One of the many shortfalls of NBA play by play data is that there is little effort given to differentiating between types of shots leading to the drawing of shooting and penalty free throws. In the unusual event of an “and one”, the shot type can typically be determined and the number of free throws [...]
It has been long known that not all assists are created equal, but most common metrics do not account for any difference in anticipated value. As my article on Offensive Statistical Plus Minus indicates, assists on close shots tend to be about 5 times more valuable than assists on jump shots. As a continuation of [...]
In my previous post I used basic box score statistics to estimate assisted% according to shot location. As a continuation of that train of thought, I am now using statistics gathered from play by play data to estimate missed “created (unassisted) shots” and “potentially assisted shots” (which I will only refer to as assisted hereafter) [...]
Advanced/detailed statistics such as assisted% on close field goals, 2 point jump shots and three point shots can significantly improve the accuracy of measuring player value. However, most levels of play other than the NBA do not offer that level of data. In order to account for this, I will create reasonable approximations for these [...]
What causes home court advantage? Is it travel, rest, referee bias, encouragement or something else? Can anything be done to increase home court advantage? Whenever I attend a game the Phillies win, my grandfather’s response is typically something to the effect of “We need to get you to more games”. Although his comment is [...]
Since on court/off court or plus/minus data has become publicly available over the past few years, an important estimate of a player’s value has been adjusted plus-minus. For one of many explanations of the idea behind using adjusted plus minus, take a look at this article:
http://www.82games.com/ilardi1.htm
Adjusted plus minus takes away many bias’ that normal plus minus does not. If Derek Fisher plays most of his minutes with Kobe Bryant and Pau Gasol, he will typically have a great plus minus, but if his team struggles when they are removed, he could have a terrible adjusted plus minus. If Manu Ginobili plays against predominantly second stringers, that will be accounted for in adjusted plus minus, but not standard plus minus. Even home court is factored in the results. However, in addition to the well documented high standard errors of these estimates (another statistical term), there are a few inherent bias’ in this measurement. Possibly, the most significant of these factors is that certain points in games are more important than others. I have heard others reference this adjustment, but haven’t seen their methods yet, so I will discuss mine.
How many times have you heard “Kobe couldn’t have won the championship with Gasol”, “Lebron’s team would be a lottery pick without him” or “Teams always play better without Marbury” (or counter arguments)? Clearly most of these statements don’t seem easy to assess. Even if we can agree how many points a player creates and [...]
In many ways, defense has always been the primary weakness of statistics in basketball (and many other sports for that matter). Many important defensive aspects are very inadequately measured. There have been strides toward creating statistics that would better measure impact on the defensive end of the floor, but few of these are publicly available in large quantities. Plus-minus numbers are good, but the most unbiased of these figures, adjusted plus-minus, is highly variable and it is difficult to assess value with much accuracy based on limited data.
The problems with current box score statistics are obvious. The longest standing defensive statistic, fouls, is valued as negative in some formulas, such as PER, but is clearly the best option in some situations. Steals and blocked shots are good statistics that indicate defensive value, but they can often merely reflect high risk, high reward actions. Most importantly, blocks and steals account for less than 12 plays per team per game on the average NBA team. A team cannot decide who they want to “use” on defense as effectively as they can on offense, thus all 5 players have assignments on nearly every play. Thus, if a team has 12 blocks and steals on 100 defensive possessions per game and, if we assume that fouls have no significant positive or negative impact (on average), this means that a player’s impact is not measured in 488 out of 500 defensive possessions, or nearly 98% of the time. Measuring defense by blocks and steals is as silly as rewarding cornerbacks trips to the pro bowl based on the number of interceptions they accumulate. Wait a second… I think that is how cornerbacks earn a pro bowl berth. Perhaps it is best to visually determine who the best players are. This way, the experts can come to a consensus and reputation will determine who is valuable defensively. Of course, Rafael Palmeiro once won a Gold Glove based on expert reputation when the general managers decided he was the most valuable defensive first baseman in the AL despite only playing 28 games at first and being designated hitter the other 135 games he played. Basketball is also clearly not immune to relying too heavily on reputation when assessing defensive value.
A few years ago, Dan Rosenbaum has used statistical models to estimate adjusted plus/minus. These results and relevant discussion can be viewed at the following sites:
http://www.82games.com/comm30.htm
http://sonicscentral.com/apbrmetrics/viewtopic.php?t=327&highlight
Dan’s second model used data from the 2002-2003 through the 2004-2005 seasons in this model. The following models use data from the 2005-2006 through the 2007-2008 seasons.
For those of you who are unfamiliar with the term, adjusted plus minus is a statistical estimate using regression analysis with each player (above a certain threshold of minutes played) as a variable. The regression model uses the estimates of each player variable that produce the smallest difference between expected margin and the actual margin in the matchups for the year(s) measured. The great thing about adjusted plus minus is that it is an unbiased estimate of player value accounting for home/away, opponent strength and teammate strength (plus other variables if you want). However, it has a high standard error and can be unreliable at times. Statistical plus minus (SPM)can be a good proxy for adjusted plus minus. Statistical plus minus assigns coefficients/weights to statistical terms such as assists and steals so that the corresponding statistical plus minus’ resulting from the model have the lowest average errors (mean residuals).
Most advanced statistics come up with an approximation of points and wins created or above replacement. However, few statistics account for the thing that almost all teams consider most important – championships. Now, clearly anyone who suggests that Robert Horry is the best player in the NBA over the last 31 years just because he participated on the most championship teams should not be considered a credible source; but no estimate of career value should be complete without analyzing the ultimate goal. Expected Championships Added (ECA) and Mean Expected Championships Added (MECA) account for the differences in the distributions of points added and championships added. I do realize that there are many other factors such as making money (for many, this is probably the true goal), respectability, as well as having long-term relevance with a fan base; but winning the title is the driving force and the culminating focus of the sport.
ECA is simply the difference between the expected number of team wins based on basketball’s Pythagorean expectation and the number of expected team wins, again using a Pythagorean estimate, after removing the estimated effect of each respective player. A player’s value of points and wins added was estimated using advanced statistical plus minus (or statistical plus minus before 2005-06).