First post. WARNING: LOTS OF MATH

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I've been lurking in these forums for a while now (for those that wander by at eproductwars, I post over there as "Jim"), and thought this would be a good time for me to chime in with some analysis.

I was looking at Grubert's post in the main HD Media forum and thought that juggling some numbers would be an amusing way to spend an hour or so:

Can some of the more math-minded people here check my math? It's late and I'm tired so it's very possible I've made a mistake, but I "think" this is right...

VideoScan + PC Magazine data
Day Week YTD SI
01/07 63.3/36.7
01/14 68.2/31.8
01/21 67.8/32.2 66.4/33.6 45.1/54.9
01/28 68.8/31.2 67.0/33.0 46.7/53.3

Let A = BR discs since inception on 1/21
Let B = HD discs since inception on 1/21

We know A = B x .8230

Let C = BR discs since inception on 1/28
Let D = HD discs since inception on 1/28

We know C = D x .8776

Let E = # of BR discs sold between 1/21 and 1/28
Let F = # of HD discs sold between 1/21 and 1/28

We know that A + E = C, and B + F = D
(Old discs since inception + sales for past week = new discs since inception)

We know that E = 68.8/31.2 F = 2.205F

So doing some fun and amusing algebraic replacement we get:

A + E = C
.8230B + 2.205F = .8776D

Reverse this equation and we get

.8776D = .8230B + 2.205F
D = (.8230B + 2.205F)/.8776 = .9378B + 2.513F

But we also know that B + F = D

B + F = .9378B + 2.513F

.0622B = 1.513F
B = 1.513F/.0622 = 24.32F

If my calculations here are correct, that means that around 1 in 24 of all HD-DVD discs sold since inception were sold between 1/21 and 1/28.

Doing the same analysis for Blu-ray yields:

B + F = D
A/.8230 + E/2.205 = C/.8776

Reverse equation

C/.8776 = A/.8230 + E/2.205

C = (A/.8230 + E/2.205) x .8776 = 1.066A + .3980E

We know A + E = C so...
A + E = 1.066A + .3980E
.6020E = .066A

EDIT: My math WAS wrong... here. Blu-ray numbers were off because I did this last division wrong.
Original text (incorrect):
A = .6020E/.066 = 10.48

This means that Blu-ray sold a bit under 1/10th of all of its discs in the week between 1/21 and 1/28.
Corrected values:
A = .6020E/.066 = 9.12

This means that Blu-ray sold a bit under 1/9th of all of its discs in the week between 1/21 and 1/28.

Does this make any sense, or have I made a mistake somewhere?


Jim

If my calculations here are correct, that means that around 1 in 24 of all HD-DVD discs sold since inception were sold between 1/21 and 1/28.
...
This means that Blu-ray sold a bit under 1/10th of all of its discs in the week between 1/21 and 1/28.

Does this make any sense, or have I made a mistake somewhere?I haven't looked at the math, but those seem like very reasonable numbers to me given the info we have. The ratios between them and the percentages of the total (basically the total for Blu-ray being about 2.5 months worth of sales at the rate of the week ending the 28th and for HD DVD being about 5.5 months worth of sales at their rate for that week) seem reasonable.

--Darin

UPDATE:
I'm currently working on calculating for new values posted by Grubert for 2/4. Looking back at my sleep-deprived calculations, I came across a math error (corrected above as shown).

I'll have some interesting figures to show shortly, and will edit this post (hopefully) if I can project the weekly sales for 2/4 from the known values.

Here is an extension of my analysis.

VERY long story short:

EDIT: Fixed some math errors I made while half asleep.


Weekly sales for 2/4/07:
Blu-ray 100
HD-DVD 45

Adjusted percentages 2/4/07
Blu-ray 69.0
HD-DVD 31.0


I think with this information, it is actually possible to project the relative sales of BD and HD discs from here on in as long as the numbers remain consistently reported (!).

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Proof of work:

Day Week YTD SI
01/21 67.8/32.2 66.4/33.6 45.1/54.9
01/28 68.8/31.2 67.0/33.0 46.7/53.3

YTD BD HD
01/21 100 50.51
01/28 100 49.21
02/04 100 48.38

SI BD HD
01/21 82.30 100
01/28 87.76 100
02/04 92.56 100

A = # of BD SI on 1/21
A = 9.12 x BD sales 1/21 to 1/28 (E)

B = # of HD SI on 1/21
B = 24.32 x HD sales 1/21 to 1/28 (F)

A = .8230B

9.12E = .8230(24.32F)
E = .8230(24.32)/9.12 x F
E = 2.195F

Let G = Weekly sales 2/4 BD
Let H = Weekly sales 2/4 HD

A + E + G / B + F + H = 92.56 / 100

9.12E + E + G / 24.32F + F + H = .9256

10.12E + G = .9256 (25.32F + H)

10.12(2.195F) + G = .9256(25.32F + H)

22.2134F + G = 23.4362F + .9256H
G = 1.228F + .9256H

Let X = BR YTD on 1/21
Let Y = HD YTD on 1/21

Y = .5051X

(Y + F) = .4921(X + E)

.5051X + F = .4921 (X + 2.195F)
.5051X + F = .4921X + 1.0816F)
.013X = .0816F
X = .0816F/.013
X = 6.277F

Y = .5051X = 3.1705F

Let X2 = YTD BD 1/28
Let Y2 = YTD HD 1/28

X2 = X + E = 6.277F + 2.195F = 8.472F
Y2 = Y + F = 3.1705F + F = 4.1705F

Let X3 = YTD BD 2/4
Let Y3 = YTD HD 2/4

X3 = X2 + G
Y3 = Y2 + H
X3 = 8.472F + G
Y3 = 4.1705F + H

Y3 = .4838 (X3)
Y3 = .4838 (8.472F + G)
4.1705F + H = 4.0987F + .4838G
H = .4838G - 0.0718F

H = .4838(1.228F + .9256H) - 0.0718F
H = .5941F - 0.0718F + .4478H
.5522H = .5223F
H = .9459F

G = 1.228F + .9256(.9459F)
G = 1.228F + .8755F
G = 2.1035F

Sales ratio for Week of 1/29/07 to 2/4/07 = G / H (Blu-ray vs. HD-DVD)

Ratio = 2.2238 BD to 1 HD-DVD

Percentages:
BD = 2.1035 / (2.1035 + .9459) = .6898 = 69%
HD = .9459 / (2.1035 + .9459) = .3102 = 31%

Normalized figures to 100:

Assuming BD = 100
100/HD = 2.1035/.9459
94.59 = 2.1035HD
HD = 44.97


Weekly sales for 2/4
Blu-ray 100
HD-DVD 45

Adjusted percentages
Blu-ray 69.0
HD-DVD 31.0



Incorrect calculation:
10.12(2.205F) + G = .9256(25.32F + H)

22.31F + G = 23.44F + .9256H
G = 1.13F + .9256H

.5051X + F = .4921 (X + 2.205F)
.5051X + F = .4921X + 1.085F)
.013X = .085F
X = .085F/.013
X = 6.538F

Y = .5051X = 3.302F

Let X2 = YTD BD 1/28
Let Y2 = YTD HD 1/28

X2 = X + E = 6.538F + 2.205F = 8.743F
Y2 = Y + F = 3.302F + F = 4.302F

Let X3 = YTD BD 2/4
Let Y3 = YTD HD 2/4

X3 = X2 + G
Y3 = Y2 + H
X3 = 8.743F + G
Y3 = 4.302F + H
Y3 = .4838 (X3)
4.302F + H = .4838 (8.753F + G)
H = 4.235F + .4838G - 4.302F
H = .4838G - .0067F

H = .4838(1.13F + .9256H) - .0067F
H = 0.5467F + .4478H - .0067F
.5522H = .54F
H = .54F/.5522 = .9779F

.9779F = .4838G - .0067F
.4838G = .9846F
G = 2.0351F

Great thread, except it makes me realise how much knowledge I've lost since High School. Algebra kind of got replaced in my mind with more important things :p

Thanks Icemage. I haven't gone through the math you did, but have a question about one thing that doesn't feel right. The YTD for BD up to 2/4 comes out to 67.39. The number I've seen for the YTD up to the previous week was 67.0. It does not seem right to me that a week of 67.5 would cause the YTD gap to close almost 4/5ths of the way from 67.0 to 67.5, when it was one week among 5. That is, unless sales were multiple times higher in that week than in all 4 previous weeks combined. If you see a mistake in that logic, please let me know.

--Darin

Thanks Icemage. I haven't gone through the math you did, but have a question about one thing that doesn't feel right. The YTD for BD up to 2/4 comes out to 67.39. The number I've seen for the YTD up to the previous week was 67.0. It does not seem right to me that a week of 67.5 would cause the YTD gap to close almost 4/5ths of the way from 67.0 to 67.5, when it was one week among 5. That is, unless sales were multiple times higher in that week than in all 4 previous weeks combined. If you see a mistake in that logic, please let me know.

