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Percentage efficiency of a rato

  1. #1
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    Percentage efficiency of a rato

    Hi Guys,

    I am new to the forum so please be gentle !!!!

    I am looking for a way to work out the percentage of a ratio

    If i require 100 GB data and get a compression ratio of 2:1 then I only require 50 GB of disk.
    However if the compression effectiveness is only 50% (1:1) then I would require 100 GB of disk. However this should be 0% = 1:1

    Can anybody help with an equation to work this out.

    Many Thanks in advance

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    Re: Percentage efficiency of a rato

    I doubt this is very difficult, but I think before we make this an Excel question, we need to make it a math question. Can you explain exactly how you are defining "compression ratio"? Wikipedia http://en.wikipedia.org/wiki/Data_compression_ratio defines compression ratio as

    compression ratio=compressed size/uncompressed size

    It appears to me that you are using a different definition. Maybe you want the quantity Wikipedia calls "space savings"?

    space savings=1-compression ratio=1-50/50=0

    Or maybe you are using some other definition of compression ratio. I expect, once we understand how you want to define these terms, the equation for calculating them should become apparent.
    Quote Originally Posted by shg
    Mathematics is the native language of the natural world. Just trying to become literate.

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    Re: Percentage efficiency of a rato

    Hi,

    I am trying to create a formula to work out the data size based on the effectiveness of the compression ratio. We have some tape drives that backup data and they can get up to 2:1 compression ratio,however, you can never get the full 2:1 in reality. So if i assume that the compression will only be 80% efficient, then how much tape capacity do i need to provide.

    compression ratio = compressed size / uncompressed size

    If I say its only 50% efficient, then I get the same as the original value, 50% of 2:1 is 1:1, therefore the same, however I think it should be 1.5:1

    Cheers

    Richard

    2:1 = 100 GB / 50 GB.

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    Re: Percentage efficiency of a rato

    I see an inconsistency: you define compression ratio (CR) as compressed size/uncompressed size, but you list your "best" compression ratio as 2:1 (suggesting that the compressed file is twice as large as the original???). I think you mean that your "best" compression ratio is 1:2 or 1/2 or 0.5 or 50%.

    There appears to be another quantity that needs to be defined -- efficiency. How are you defining efficiency?

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    Re: Percentage efficiency of a rato

    Sorry, yes you're right, compression ratio = uncompressed size / compressed size.

    Many thanks for your reply. I am sure I am making this more complicated than it really is .

    I am not trying to work out the compression ratio as am providing this. I know a certain type of tape drive can compress the data @ 2:1 (others are different), but I know in reality that you never get the full 2:1, so I want to use the efficiency of the compression as a percentage. I then want to work out how much data this will actually be.

    So if I have 100 GB of data. If I back it up and get a compression ratio of 2:1 then it will require 50 GB of tape capacity. However if I only get (say 80% efficiency) of the 2:1, then how much is the tape capacity. The problem I am having is that if I assume 50%, then this is coming out at 1:1 which is 100 GB. What I want is 0% to be 1:1 and 100% to be 2:1. I am trying to work out a formula express this for any compression ratio and efficiency factor that I supply in the equation.

    Cheers

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    Re: Percentage efficiency of a rato

    I'm a firm believer that we must first understand the math before we can really put something into Excel. At this point, it appears to me that you are still trying to figure out how to define efficiency. Preface these remarks -- I am not an expert, so I don't know if experts in this field would use this same definition of efficiency. Here's a way to define efficiency that makes sense to me. Basically it is a simple proportionality.

    1) bestefficiency = 1, worstefficiency=0, bestCR=1/2, worstCR=1, actualCR=compressedsize/uncompressedsize.
    2) proportionality formula (bestefficiency-worstefficiency)/(bestCR-worstCR)=(actualefficiency-worstefficiency)/(actualCR-worstCR)

    From this formula, you can enter the actualefficiency you expect to see and solve for actualCR -- from which you can estimate how much storage you need to provide. Or you can put in the actualCR you are getting, and solve for actualefficiency to get a measure of efficiency.

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