Friday, April 18, 2014

NBA Competitive Balance

Yesterday I blogged about the relationship between pay and performance in the NBA.  Today I want to look at competitive balance in the NBA.  For those interested, here is a step-by-step guide to calculate the Noll-Scully measure of competitive balance.

Since the 1999/00 regular season here is the results.  As you can see for the 2013/14 season the NBA's level of competitive balance is very similar.

Season Noll-Scully
1999-00 2.916
2000-01 2.846
2001-02 2.495
2002-03 2.612
2003-04 2.465
2004-05 2.803
2005-06 2.469
2006-07 2.396
2007-08 3.056
2008-09 3.117
2009-10 2.951
2010-11 2.910
2011-12 2.537
2012-13 2.811
2013-14 2.853

Compared to other leagues (American football, hockey and baseball) the NBA is fairly uncompetitive, with higher Noll-Scully measures than any of those leagues during the same time period.

Thursday, April 17, 2014

NBA Payroll and the Playoffs

Last year (November 14) I wrote about being skeptical that payroll and performance are significantly related in the NBAKristi Dosh (ESPN writer) is not skeptical about the relationship between pay and performance in the NBA and predicted that the top 10 payrolls will make the playoffs.  So, how did that work out?

Dosh predicts that the following teams will make the 2013-14 NBA playoffs:  Nets, Knicks, Heat, Bulls, Lakers, Raptors, Clippers, Celtics, Thunder and Pacers and the teams in bold did not actually make the playoffs.  As I have written previously, "I think this would be much more convincing if the top 16 teams in terms of payroll made the playoffs for say ten NBA seasons.  That would give much more credibility to this type of statement.  Since this statement only looks at ten of the possible sixteen playoff spots the prediction is only 62.5% accurate - or leaves 37.5% of the playoffs teams unexplained.  For statisticians this is a large error."  Now the error is compounded with three of the teams in the top ten of payroll not making the playoffs, which is a forecast error of 30%!

As we have written in The Wages of Wins, relative payroll is not a good predictor of team performance in the sense that it does not have a lot of commonality between the two variables.
Here is a look at the statistical relationship between NBA payroll and NBA regular season performance over different time periods.

Since the 2004/05 NBA season (i.e. the last decade) the relationship between relative payroll and regular season performance is statistically significant (95% level), but relative payroll only "explains" 7.2% of the variation in regular season performance (which is statistically called r-squared) adjusted for heteroskedasticity in the data (unequal scatter).  If we look at the adjusted r-squared that falls slightly to 6.9%.

Taking the time period of Mrs. Dosh (2011/12 to now) the statistical relationship between relative payroll and regular season performance is statistically significant (95% level) and the amount that relative payroll is in common with regular season performance is higher with an r-squared of 0.188 and an adjusted r-squared of 0.179.  Still relative payroll misses over 80% of the variation in regular season performance.  I will let you decide if that is a good predictor or not.

Finally, just taking this season into account, now the statistical relationship between relative payroll and regular season team performance is statistically insignificant at the 95% level.  Meaning from a statistical viewpoint that payroll is NOT related to team regular season performance.

Wednesday, April 16, 2014

NHL Regular Season Goalie Performance for 2013-14

For the past few years I have been looking at NHL goalies and evaluating their regular season performance. So now that the 2013/14 NHL regular season is in the books, let's look at NHL goalie performance using our NHL goalie measure called Wins Above Average.  For those interested in how I calculate this measure, here is a step-by-step guide to measure WAA.  As mentioned in the previous link, I will need a measure of the impact that goals against has on team points, and for the 1995 to 2013 NHL regular seasons, this is equal to -0.340858.

So who is the best NHL goalie for the regular season?  Tuukka Rask, followed very closely by Semyon Varlamov.  Here are the top 20 goalies this season ranked by WAA.

