Kotaku is reporting that Sony will not be bringing its Japanese UMD Passport program to North America, removing the only method for PlayStation Vita owners to play their collection of PlayStation Portable universal media discs (UMDs) on the new handheld (PSP games downloaded from the PlayStation Network will still work on the Vita, however). While this is obviously bad news for anyone who wants to play their battered old copy of Lumines on a slightly larger screen, it made us wonder how important backward compatibility really is to a system's retail success.

We were perfectly ready to speculate wildly on that very topic, but it turns out there's no need. Someone has actually crunched the numbers and tried to develop a statistical model to show just how valuable backward compatibility is for a portable system's overall market share. And the results show that Sony just might pay a price for its decision to ignore all the UMD owners out there.

The paper

In May of 2010, Munich School of Management faculty Jörg Claussen, Tobias Kretschmer and Thomas Spengler published "Market leadership through technology - Backward compatibility in the U.S. Handheld Video Game Industry". Over 25 pages, the paper lays out a formula for estimating a portable console's eventual market share based on everything from backward compatibility and system price to the size and age of its game library and even the unit's physical weight (as a rough measure of portability).

The goal was to try to separate out how much of a portable system's success is driven by the ability to play a large library of the previous generation's games, and how much is instead driven by other factors. Previous papers have run similar analyses for other industries, finding, for example, that a hypothetical audio CD standard that included backward compatibility with vinyl records "would have accelerated diffusion by 1.5 years."

By applying their model to actual NPD sales data from the middle of the original Game Boy's reign in 1995 through to the rise of the PSP in 2007, the paper made a number of key findings that could apply to the Vita.

Previous generation software sales matter

Not all backward compatibility is created equal, of course—the value of the feature depends on the size and quality of the previous software generation that is being supported. But the paper's authors argue that the quality, variety and size of that library matter less than the overall software sales the previous generation managed to achieve.

The authors reason that customers buying a newly launched system are unlikely to go out and buy a lot of outdated games from the previous generation (they seem to be disregarding people who didn't own the old system, but we'll leave that for now). Rather, they say, the value of backward compatibility is primarily in the ability to take a large library of existing software you and your friends already own along with you on a new platform. Thus, higher overall software sales for the previous generation "increases the likelihood that a potential adopter has access to some of these games and can benefit from backward compatibility," or that "she could get old games from friends or through second-hand trading."

After running the numbers, the authors found that "one extra game title for the current generation has the same impact on demand as 82,979 game titles sold for the parent generation." In other words, the 45.6 million North American Game Boy Color cartridges floating around when the Game Boy Advance was released were worth as much as 550 additional launch games for the new system (for context, the Game Boy Advance didn't actually get 550 distinct games until August 2004, about three years after its North American launch).

For the Vita, the impact may be even greater. According to NPD, there have been 84.5 million retail PSP games sold in the United States. If all those titles were easily playable on the Vita, it would be as if the system were launching with over 1,000 distinct titles, according to the model. That's quite a hypothetical boost, considering the system is actually launching with just 25 titles.

Competing with yourself

Any system that launches with full backward compatibility, of course, runs the risk of making its parent company compete with itself, to an extent. After all, if players have access to a large library of old games for the previous generation, they might be less likely to want brand new games for their new system. This, in turn, reduces developers' incentive to make new games for the system, and thereby reduces the demand for that system among potential buyers.

How big is this effect? The paper's model estimates that every million backward compatible games sold for the previous generation reduces the effective launch day lineup for a new system by 1.2 titles. This means that, without backward compatibility, the Game Boy Advance would have theoretically launched with a powerful library of 75 games, rather than its actual launch day lineup of 21 titles.

That might sound like a big negative, but remember, it's being applied against the overwhelming positive effects on system demand mentioned in the last section. So the drag of intra-Sony competition from backward compatibility would lower the Vita's hypothetical launch "demand" value from over 1,000 games to around that of around 900 games, according to the model. In other words, you don't have to worry much about internal competition.

The impact of console power and age

While plenty of people are clamoring for backward compatibility on the Vita now, the feature would intuitively seem to be less important as time goes on and more Vita-exclusive software gets released (and PSP games continue to show their age). The paper's model takes this into account too, finding that each month a new system is on the market, the value of backward compatibility is reduced by about 0.5 to 2 percent, depending on how many other variables are thrown into the mix. In other words, while backward compatibility might be a big issue to many potential Vita buyers now, it's likely to be 10 to 25 percent less important a year from now.

But there's another factor that could be at work here: console power. The idea goes something like this: if a new system is leaps and bounds better than an old system, the games on the old system are going to look incredibly outdated in comparison, making the ability to play those old games on the new system less important.

Plenty of devoted retro gamers are no doubt rolling their eyes at this point, but there might be something to the idea, according to the data. Using CPU clock speed as an (extremely rough) estimate for portable console power, the researchers found that a larger technological bump between generations did indeed decrease the statistical value of backward compatibility.

The researchers even suggest that this may be part of the reason the PSP was able to make inroads against the Nintendo DS when other Nintendo competitors had failed to do so. Since the DS was so much better than the Game Boy Advance, the reasoning goes, all those backward compatible GBA titles were less effective as a shield to protect Nintendo from the competition.

In Sony's case, the company is going from a 333MHz maximum clock speed on the PSP to a cool 2GHz quadcore processor on the Vita, a leap the paper's model would suggest makes backward compatibility next-to-meaningless. In other words, the Vita is going to be so much better than the PSP that you're gonna want to throw out all your old UMDs anyway. From a statistical point of view, at least.

Caveats and counterfactual

While this paper gives a veneer of statistical rigor to measuring backward compatibility's impact, there are obviously a lot of potential reasons not to take it too seriously. For example, the model is working from an inherently limited set of examples—there are only four portable console generations to consider in the 12 years the paper examines. For another, Nintendo was by far the dominant player in all four of those generations, usually facing extremely limited competition. Would other companies see the same impact from their own backward compatibility in different circumstances?

The paper also specifically focuses on how backward compatibility impacts the current market leader in the portable console space—the effects might be different for an also-ran system maker. And, of course, there are plenty of intangibles that could be causing sales fluctuations that the model currently attributes to backward compatibility.

The best way to evaluate the paper's model may be a counterfactual experiment that the authors themselves put forward. The premise: what if Tiger's long-forgotten Game.com had somehow managed to be compatible with the original Game Boy's massive library of cartridges, just like the Game Boy Color that it was competing with? What would the model say about the relative fates of the two systems if this one important difference were applied to reality?

Well, it turns out the feature may have actually been decisive in the console wars. According to the model, with the Game Boy library at its back, the counterfactual Game.com would have sold 230,000 more systems each month, eating away at 83,000 monthly Game Boy Color sales. After one year of this, the Game.com would actually have been the market leader with roughly 70 percent of portable game console sales, compared to about 23 percent for the Game Boy Color (the weakened Virtual Boy and Game Gear would have taken the remainder).

On the one hand, this seems to discount the large draw Nintendo's continuing first-party franchises would have on the Game Boy Color market, especially compared to the Game.com's less impressive set of first-party exclusives. On the other hand, if buying a Game.com had meant not having to give up your addiction to Tetris on the original Game Boy, maybe gamers and developers would have given it a second look.

We'll never really know for sure what would have happened to a Game.com with Game Boy support, or how things would be different for a North American Vita that could play a wide library of existing PSP UMDs. But it sure is fun to wildly speculate about—especially if you have some data backing you up!