In my last post I complained about efficiency not being discussed enough by NBA announcers and commentators. I pointed out that some of the best scorers have relatively low FG% or TS%. However, via the comments it was pointed out that top scorers need to take more difficult shots and thus are expected to have lower efficiency. The plot below (made with this R script) seems to confirm this (click image to enlarge) . The dashed line is from regression and the colors represent guards (green), forwards (orange) and centers (purple).

Among this group TS% does trend down with points per game and centers tend to have higher TS%. Forwards and guards are not very different. However, the plot confirms that some of the supposed all time greats are more ball hogs than good scorers. 

A couple of  further observations. First, Adrian Dantley was way better than I thought. Why isn’t he more famous? Second, Kobe is no Jordan. Also note Jordan played several seasons past his prime which lowered his career averages. So I added points for five of these players using only data from their prime years (ages 24-29). Here Jordan really stands out. But so does Dantley! 

pd - Note that these plots say nothing about defense, rebounding, or passing. This in-depth analysis makes a convincing argument that Dennis Rodman is one of the most valuable players of all time.

where N_platters is the number of platters on the spindle, Ω is the rotational speed in revolutions per minute (RPM) and D_platter the platter diameter in inches. The electrical power is then measured in Watts. The good news is that all of the variables in (1) can be read off from the data sheet of the respective disk vendor^†. In principle, this makes it very valuable for doing green storage capacity planning. Note that the disk capacity, e.g., GB (the usual capacity planning metric) does not appear in (1).

The outstanding question is: where do those funny non-integral exponents come from?

Theoretical Justification

1. Factorize the exponential factors as: (Ω³ × D³) × D²
2. D² factor comes from the area of the rotating platter
3. Ω × D/2 is the angular speed v at any point on the platter
4. The reason it appears as v³ comes from two additional contributions
5. A v² contribution comes from the Bernoulli pressure of the air on the rotating platter
6. The other v factor comes from converting the pressure (force per unit area) to power (force through distance moved per unit time)

I've published the theoretical details on arXiv. Now, let's look at an example of how you might use this result as part of trying to meet green power requirements in your data center.

Disk Sizing Example

The other benefit of this approach comes from any disk specs that are the same between "old" and "new" devices. They will cancel each other out and thereby contribute a simple unit factor.

Suppose you currently have Hitachi Deskstar P7K500 3.5 inch drives that spin at 7200 RPM and consume 10.9 Watts. You'd like to use (2) to determine the impact on your power budget of going to Western Digital Caviar GP 3.5 inch drives which have variable speed between 5400 and 7200 RPM; we'll assume an average rotational speed of 6000 RPM. Both HDD models have N = 2 platters.

We can conveniently write (2) as an R function:

dkpwrnew <- function(dknew, dkold) {
 nrat <- dknew[1]/dkold[1]
 wrat <- dknew[2]/dkold[2]
 drat <- dknew[3]/dkold[3]
 return(dkold[4] * nrat * wrat^2.8 * drat^4.5)
}

> dWDigital <- c(2, 6000, 3.5)
> dkHitachi <- c(2, 7200, 3.5, 10.9)

> dkpwrnew(dWDigital, dkHitachi)
[1] 6.542128

1 Introduction

“The 3.11 Tohoku Earthquake in Japan”, It did serious damage to Japan. I have attempted gaining deeper a understanding of seismic activity after showing “Japan Quake Map” on R-bloggeres. This posting is a summary about earthquakes in Japan on 2011.

2 Japan Quake Map

The movie of “Japan Quake Map 2010-2011″ was updated on Youtube. Sampling period is from Jan 1, 2010 through Dec 31, 2011. Data source is website of Japan Weather Association.

3 Histogram

The following is a daily histogram about earthquakes in Japan from Jan 1, 2010 through Dec 31, 2011.

4 Scattergram

The following is three-year scattergram animation about earthquake in the year 2009, 2010 and 2011. The animation was created with R, ggplot2 and ImageMagick. Click on image for full size image.

5 Gutenberg-Richter law

The following is a Magnitude-Frequency distribution about earthquakes in Japan from January 1885 through December 2011. Number of samples is 42870. This dataset is included only data bigger than Magnitude 4.0.

6 Predict

After “The 3.11 Tohoku Earthquake”, Seismological Society of Japan admitted defeat because they couldn’t predict it and prevent serious damage.
On the other hand, A professor at University of Tokyo announced that they have estimated a 70 percent chance of a magnitude 7.0 earthquake occurring directly beneath Japan’s capital city of Tokyo within 4 Years.(souce : DAILY YOMIURI ONLINE)
But many people are skeptical about that. Anyway, I hope that valuable prediction models will be developed as soon as possible.

7 Gratitude

I’d like to introduce two website below, if you kindly wish to send your donations.
First is Japanese Red Cross Society.
Second is Google Crisis Response.
I’d like to express our thanks to all of you for helping us.

My Paris colleague (and fellow-runner) Aurélien Garivier has produced an interesting comparison of 4 (or 6 if you consider scilab and octave as different from matlab) computer languages in terms of speed for producing the MLE in a hidden Markov model, using EM and the Baum-Welch algorithms. His conclusions are that

• matlab is a lot faster than R and python, especially when vectorization is important : this is why the difference is spectacular on filtering/smoothing, not so much on the creation of the sample;
• octave is a good matlab emulator, if no special attention is payed to execution speed…;
• scilab appears as a credible, efficient alternative to matlab;
• still, C is a lot faster; the inefficiency of matlab in loops is well-known, and clearly shown in the creation of the sample.

(In this implementation, R is “only” three times slower than matlab, so this is not so damning…) All the codes are available and you are free to make suggestions to improve the speed of of your favourite language!

The above map (and this one) was produced using R and ggplot2 and serve to demonstrate just how sophisticated R visualisations can be. We are used to seeing similar maps produced with conventional GIS platforms or software such as Processing but I hadn’t yet seen one from the R community (feel free to suggest some in the comments). The map contains three layers: buildings, water and the journey segments. The most challenging aspect was to change the standard line ends in geom_segment from “butt” to “round” in order that the lines appeared continuous and not with “cracks” in, see below.

I am grateful to Hadley and the rest of the ggplot2 Google Group for the solution. You can see it here. From this point I layered the plots using the geom_polygon() command for the buildings and water bodies and my new function geom_segment2() for the journey segments- these were simply the start and end latitudes and longitudes for each node in the road network and the number of times a cyclist passed between them.