Player Team
1 Tuukka Rask BOS
2 Semyon Varlamov COL
3 Carey Price MTL
4 Ben Bishop TBL
5 Jonathan Bernier TOR
6 Sergei Bobrovsky CBJ
7 Cam Talbot NYR
8 Josh Harding MIN
9 Anton Khudobin CAR
10 Henrik Lundqvist NYR
11 Alex Stalock SJS
12 Martin Jones LAK
13 Jaroslav Halak STL, WSH 1.692
14 Ben Scrivens LAK, EDM 1.677
15 Kari Lehtonen DAL
16 Roberto Luongo VAN, FLA 1.399
17 Cory Schneider NJD
18 Chad Johnson BOS
19 Ryan Miller BUF, STL 1.338
20 Frederik Andersen ANA

Tuesday, April 15, 2014

NHL Pay and Performance

Yesterday I blogged about competitive balance in the NHL, and today I want to extend that to take a look at pay and performance in the NHL during the regular season.  Recently a new website has emerged which focuses on the payroll cap in the NHL, called  It is excellent and I know of no better website for salary and team payroll information on the internet.  So, I am going to use their information to estimate the relationship between regular season payroll and regular season performance from the 2009/10 NHL regular season to the 2013/14 regular season.

To do that, I will run a linear regression on relative payroll and team points (team performance measure).  For those interested, here is a step-by-step guide as to how to do this yourself.  You may be wondering why I use relative payroll and why I am focusing on the statistical measure called r-squared.  I answer (or link) to those directly below.

Why relative payroll?  This is for statistical purposes, but simply stated - the average of team payrolls are rising over the time period and the average of team performance is remaining relatively constant.  So if you just take a look at payroll and performance you are comparing a variable that is increasing to one that is constant (or stationary) and you will get a lower statistical relationship that what is truly taking place.  In fact the correlation coefficient (called r) between payroll and performance falls dramatically over this time period as opposed to the coefficient of determination (r-squared).  For this time period, for payroll and performance r = 0.034 while for relative payroll and performance r = 0.235, and thus for payroll and performance r-squared = 0.001 and for relative payroll and performance r-squared = 0.055.

Why do I use r-squared?  I have answered that here.

So, what is the relationship between team relative payroll and team regular season performance?  For the the 2009/10 NHL season to the 2013/14 NHL regular season that I have data from capgeek, relative payroll is statistically significant (at the 99% confidence level) with respect to team points. Yet, in terms of the common variation between the two variables, there is not much with the R-squared = 0.055.  If I include payments of long-term injured reserve and also include bonuses, the r-squared actually decreases.  Thus relative payroll "explains" less than 6% of NHL team regular season performance since 2009/10.

Hence, I conclude that NHL regular season team payrolls are not a good indicator of NHL regular season performance.

Monday, April 14, 2014

NHL Competitive Balance

With the 2013-14 NHL regular season in the books, let's take a look at how competitively balanced the season was (using the Noll-Scully measure of competitive balance) and compare this with recent seasons.

There are two ways of measuring competitive balance in hockey since unlike baseball or basketball, hockey games can end up tied at the end of regulation.  So I will report both the binomial and the trinomial Noll-Scully measure.  Additionally, there are two ways of reporting both the binomial and trinomial Noll-Scully measure:  one using the standard deviation of a sample and the other using the standard deviation of the population.  Again, I will report both.

Additionally, I will have to compute (for the trinomial distribution) the probability of a tie under equal playing strength.  In the past, I used Richardson's estimate from Stanley Cup playoff games.  In this case I will change and just assume that the probabilty of games that go into overtime occurs among teams with equal playing strength.  Feel free to quibble with this, as this is simplification of the estimated probability.  For transparency, I will also report for each season this probability estimate.

OK, with the measurement details noted, here are the Noll-Scully competitive balance numbers for the last NHL season.  The first table used the binomial measure and the second table uses the trinomial measure.    The first column of numbers uses a sample standard deviation and the second column uses the population standard deviation. 

Binomial Distribution Sample Population
Standard Deviation of Winning Percent = 0.093023 0.091459
Average of Winning Percent = 0.5624 0.5624
Square root of Games Played = 9.055385 9.055385

Noll-Scully Measure of Comp. Balance = 1.497792 1.472617

Trinomial Distribution Sample Population
Richardson EEJ 2000

Idealized Standard Deviation= 0.047192 0.047192
Probability of a Tie = 0.269512 0.269512
Number of Games Played = 82 82
Noll-Scully Measure of Comp. Balance = 1.971147 1.938017

Compared to recent years, this year was less competitive balanced, but overall the level of competitive balance in the NHL is still rather similar to recent historical numbers.

Wednesday, April 2, 2014

World Cup and Economic Impact

Moody's forecasts that the World Cup will not have a large economic impact.  While there will be lots of tourists generating economic activity, there will also be a decline in economic activity that normally takes place to offset the gains.  Sports economists have found this same result numerous times here in the US.