The Sigil
Mr. 3000 (Words per post)
As far as calculating loss, I think it's HIDEOUSLY difficult to come up with an actual loss amount, even given "X users at Y IP addresses opened a book Z times."
The problem comes into play because you have to consider the supply-demand curve. Yes, 1200 unique IP addresses obtained the book and use it on a regular basis... but they obtained it from a skewed curve where the price was zero. Remember that the number of people who will obtain something usually increases as price point goes down.
I'm going to ignore the supply curve for a moment and look at the demand curve. For a simple curve, let us assume we have some Product X. If P is the price in dollars, the number of people willing to buy Product X might be:
1000 - (100 x P). Thus, if P is $1, the number of buyers is 900 (and the publisher could rake in 900x$1 or $900). If P is $2, the number of willing buyers is 800 ($1600). And so on.
Obviously, the "sweet spot" here would be $5... the publisher has 500 people willing to pay $5 each for a profit of $2500.
However, if the product were made available for free, the publisher would have 1000 people willing to pay $0 each.
Let us make a very optimistic assumption and say that the publisher prices it at $5 and every single person willing to buy it at that price does so (buys it legally). The publisher makes $2500. The publisher also notices that an additional 500 people obtain illicit copies for free (to bring the total to the 1,000 people who would be willing to buy the product for free). Does the publisher have a loss on his hands? No... because the 500 people who downloaded it for free would not have purchased it at $5.
However, let us assume the publisher prices it at $5 and 300 people pay full price and 700 people, including 200 who would be willing and able to pay that $5 but of course like the $0 price better, download it. Now he is out $1000, because that's 200 lost sales.
But suppose the curve looks instead like this: 1000 - (28 x P^2)? In picking a $5 price point, your sales will drop to 300 instead of 500. (Assuming one dollar increments for P, the publisher on this curve should have guessed $3, which would yield 748 sales and $2244).
But the fundamental question is, how do you know that 1000 - (100 x P) represents your price curve? What if is it is actually 1000 - (28 x P^2)? In other words, if you have 300 sales and 700 pirates, how do you know if there are 0 potential buyers who resorted to piracy or 200 potential buyers who resorted to piracy? The answer is - you CAN'T.
This is a point I think Dana is forgetting (it's also the point the RIAA keeps missing) - nobody knows the formula in real life for the demand curve of Product X! In Ralts case, he has but two data points... the number of legitimate sales at a price point Y and the total number of "sales" at a price point of zero. Since we cannot be sure the curve is simple (it might be logarithmic, it might be a square function, etc.) we cannot meaningfully interpret what the total lost sales are.
Let me repeat that... because we do not know the function that defines the demand curve, we cannot meaningfully intepret total lost sales. We can guess. We can rave. But because we don't know what the demand curve looks like, it's just that... guessing.
In fact, I think just about the only chance we have to find a demand curve is to conduct an experiment where we somehow "exclude" piracy from the equation entirely and offer the item for, say, $10... then when sales peter off, lower the price to $9... then to $8... etc. so we get data for each price point, which allows us to plot the curve properly and get a better guess on what the underlying formula is.
Of course, since we CANNOT exclude piracy, we cannot get a meaningful number set through this method... by the time the price gets down to $8, some piracy has likely already occurred among those who would pay $3.
The only other chance a publisher has is to perhaps conduct a large poll among their buyers... perhaps on a free product, since that should have a high legitimate penetration to potential buyers, regardless of their favored price point... "what is the highest price you would have paid for this work?" and try to figure out the data accordingly.
Until we see some data that represents CURVES, rather than just two data points, we're just going to have guesswork with numbers that can't be meaningfully interpreted.
--The Sigil
The problem comes into play because you have to consider the supply-demand curve. Yes, 1200 unique IP addresses obtained the book and use it on a regular basis... but they obtained it from a skewed curve where the price was zero. Remember that the number of people who will obtain something usually increases as price point goes down.
I'm going to ignore the supply curve for a moment and look at the demand curve. For a simple curve, let us assume we have some Product X. If P is the price in dollars, the number of people willing to buy Product X might be:
1000 - (100 x P). Thus, if P is $1, the number of buyers is 900 (and the publisher could rake in 900x$1 or $900). If P is $2, the number of willing buyers is 800 ($1600). And so on.
Obviously, the "sweet spot" here would be $5... the publisher has 500 people willing to pay $5 each for a profit of $2500.
However, if the product were made available for free, the publisher would have 1000 people willing to pay $0 each.
Let us make a very optimistic assumption and say that the publisher prices it at $5 and every single person willing to buy it at that price does so (buys it legally). The publisher makes $2500. The publisher also notices that an additional 500 people obtain illicit copies for free (to bring the total to the 1,000 people who would be willing to buy the product for free). Does the publisher have a loss on his hands? No... because the 500 people who downloaded it for free would not have purchased it at $5.
However, let us assume the publisher prices it at $5 and 300 people pay full price and 700 people, including 200 who would be willing and able to pay that $5 but of course like the $0 price better, download it. Now he is out $1000, because that's 200 lost sales.
But suppose the curve looks instead like this: 1000 - (28 x P^2)? In picking a $5 price point, your sales will drop to 300 instead of 500. (Assuming one dollar increments for P, the publisher on this curve should have guessed $3, which would yield 748 sales and $2244).
But the fundamental question is, how do you know that 1000 - (100 x P) represents your price curve? What if is it is actually 1000 - (28 x P^2)? In other words, if you have 300 sales and 700 pirates, how do you know if there are 0 potential buyers who resorted to piracy or 200 potential buyers who resorted to piracy? The answer is - you CAN'T.
This is a point I think Dana is forgetting (it's also the point the RIAA keeps missing) - nobody knows the formula in real life for the demand curve of Product X! In Ralts case, he has but two data points... the number of legitimate sales at a price point Y and the total number of "sales" at a price point of zero. Since we cannot be sure the curve is simple (it might be logarithmic, it might be a square function, etc.) we cannot meaningfully interpret what the total lost sales are.
Let me repeat that... because we do not know the function that defines the demand curve, we cannot meaningfully intepret total lost sales. We can guess. We can rave. But because we don't know what the demand curve looks like, it's just that... guessing.
In fact, I think just about the only chance we have to find a demand curve is to conduct an experiment where we somehow "exclude" piracy from the equation entirely and offer the item for, say, $10... then when sales peter off, lower the price to $9... then to $8... etc. so we get data for each price point, which allows us to plot the curve properly and get a better guess on what the underlying formula is.
Of course, since we CANNOT exclude piracy, we cannot get a meaningful number set through this method... by the time the price gets down to $8, some piracy has likely already occurred among those who would pay $3.
The only other chance a publisher has is to perhaps conduct a large poll among their buyers... perhaps on a free product, since that should have a high legitimate penetration to potential buyers, regardless of their favored price point... "what is the highest price you would have paid for this work?" and try to figure out the data accordingly.
Until we see some data that represents CURVES, rather than just two data points, we're just going to have guesswork with numbers that can't be meaningfully interpreted.
--The Sigil
Last edited:
