Recent Console Attach Rates

[Rangers]

To be truly apples to apples (at least somewhat) you'd need to find the attach rate for 360 when it was at the same point in it's life cycle as PS3 and Wii are now.

I dont know what that was, but I suspect it was higher.

It's also not good for PS3 that Wii is actually ahead of it, that was pretty shocking to me. Wii play or not. The conventional wisdom is that Wii owners buy the least games.

 

[fallguy]

Wii does have the cheapest games. At least thats how it looks when shopping for games. Loads of $20-$30 shovelware.

 

[mrcorbo]

@ paawl OK, I see it now. Thanks.

I found a press release from January 2007 which had the 360's attach rate at 5.1. At this time the average time of ownership (I'm going to start abbreviating this as ATO) was 6.2 months. 5.1:6.2 = 0.82(!) 0.82 * 12 = 9.8 games per year.

Now I'm sure of it, the PS3 and Wii are showing inflated game sell rates relative to the 360 because of their relatively low ATO, likely for the reasons stated by Mintmaster and AlphaWolf. A new console owner is going to buy games at a higher rate initially than they will over time. I think you may be unable to make a valid comparison (save doing ones like the above where you try to compare historical data for the 360 with current data for the PS3 and Wii) until the ATO for PS3 and Wii actually reaches 12.0 months. That's the point where I think you have enough accumulated data to accurately model what an average user's purchasing behavior is going to be over a year.

And it isn't a misconception. The 360 was and is selling a lot of software. It's nearly matching the performance of the PS3 and Wii now and when it was in a similar point in it's lifecycle it was showing a sell rate of 2.4 and 1.3 games per year higher respectively.

 

[mrcorbo]

More fun with numbers:

I created a scaling factor by dividing the change in sell rate for the 360 between Dec '06 and March '08 and dividing it by the change in ATO over the same period. This gives a result of .47 (rounded) per additional month added to ATO.

I'm not presenting this as an accurate prediction (there's way too many variables that aren't covered to do that), but just to provide context. If the PS3 and Wii numbers are scaled by this factor [Current Sell Rate - (0.47 * Change in ATO)] to the current ATO of the 360 they end up at a sell rate of 4.7 and 5.8 games per year respectively.

Further, to show how much these numbers can fluctuate over a short period of time this early in their lifecycles, the sell rate of the 360 after December's NPD's was showing as 7.7 games per year and is now down to 7.1 after just three months of non-holiday sales and no major releases.

 

[paawl]

I found a press release from January 2007 which had the 360's attach rate at 5.1. At this time the average time of ownership (I'm going to start abbreviating this as ATO) was 6.2 months. 5.1:6.2 = 0.82(!) 0.82 * 12 = 9.8 games per year.

Good work! I'll have to repeat the analysis myself when I get a chance. Unfortunately, that won't be until this Thursday, at the earliest. In the meantime, I'll have to trust you.

Now I'm sure of it, the PS3 and Wii are showing inflated game sell rates relative to the 360 because of their relatively low ATO, likely for the reasons stated by Mintmaster and AlphaWolf.

I'm not so sure, the PS3's calculated annual attach rate increased from 6.5 to 7.5 as the ATO increased from 6.5 to 7.5 months during the September to March period, which may only indicate that there were big PS3 games released during this period.

I think you may be unable to make a valid comparison (save doing ones like the above where you try to compare historical data for the 360 with current data for the PS3 and Wii) until the ATO for PS3 and Wii actually reaches 12.0 months. That's the point where I think you have enough accumulated data to accurately model what an average user's purchasing behavior is going to be over a year.

Agreed, if your goal is to crown a winner. However, if your goal is merely to show that results for each console are similar enough that a big game or two could swing the result any way, then I think the data we have may still be useful. That said, these analyses can only get more accurate with time. It's always easier to predict the past than to predict the future.

 

[Teasy]

Ill be buying Wii Play tomorrow, along with Mario Kart. Because we have just one Wii remote right now, and we'll need at least two. Might buy another one, as Im sure many Wii owners will do. So counting Wii Play can be very misleading. One Wii owner can own 2-3 copies of it, depending on how many Wii remotes they have. Because its still the cheapest way to get one

Wii Play costs $49.99, the Wii Remote costs £39.99... It isn't cheaper at all to buy Wii Play, its merely better value because in effect your getting a new game for $10. There's no way people are going to own multiple copies of the game.

