Top Twenty players in FT% versus the number of players in the league.

And a look at the number of players by year:

For what it's worth, there is an R^2 value of .82 for Number of Players vs. Top Twenty FT% and an R^2 value of .76 for Year vs. Top Twenty FT% for fitted linear models. The two models have too much serial correlation to be taken seriously. Year and Number of Players has a .93 correlation value.

A hopefully correct method for examining the best FT shooters is to look at the Top Tenth Percentile of FT% for each year:

There appears to be a slight increase in the FT% of the top tenth percentile but once again there is serial correlation. A Durbin Watson test confirms this; D-W Statistic of .978--anything below 1.38 for this sample size is suspicious--with a p-value of 0 and estimated rho value of .51. I did a basic transformation of the Year (X) and Top Tenth Percentile FT% (Y) variables:

Ytransformed = Yi+1 - rho*Yi 

Xtransformed = Xi+1 - rho*Xi

I then fit a new model of Xtransformed verus Ytransformed. The D-W statistic was 1.89 with a p value of .58 and an estimated rho of .05, thus removing the serial correlation. A summary of this model:

With such a poor fitting model (R^2 of .1056) the data does not really explain anything. If I were going to make an inference I would point out the underlined value of .0004034 (b1). The regression coeffecient for X for the transformed model will remain the same when the model is tranformed back to Y = b1*X + b0. So over the 57 years of data, 57*b1 = 2.3% increase in the Top Tenth Percentile FT%. This is really stretching the model but there may be a slight increase (2.3% over 57 years) among the best FT shooters.