--Darin

Darin,

Please note that my numbers, as they are numeric projections, are probably +/- 2-3% (this is a guess, because I don't know how much impact rounding errors will have on the final figures.. but it's definitely there).

Nonetheless, point taken. I'm far too tired to recalculate this at the moment, but I'll try and find some time this weekend to revisit the numbers if someone else doesn't do so before I get to.

I still need to check the numbers for internal consistency.

First post. WARNING: LOTS OF MATH

---

I've been lurking in these forums for a while now (for those that wander by at eproductwars, I post over there as "Jim"), and thought this would be a good time for me to chime in with some analysis.

I was looking at Grubert's post in the main HD Media forum and thought that juggling some numbers would be an amusing way to spend an hour or so:

Can some of the more math-minded people here check my math? It's late and I'm tired so it's very possible I've made a mistake, but I "think" this is right...

VideoScan + PC Magazine data
Day Week YTD SI
01/07 63.3/36.7
01/14 68.2/31.8
01/21 67.8/32.2 66.4/33.6 45.1/54.9
01/28 68.8/31.2 67.0/33.0 46.7/53.3

Let A = BR discs since inception on 1/21
Let B = HD discs since inception on 1/21

We know A = B x .8230

Let C = BR discs since inception on 1/28
Let D = HD discs since inception on 1/28

We know C = D x .8776

Let E = # of BR discs sold between 1/21 and 1/28
Let F = # of HD discs sold between 1/21 and 1/28

We know that A + E = C, and B + F = D
(Old discs since inception + sales for past week = new discs since inception)

We know that E = 68.8/31.2 F = 2.205F

So doing some fun and amusing algebraic replacement we get:

A + E = C
.8230B + 2.205F = .8776D

Reverse this equation and we get

.8776D = .8230B + 2.205F
D = (.8230B + 2.205F)/.8776 = .9378B + 2.513F

But we also know that B + F = D

B + F = .9378B + 2.513F

.0622B = 1.513F
B = 1.513F/.0622 = 24.32F

If my calculations here are correct, that means that around 1 in 24 of all HD-DVD discs sold since inception were sold between 1/21 and 1/28.

Doing the same analysis for Blu-ray yields:

B + F = D
A/.8230 + E/2.205 = C/.8776

Reverse equation

C/.8776 = A/.8230 + E/2.205

C = (A/.8230 + E/2.205) x .8776 = 1.066A + .3980E

We know A + E = C so...
A + E = 1.066A + .3980E
.6020E = .066A

EDIT: My math WAS wrong... here. Blu-ray numbers were off because I did this last division wrong.
Original text (incorrect):
A = .6020E/.066 = 10.48

This means that Blu-ray sold a bit under 1/10th of all of its discs in the week between 1/21 and 1/28.
Corrected values:
A = .6020E/.066 = 9.12

This means that Blu-ray sold a bit under 1/9th of all of its discs in the week between 1/21 and 1/28.

Does this make any sense, or have I made a mistake somewhere?


Jim
Something more fundamental?

WHO THE HELL IS BUYING ALL THOSE HD-DVD DISKS?

Latest numbers show total Blu-Ray capable players(PS3s + standalones) at about 1.1 million in the US vs about 225,000 total HD-DVD capable. Amazon hi-def disk sale numbers are that HD-DVDs account for about 1 in 3, or even 1 in 2. So, if all these numbers are even reasonably accurate, then HD-DVD disk sales, on a proportional basis, are actually outselling BluRay, O R something with all these digits from the various sources is being artificially manipulated. Do the math. These numbers just make no sense.

Enjoy!

Milt R. Smith
mrsmith2002@yahoo.com

I know Sony's not a reliable source, but for grins and giggles let's use their interpretation of NPD's 439,000 BD/438,000 HD disc sale approximation. We don't have a date to attach this to, but let's assume that it's somewhere close to January 28, since Sony made their announcement on the figures in early February.

Leaving aside for the moment that NPD and Nielsen/VideoScan disagree somewhat about the relative volume ratio of BD to HD, if we just ballpark and say that somewhere around 900,000 total movie discs were purchased by 1/28/07.

Using your figures, that would indicate an attach rate of just over 2 HD discs per player for HD, and less than half a disc per player for Blu-ray.