 

[aaronspink]

Wii Play costs $49.99, the Wii Remote costs £39.99... It isn't cheaper at all to buy Wii Play, its merely better value because in effect your getting a new game for $10. There's no way people are going to own multiple copies of the game.

The problem is in some places it is easier to find Wii Play than a Wii mote! I know someone who has 3 copies of Wii Play because he couldn't find any unbundled Wii Motes.

Aaron Spink
speaking for myself inc.

 

[Teasy]

Fair enough I don't know how easy Wii Play is to find in the US vs a controller on its own.

 

[dobwal]

You shouldn't assume either because neither are accurate.

As I suggested should be done before (and was hoping someone else would actually do it) here are the average time of ownership for the three consoles.

360 - 12.3 months
PS3 - 7.0 months
Wii - 7.0 months

The resulting ratio when comparing these to the lifetime attach rate gives you:

360 - 7.5:12.3 = 0.61
PS3 - 4.6:7 = 0.66
Wii - 5.3:7 = 0.76

This last number represents the rate that that console's user base buys games over time (as expressed in months).

I have a problem with this as the attachment rate is generated with no time in mind. An overall attachment rate tells us the average owner owns 7.5 games whether they have owned the 360 for 1 day or since launch.

You can't assume that since the average 360 owner owns 7.5 games that the average attachment rate for a 360 thats 12.3 months old is 7.5.

You assumption is no different than stating that

360 - 7.5:1.0= 7.5 (which states that the average 1 month owner of the 360 buys at a rate of 7.5 games a month)

360 - 7.5:24.6=0.30 (which states that the average launch owner of the 360 buys at a rate of 0.30 games a month)

You're treating the 7.5 figure as a constant which in reality is not true. The true average attachment rate based on time of ownership is a fluid, not static, and for all consoles is probably larger the longer a console is owned. So, in all likely hood the average attachment rate for a 360 that been owned for 12.3 months is higher the 7.5.

Looking at the monthly attachment rates (total software sold over a month/LTD at that month) will give the average buy rate for the a console for any given month. This is what Pachter is probably using to come up with his rate. Looking at monthly attachment rates over a certain time period and extrapolating it out to a year.

 

[mrcorbo]

I have a problem with this as the attachment rate is generated with no time in mind. An overall attachment rate tells us the average owner owns 7.5 games whether they have owned the 360 for 1 day or since launch.

No, it doesn't say any such thing. By it's nature, since it's referring to an "average" owner it isn't going to be expected to reflect the purchasing habits of any individual owner you may choose to pull out of the overall population. It reflects the purchasing habits of all the owners combined, which includes new owners who may only own a couple of games to owners who bought the console at launch and own a dozen games or more. The only time the attachment rate should be expected to approximate the actual number of games an individual owner has purchased is if that individual owner has also owned the console for the average amount of time.

You can't assume that since the average 360 owner owns 7.5 games that the average attachment rate for a 360 thats 12.3 months old is 7.5.

I'm not assuming anything. That's what the data says. The average 360 owner has purchased 7.5 games and the average 360 owner has owned their console for 12.8 months. These are facts.

You assumption is no different than stating that

360 - 7.5:1.0= 7.5 (which states that the average 1 month owner of the 360 buys at a rate of 7.5 games a month)

360 - 7.5:24.6=0.30 (which states that the average launch owner of the 360 buys at a rate of 0.30 games a month)

You missed the entire point. The point of dividing the average number of games bought by the average time of ownership is to show an average rate of game purchases. It is this average rate of purchases you would have to use, not the overall attach rate as you attempted to do above, to calculate the number of purchases you would expect a console owner to purchase in a given amount of time.....assuming the rate of purchases is constant.

I think that it has been conclusively shown that this does not reflect the actual behavior of console owners. They buy games at varying rates according to such factors as length of time owned (higher purchase rate early), presence or lack of big releases, and time of year (holidays, etc.). The more data you have, though, the more these temporary effects will be moderated by an overall sustained purchase rate so that you can make more accurate assessments. None of the consoles are at this point yet, but the 360 is closer, for reasons that should be obvious.

