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eBA Encyclopedia Statistics Terminology: Heat Map

2011-08-01T18:33:00+00:00

A heat map is a graphical representation of data where the values taken by a variable in a two-dimensional map are represented as colors. A very similar presentation form is a tree map. The term is also used to mean its thematic application as a choropleth map.

There are several different kinds of heat map:

• Web heat maps have been used for displaying areas of a Web page most frequently scanned by visitors.

• Biology heat maps are typically used in molecular biology to represent the level of expression of many genes across a number of comparable samples (e.g. cells in different states, samples from different patients) as they are obtained from DNA microarrays.

• The tree map is a 2D hierarchical partitioning of data that visually resembles a heat map.

• A mosaic plot is a tiled heat map for representing a two-way or higher-way table of data. As with treemaps, the rectangular regions in a mosaic plot are hierarchically organized. The means that the regions are rectangles instead of squares. Friendly (1994) surveys the history and usage of this graph.

Image: Information Aesthetics

Each NBA Basketball Team Heat Map shows who was coaching the basketball team that year, who were the top offensive players on the team, and by how many possessions each team won or lost over a 5 year period.

The overall goal of the charts is to be able to observe how time, coaches and players create point spread trends. Win percentage paints a narrow picture of how key personnel react to being put into different game situations. Year-over-year trends may help people see why their team is gaining or losing ground to the competition.

Each color is a point range that the team won or lost by in that year. Green to red bars are wins, while blues are losses. The lower area provides team information for each year. The right bar shows the average share of games won ad lost by each 3-point range over the last 5 year in the NBA.

One of the discovered insights is how certain teams and coaches are more likely to win by 3 or fewer points than they lose by the same margin.

Prof. Roberto Azar
© Copyright 1998-2011 eBA-Stats.com®

FTA and PF at Season and Playoffs

2011-07-20T14:58:00+00:00

"... Are there at the eBA Basketball Statistics Analysis System Archives any statistical record of FTA and Personal Fouls inconsistencies during regular season games and playoff games ?
My real question is at what point does the deviation between fouls called on two teams become statistically outside the domain of convention ?

In like manner, is there a point where the difference with some standard measurements becomes so great that it is so statistically improbable that it is an indicator of a game refereed clearly in the favor of one team ?

This is a good topic when the media is demanding an unfairly behaviour of certain basketball officials... "

Photograph: refusuck.blogspot.com

Applying the information available from box scores, with the crew of 3 officials included, using 18 years quality of data, we found nothing at the eBA Basketball Statistics Analysis System Archives. No individual official, as a factor in the crew of 3 model, had an important effect on the number of FTA and Personal Fouls in a game.

Some other numbers seem to link fouls called to single officials, rather than the crew of 3 officials we had to use in our model. Concentrating on single officials would make bigger the power of any analysis, for sure, but I still consider unlikely that the results would be statistically significant.

Prof. Roberto Azar
© Copyright 1998-2011 eBA-Stats.com®

"Up To The Line" Concept & Possessions

2011-07-19T14:14:00+00:00

At the NBA is employed a system by which every missed free throw results in either an individual rebound or a team rebound making that= individual rebounds + team rebounds= missed field goals + missed free throws, with the intention to match every missed shot with a rebound of some kind, providing a two=way check on the scoresheet to make sure that missed shots and rebounds are accurately accounted for.

On the contrary, with reference to this discussion, the eBA System prefers the use of the concept UP TO THE LINE.

In a previous message I stated: "... A typical formula to calculate the basketball possessions is:

Possessions=FGA Field Goals Attempted - OR Field Goals Attempted +TO Field Goals Attempted +0.4* Free Throws Attempted

In those traditional statistics systems, because two free throws do not always equal one possession (for example, in some situations one or three free throws may be awarded), they employs the multiplier 0,44 ( and sometimes 0,5 ) for free throws attempted, which is not always exact.

Photograph: Eli Lucero for Le High Valley Live

The eBA Basketball Statistics Analysis System looking for exactness, register the real number of times the team reached the line for 2 or 3 free throws with the concept UP TO THE LINE, remarking between parenthesis the number of times the last throw was MADE.

With regard the rebounds, it is referred only to possessions, that's means the eBA Basketball Statistics Analysis System doesn't register a rebound in the first of two or three, or second of three free throws as related above. ..."

Therefore, it is not possible to calculate absolutely the possessions using the box score data, because, in the midst of other argues studied in the eBA Basketball Statistics Analysis System, possessions-ending free throws are not recognized in the box scores (read here this thread about the .44 factor and the eBA System), some quarters bring to an end with offensive rebounds without follow-up shots, and not all rebounds are credited in box scores (read here the thread about the 'Extra Possessions at the end of the Quarters').