I could possibly understand the Blu-ray number being low, but 2 discs per HD player? There's something seriously wrong with either Sony's interpretation of NPD's numbers or Toshiba's numbers. I'll leave it as an exercise for the reader as to which of the two sources is more believable (hint: I think both are biased).

---

Now, if you'd like to challenge the logic of my numerical analysis within the context of Neilsen/VideoScan instead of going off-topic, we can move on and see if I've made any actual mistakes in interpreting the data.

Something more fundamental?

WHO THE HELL IS BUYING ALL THOSE HD-DVD DISKS?

Latest numbers show total Blu-Ray capable players(PS3s + standalones) at about 1.1 million in the US vs about 225,000 total HD-DVD capable. Amazon hi-def disk sale numbers are that HD-DVDs account for about 1 in 3, or even 1 in 2. So, if all these numbers are even reasonably accurate, then HD-DVD disk sales, on a proportional basis, are actually outselling BluRay, O R something with all these digits from the various sources is being artificially manipulated. Do the math. These numbers just make no sense.What doesn't make sense to you? Sony knew when they decided to go with the strategy they did with the PS3 that it would likely result in lower attach rates, but more movies sold. They could have chosen to sell people a $50 add-on module for playing Blu-ray movies that would have likely decreased the number of discs sold, but increased the attach rates.

I don't know why so many people around here seem to be having trouble understanding that the approach Sony took is likely to lead to lower attach rates, yet could be a very effective tactic toward the goal of selling lots of discs. I'm starting to wonder if some people are playing this game of ignoring that in order to make it seem like the winner must be the one with the higher attach rates, even though that isn't logical. As I've said elsewhere, if Microsoft sent every XBOX360 owner an HD DVD add-on it would likely lower the attach rates, but raise the number of movies sold. Those who think attach rates are the determining factor might believe that Microsoft doing that would decrease the likelyhood of HD DVD winning, when the opposite is true.

If a format wanted the highest attach rate possible they would discourage average users from buying in favor of only the most extreme buyers, but they are smart enough to know attach rates are only one means to the end (selling lots of discs) and if they sell a player to somebody who buys 5 discs a year, that helps their format even if it lowers the average attach rate.

--Darin

The importance of attach rates is that they can predict sustained sales over time that can be increased quicker by increasing the installed player base.

Say 1 Million PS3s sell 250,000 movie disk units, in a month
0.25 attach rate per month

Say 125,000 HD DVD HD A2 sell 250,000 movie disk units in the same month
2.0 attach rate


If the attach rates stay the same and HD DVD sells 600,000 players you have 1,200,000 movie tiles sold in a month

If the PS3 attach rate remains the same, you would have to sell 4.8 million PS3's to match the 600,000 HD DVD player sales.

The studios want sales, the CE wants player sales. The attach rate is useful as an indicator of those sales will be with a given installed base.

A higher attach rate is indicative that movie sales will accelerate faster as the player base is expanded.

The importance of attach rates is that they can predict sustained sales over time that can be increased quicker by increasing the installed player base.

actually the opposite is true. A player in the home means that if a person wants to buy a movie he wants he can. Also attach rate should naturally drop to a reasonable level as the players gain market share.

UPDATE:

Finally found some time to rework my math and found a mistake in the calculation for item E (HD sales from 1/21 to 1/28) which altered all the figures. Wasn't a huge difference, but it did shift the numbers slightly to be more in line with what was reflected in the YTD and SI numbers.

If my calculations here are correct, that means that around 1 in 24 of all HD-DVD discs sold since inception were sold between 1/21 and 1/28.This means that Blu-ray sold a bit under 1/9th of all of its discs in the week between 1/21 and 1/28. Obviously if correct for the reported universe that means that Blu-ray sales have accelerated if 1/9 of the sales occurred in the week since Blu-ry has be out since last summer.

But if 1/24 of total HD DVD sales occured in that week, that would also mean that HD DVD sales have also accelerated, obviously not as much as Blu-ray, but greater than they were earlier in the year. HD DVD sales have at least held steady, despite the lack of new titles being released, which would imply that new owners are maintaining a high attach rate.

HD DVD sales don't appear to have fallen, even though Blu-ray sales have risen, and thats showing from the long term since inception and 45 day out Amazon charts we have available.