You're treating the 7.5 figure as a constant which in reality is not true. The true average attachment rate based on time of ownership is a fluid, not static, and for all consoles is probably larger the longer a console is owned. So, in all likely hood the average attachment rate for a 360 that been owned for 12.3 months is higher the 7.5.

No. It's not being treated as a constant and as you can see in subsequent posts I've even done additional calculations based on how it has changed over time.

Looking at the monthly attachment rates (total software sold over a month/LTD at that month) will give the average buy rate for the a console for any given month. This is what Pachter is probably using to come up with his rate. Looking at monthly attachment rates over a certain time period and extrapolating it out to a year.

Do you realize that what you're saying here is that using more than 12 months of data to estimate the buying behavior of console owners over 12 months is less accurate than using fewer than 12 months of data to do the same thing?

 

[dobwal]

I'm not assuming anything. That's what the data says. The average 360 owner has purchased 7.5 games and the average 360 owner has owned their console for 12.8 months. These are facts.

Thats not what the data says and that why people says statistics lie half the time.

If you look at the population of the 360 you will see that the average attachment rate is 7.5 and average time of ownership is 12.3 months. Both those numbers are generated without the other in mind. You can't inherently says from those figure that the average attachment of a 360 owned for 12.3 months is 7.5.

Look at these two scenarios where the 360 launched 24 months ago (hypothetically)

Scenario 1:

Three people bought 360s at launch and each owns 12 games
Three people bought 360s at 12 months and each own 9 games.
Three people bought 360s yesterday and each own 2 game.

Scenario 2:

Three people bought 360s at launch and each owns 17 games
Three people bought 360s at 12 months and each own 5 games.
Three people bought 360s yesterday and each own 1 game.

Each scenario has a LTD of 9 owners and each scenario produces an overall attachment rate of 7.6. However the average attachment rate for people who have owned the 360 for 12 months (the average time of ownership) in either scenario isn't 7.6. One is an average of 9 and other is an average of 5.

An average time of ownership and the overall average attachment rate is not sufficient to calculate the average attachment rate of any specific time of ownership. All the overall attachment rate figure of 7.5 simply says is that if all the games bought by 360 owners were equally distributed each owner would have 7.5 games. However, in reality, the games aren't equally distributed and without samples we won't know how 360 games are distributed when time of ownership is taken in to account.

 

[paawl]

dobwal, you can argue all you want that the attachment rate is different for different owners (of course it is!), and that it varies with time (of course it does!), but you're quite mistaken if you think that the average length of ownership for Xbox 360s is 12.8 months, and that the average number of games owned per console is 7.5, and that the average number of games purchased per console per month is not 7.5/12.8 games. This last, incontrovertible fact follows from the first two, and it means no more and no less than exactly what it says, that the average number of games purchased per console per month is 7.5/12.8. It doesn't say that the rate wasn't higher in September, when Halo was released, and it doesn't say it wasn't lower in March, when nothing good came out, but I don't know why anyone would expect that kind of predictive accuracy from a simple average.

BTW, the reason most people say that statistics lie is because they lack basic numeracy and therefore don't understand statistics.

 

[AlphaWolf]

So if the model has no predictive accuracy, exactly what good is it?

 

[mister slim]

So if the model has no predictive accuracy, exactly what good is it?

Not having 100% accuracy is not equivalent to having 0% accuracy.

 

[AlphaWolf]

Not having 100% accuracy is not equivalent to having 0% accuracy.

exactly how much accuracy does it have? Enough to be useful? Doesn't seem so. There's way too many unaccounted for variables.

 

[Shifty Geezer]

Seems to me the problem with these analytical averages is people only ever use mean averages, giving rise to such nonsense statements as '2.4 children'. Different 'averages' give different insights. There's no one average value that accurately represents The Truth, unless you get lucky! eg. If Mr. A earns £60k a year, and Mr's B, C, D and E each earn £10k a year, the Mean average would tell us the average earnings is £20k a year. If you aim your product for that priceband, you miss out 80% of the market! The Mode and Median give a more meaningful result in this instance, the average person earns $10k with a few large exceptions.

