After a market uproar about its claim that buying advertisements is really an Internet-age capital investment in disguise, Groupon has finally begun to explain how the millions of dollars of spending in Internet marketing in the past 18 months is paying off.

On Sept. 23, the world's biggest online group-buying company finally gave statistics on how often people buy Groupons after they sign up for the daily-discount emails, and the news is pretty good. There are up to 17 different mentions of repeat business in the new prospectus, up from three -- and none of them helpful -- the last time. We learned that Groupon had 12.1 million repeat customers by the end of the first half of the year, up elevenfold from a year earlier. And we know that the average repeat customer has bought four Groupons since joining, up from three deals per member a year ago. So people who join Groupon do come back, and they may even be coming back at increasing rates.

But there's plenty we still don't know. Most important, we don't know how many of those repeat customers bought Groupons during the second quarter (and how many they bought), or even the first half of 2011, specifically. We don't know what contribution repeat clients made to the company's most recent profits and losses.  We don't have much to tell us whether people's interest fades within a month or so of signing up for Groupon's daily-deal e-mails, or if spending now reels in customers who will buy deals for two or three years, because there's no distinction between the behavior of people who have been customers for a year or more and those who just signed up.

The whole argument from Groupon CEO Andrew Mason has been that today's spending will allow a radical cut in marketing spending later, as it did at Amazon.com (Nasdaq: AMZN), turning  Groupon's $253.9 million first-half loss attributable to common shareholders into a profit later. We still don't really know if that's true or not.

Groupon needs to go further down the same path, making the disclosures simpler to follow and doing more math for us. The right answer is still for the company to tell us directly how many Groupons were purchased each quarter by new customers, how many Groupons people bought once they have been on the mailing list for three to 12 months, a year to two years, and more than two years. If people are still spending after two years, then we know that the marketing budget can, as Mason insists, come down over time. If I sign up for Groupon, quickly buy four deals, and then forget about it, that's one thing. If I buy one a quarter for a year, with every sign I'll keep on buying, that's a far more valuable relationship for Mason to have. He needs to tell us which one is happening.

If management does proffer the clear explanation small investors like us need, it will help us compare Groupon with competitors such as Google (Nasdaq: GOOG) Offers, Amazon-backed  LivingSocial, and Travelzoo (Nasdaq: TZOO). If it won't tell us, we have to hope that the $20 shares we buy are really worth $40 -- but we'll just be guessing.