The importance of attach rates is that they can predict sustained sales over time that can be increased quicker by increasing the installed player base. actually the opposite is true. A player in the home means that if a person wants to buy a movie he wants he can. Also attach rate should naturally drop to a reasonable level as the players gain market share. Thats certainly Sony's hope on the PS3. But the PS3 has been delayed and may be falling short of Sony's sales projections.

Attach rates for the PS3 can certainly change, But that's asking for a consumer behavior change for the device. The first batch of PS3 owners were also including a lot of first adopter Blu-ray owners, but that may not carry over to a larger purchase pool.

If Blu-ray became as cheap as DVD maybe people more will convert over, but for the most part a consumer will normally not change his behavior dramatically after purchase. Sony is indeed trying to buck that trend. But trying to enlarge an attach rate after the device is in the home is behavior modification. Its just never been done on the scale Sony is hoping for here. Its a huge gamble on Sony's part.

What HD DVD has on the other hand is a simpler issue. It has to produce and sell 1/8 or so as many standalone players that are currently selling below the PS3 price point. If the attach rate stays close to what it has to be, its a much simpler CE manufacturing and marketing task. HD DVD simply has to sell less units at a lower price to keep up. Latest numbers show total Blu-Ray capable players(PS3s + standalones) at about 1.1 million in the US vs about 225,000 total HD-DVD capable. Amazon hi-def disk sale numbers are that HD-DVDs account for about 1 in 3, or even 1 in 2. So, if all these numbers are even reasonably accurate, then HD-DVD disk sales, on a proportional basis, are actually outselling BluRay That's the advantage of a huge attach rate disparity. It leverages the existing installed base for the software. Software can always be produced faster than hardware, and the existing software base is new again to every new player owner.

There needs to be a critical mass of software to support an individuals player purchase decision and a critical mass of players available to support a software release from the content providers.

But once those critical masses are reached a type of chain reaction can result with a positive virtuous circle being created.

One possibility is that HD DVD sales may dramatically increase when the new 2007 releases finally arrive as there will be more dedicated HD DVD player homes to sell them too.

Most DVD sales occur within 90 days of a release. It pretty remarkable that older catalog titles are still selling well on HD DVD. One very probable explanation is that they are being sold to new player owners.

HD DVD sales don't appear to have fallen, even though Blu-ray sales have risen, and thats showing from the long term since inception and 45 day out Amazon charts we have available.
As things stand, sales for both formats appear to have fallen for the week of 1/29 to 2/4. Why that might be, I have no idea, since this includes the release date of a few more BR titles than HD-DVD (granted, none of which were particularly high profile aside from Saw III), and also coincides with Toshiba's Superbowl $200 discount push on a HDTV + HD-DVD player combo. You would think that these items would have boosted sales for the period over the previous week, but that appears to not be the case.

It will certainly be interesting to see what next week's numbers indicate, as it pits 5 Blu-ray releases (American Psycho, First Blood, Reservoir Dogs, Running with Scissors, Tailor of Panama, Young Guns) against Hollywoodland for HD-DVD.

I meant fallen in a more long term sense.

I think you have done some fantastic work here.

Appreciate your hard work Icemage.

But if 1/24 of total HD DVD sales occured in that week, that would also mean that HD DVD sales have also accelerated, obviously not as much as Blu-ray, but greater than they were earlier in the year. HD DVD sales have at least held steady, despite the lack of new titles being released, which would imply that new owners are maintaining a high attach rate.If what the VP of Toshiba America said was right that meant less than 30k players before the Gen2s, then just 14 weeks ago HD DVD had that number of players or less in the US. So, sales might not be down from last summer, but they could be down since November and December. In order to maintain a high attach rate for the format they should sell 6 times as many discs per week when there are 180k players as when there were 30k players. Selling the same number of discs with way more players would mean a falling annualized attachment rate. From that standpoint 1/24th of sales when the majority of players are less than 12 weeks old doesn't seem as good, but then the releases so far this year haven't really been the best.
It pretty remarkable that older catalog titles are still selling well on HD DVD. One very probable explanation is that they are being sold to new player owners.I figure that with the statement about "Batman Begins" selling 4100 copies in the first 3 weeks of the year, they might have sold about 10k for the month (given the extra time and that Videoscan doesn't cover 100% of the market). Given that some of those were to people who bought their players in November and December (when likely well over 100k players sold), I don't think that necessarily implies a lot of new owners in January. It wouldn't surprise me if half of new owners buy that title, as it is a good one (and seems to be the best selling long term title on HD DVD).

--Darin