As long as people are just talking 'average attach rates' as a concept then the discussion can go on ad-infinitum about what information is missing or present. There are different averages, different states to consider. It's more complex than one decimal number.

I guess the crux of the issue isn't the number to use, but how software is selling on the different platforms. If there's a platform where sales are always stronger, a dev wants to know to consider how to invest their efforts, and likewise if a platform userbase is apathetic to buying new software. Categorization in this way is more useful than arguing over decimal values!

 

[mrcorbo]

So if the model has no predictive accuracy, exactly what good is it?

In this case it's an attempt to provide context to allow for a more valid comparison of the software sales of the 3 current-gen consoles. Since we know what the purchase rate looked like for the 360 at various times in it's history (thanks to Microsoft's regularly pimping their attach rate in their press releases) we can see how various events in that history effected it. If you assume that those same effects are altering the purchase rate of the other 2 consoles in similar ways you can factor them into your comparison and get a more valid one.

All the numbers I've been throwing around have been an effort to show a statistical basis for the following:

• There is no such thing as a constant sales rate. There are several factors that can and do effect the sales rate and they need to be factored into any analysis.
• Time since launch is not a valid way to scale the attach rates of different consoles to make them comparable. Using the average time of ownership is better.
• Console owners show inflated software sales with lower time of ownership.

• Holiday sales can greatly effect the sales rate when there is not enough regular sales data to moderate its effect.

Some of this may seem like common sense, but I think it's useful to have a set of data points that not only proves their validity, but actually gives you a sense of the degree to which these factors can have an effect.

Don't get hung up on the specific numbers, but instead dig a little deeper and try to see what those numbers are telling you.

And about the deficiencies of using averages - While a corner case can easily skew the results when you have a small population we are talking about numbers derived from populations in the millions. It's going to be a lot harder for extreme cases to effect the result. The numbers may not be perfect, but they are good enough for the purposes for which they are being used here.

 

[AlphaWolf]

Don't get hung up on the specific numbers, but instead dig a little deeper and try to see what those numbers are telling you.

And about the deficiencies of using averages - While a corner case can easily skew the results when you have a small population we are talking about numbers derived from populations in the millions. It's going to be a lot harder for extreme cases to effect the result. The numbers may not be perfect, but they are good enough for the purposes for which they are being used here.

To verify common sense?

 

[dobwal]

And about the deficiencies of using averages - While a corner case can easily skew the results when you have a small population we are talking about numbers derived from populations in the millions. It's going to be a lot harder for extreme cases to effect the result. The numbers may not be perfect, but they are good enough for the purposes for which they are being used here.

Lets test your numbers. I simply applied your numbers to the hardware numbers you posted.

Predicted Total Monthly Software=(ConsoleMonthly)*(MrCorbo's AverageBuyrate)*(Number of Months of Ownership)

Total Predictive LTD of Software Sold = Sum of Predicted Total Monthly Software figures

Predicted Attachment Rate = (Total Predictive LTD of Software Sold)/(LTD of Consoles)

If your average buyrate for the consoles are accurate then applying them to NPD monthly console numbers should produce an accurate overall attachment rate.

Your average buyrates predicts that the attachment rates as of now shoud be

360 = 8.1
PS3 = 5.3
Wii = 6.8

the actual attachment rates are

360 = 7.5
PS3 = 4.6
Wii = 5.3

average buyrates that would reflect NPD's attachment rates are

360 = 0.57
PS3 = 0.54
Wii = 0.59

and not

360 = 0.61
PS3 = 0.66
Wii = 0.76

Regardless of these calculations there are phenemnoms thats influencing these numbers thats not fully explain by the data.

The 360 had an attachment rate of 4.6 back in Aug 06. Based on hardware numbers that would set the average buyrate at that time to ~ 0.80. Furthermore, as of June 07 the 360 had an attachment rate of 6.1 that puts the average buyrate at ~0.62. The 360's average buyrate has been decreasing over time. The data we have doesn't explain why.

