Weissman score


The Weissman score is a fictional efficiency metric for lossless compression applications. It was developed by Tsachy Weissman, a professor at Stanford University, and Vinith Mishra, a graduate student, at the request of producers for HBO's television series Silicon Valley, a television show about a fictional tech start-up. It compares both required time and compression ratio of measured applications, with those of a de facto standard according to the data type.
The formula is the following; where r is the compression ratio, T is the time required to compress, the overlined ones are the same metrics for a standard compressor, and alpha is a scaling constant.
Weissman score was used in Dropbox Tech Blog to explain real-world work on lossless compression.

Example

This example shows the score for the data of Hutter Prize, using the paq8f as a standard and 1 as the scaling constant.
ApplicationCompression ratioCompression time Weissman score
paq8f5.4676003001.000000
raq8g5.5149904200.720477
paq8hkcc5.6825933001.039321
paq8hp15.6925663001.041145
paq8hp25.7502793001.051701
paq8hp35.8000333001.060801
paq8hp45.8688293001.073383
paq8hp55.9177193001.082325
paq8hp65.9766433001.093102
paq8hp126.1042765400.620247
decomp86.2615745400.63623
decomp86.2762955400.637726

Limitations

Although the value is relative to the standards against which it is compared, the unit used to measure the times changes the score. This is a consequence of the requirement that the argument of the logarithmic function must be dimensionless. The multiplier also can't have a numeric value of 1 or less, because the logarithm of 1 is 0, and the logarithm of any value less than 1 is negative ; that would result in scores of value 0, undefined, or negative.

Examples