It might be because the buyrate of the older buyers have remained stable but new buyers tend to be less hungry. This is a possibility as early adopters are looked at as being highly represented by hardcore gamers. The longer the 360 is on the market the more 360s are sold and the less hardcore gamers make up of the overall userbase, diluting their influence on the overall attachment rate. Or it maybe that the whole userbase has grown less hungry.

All we have is the 360 maintaining a higher attachment rate over time than the other 2 consoles so MS is simply attributing that fact to a higher penetration of the hardcore gamers. Showing the current buyrates isn't going to disprove MS's theory because the actual average buyrates have little ability to distinguish between the different market segments.

Xbox 360				
Time---ConsolePurchases---AverageBuyrate---#ofMonths---Predicted#of Monthly SoftwareSales based on Average Buyrate
Nov-05	326,000	0.61	29	5,766,940
Dec-05	281,000	0.61	28	4,799,480
Jan-06	250,000	0.61	27	4,117,500
Feb-06	161,000	0.61	26	2,553,460
Mar-06	192,000	0.61	25	2,928,000
Apr-06	295,000	0.61	24	4,318,800
May-06	221,000	0.61	23	3,100,630
Jun-06	277,000	0.61	22	3,717,340
Jul-06	206,000	0.61	21	2,638,860
Aug-06	205,000	0.61	20	2,501,000
Sep-06	259,000	0.61	19	3,001,810
Oct-06	218,000	0.61	18	2,393,640
Nov-06	511,000	0.61	17	5,299,070
Dec-06	1,130,000	0.61	16	11,028,800
Jan-07	294,000	0.61	15	2,690,100
Feb-07	228,000	0.61	14	1,947,120
Mar-07	199,000	0.61	13	1,578,070
Apr-07	174,000	0.61	12	1,273,680
May-07	155,000	0.61	11	1,040,050
Jun-07	198,000	0.61	10	1,207,800
Jul-07	170,000	0.61	9	933,300
Aug-07	277,000	0.61	8	1,351,760
Sep-07	528,000	0.61	7	2,254,560
Oct-07	366,000	0.61	6	1,339,560
Nov-07	770,000	0.61	5	2,348,500
Dec-07	1,260,000	0.61	4	3,074,400
Jan-08	230,000	0.61	3	420,900
Feb-08	255,000	0.61	2	311,100
Mar-08	262,000	0.61	1	159,820
				
				
Total # of Consoles Sold------Predictive # of Software 
------------------------------Sold based on Average BuyRate	
9,898,000---------------------80,096,050	

Average Attachment Rate (AR)--------Average BuyRate that would
based on Predictive BuyRate---------mirror numbers pub by NPD's AR of 7.5 	
8.09--------------------------------0.57

PS3				
Time---ConsolePurchases---AverageBuyrate---#ofMonths---Predicted#of Monthly SoftwareSales based on Average Buyrate
Nov-06	197,000	0.66	17	2,210,340
Dec-06	491,000	0.66	16	5,184,960
Jan-07	244,000	0.66	15	2,415,600
Feb-07	127,000	0.66	14	1,173,480
Mar-07	130,000	0.66	13	1,115,400
Apr-07	82,000	0.66	12	649,440
May-07	82,000	0.66	11	595,320
Jun-07	99,000	0.66	10	653,400
Jul-07	159,000	0.66	9	944,460
Aug-07	131,000	0.66	8	691,680
Sep-07	119,000	0.66	7	549,780
Oct-07	121,000	0.66	6	479,160
Nov-07	466,000	0.66	5	1,537,800
Dec-07	798,000	0.66	4	2,106,720
Jan-08	269,000	0.66	3	532,620
Feb-08	281,000	0.66	2	370,920
Mar-08	257,000	0.66	1	169,620
				
Total # of Consoles Sold------Predictive # of Software 
------------------------------Sold based on Average BuyRate
4,053,000---------------------21,380,700	

Average Attachment Rate (AR)--------Average BuyRate that would
based on Predictive BuyRate---------mirror numbers pub by NPD's AR of 7.5  	
5.28--------------------------------0.54

Wii				
Time---ConsolePurchases---AverageBuyrate---#ofMonths---Predicted#of Monthly SoftwareSales based on Average Buyrate
Nov-06	511,000	0.76	17	6,602,120
Dec-06	1,130,000	0.76	16	13,740,800
Jan-07	294,000	0.76	15	3,351,600
Feb-07	228,000	0.76	14	2,425,920
Mar-07	199,000	0.76	13	1,966,120
Apr-07	174,000	0.76	12	1,586,880
May-07	155,000	0.76	11	1,295,800
Jun-07	198,000	0.76	10	1,504,800
Jul-07	170,000	0.76	9	1,162,800
Aug-07	277,000	0.76	8	1,684,160
Sep-07	528,000	0.76	7	2,808,960
Oct-07	366,000	0.76	6	1,668,960
Nov-07	770,000	0.76	5	2,926,000
Dec-07	1,260,000	0.76	4	3,830,400
Jan-08	230,000	0.76	3	524,400
Feb-08	255,000	0.76	2	387,600
Mar-08	262,000	0.76	1	199,120
				
Total # of Consoles Sold------Predictive # of Software 
------------------------------Sold based on Average BuyRate
7,007,000---------------------47,666,440
	
Average Attachment Rate (AR)--------Average BuyRate that would
based on Predictive BuyRate---------mirror numbers pub by NPD's AR of 5.3   	
6.80--------------------------------0.59

 

[mrcorbo]

@ dobwal - My initial calculations set the "# of months" value of the latest hardware sales as zero. Yours set it as 1. The former implies all hardware sales took place on the last day of the month and the latter implies that they all took place on the first day of the month. That's why there is a discrepancy between our calculations. Your numbers would put the ATO at 13.3 months, which naturally, if you took more time to reach the same attach rate would result in a lower purchase rate. Neither value makes sense, actually. paawl made the reasonable suggestion to use 0.5 months as a starting value, instead, so latest month would be 0.5 next would be 1.5, etc.

New numbers based on this change (and I also did less rounding this time, only rounding the final figure) come up as:

ATO:

360 - 12.8
PS3 - 7.5
Wii - 7.5

Purchase Rate:

360 - 0.59 games per month, 7.1 games per year
PS3 - 0.61 gpm, 7.4 gpy
Wii - 0.70 gpm, 8.5 gpy

Regardless of these calculations there are phenemnoms thats influencing these numbers thats not fully explain by the data.

The 360 had an attachment rate of 4.6 back in Aug 06. Based on hardware numbers that would set the average buyrate at that time to ~ 0.80. Furthermore, as of June 07 the 360 had an attachment rate of 6.1 that puts the average buyrate at ~0.62. The 360's average buyrate has been decreasing over time. The data we have doesn't explain why.

It might be because the buyrate of the older buyers have remained stable but new buyers tend to be less hungry. This is a possibility as early adopters are looked at as being highly represented by hardcore gamers. The longer the 360 is on the market the more 360s are sold and the less hardcore gamers make up of the overall userbase, diluting their influence on the overall attachment rate. Or it maybe that the whole userbase has grown less hungry.

All we have is the 360 maintaining a higher attachment rate over time than the other 2 consoles so MS is simply attributing that fact to a higher penetration of the hardcore gamers. Showing the current buyrates isn't going to disprove MS's theory because the actual average buyrates have little ability to distinguish between the different market segments.

This is the point. All of my initial posts were a response to the OP, which was attempting to show that MS's claims didn't hold up. My initial problem was with the OP trying to normalize the attach rates of the 3 consoles by time since launch. So I came up with the Attach Rate/ATO calculation as a better alternative. Next, I wanted to see if there was some statistical backup for points made by other posters that new console buyers show higher purchase rates and by extension as the console owner poulation increases you would see a decline in purchase rate.

Hence the initial buy rate calculation and the subsequent attempts to make what I thought was a more valid comparison by attempting to show what the 360's purchase rate was when it was in a similar position to where the other 2 consoles are now in ATO. I even showed what the purchase rate of the other 2 consoles would be if they followed a similar trend when they got to the point where the 360 is now. This satisfies me, at least, that MS's claims do hold up and the conventional wisdom that the 360 is selling software at an unusually high rate is not just based on succesful PR.