Why is Jerry Yang clinging so desperately to Yahoo's search business, when Microsoft has made no secret of its willingness to buy it for billions of dollars? Sheer stubbornness, it seems. Heather Hopkins, an analyst at traffic-trends researcher Hitwise, has run the numbers, and found that Yahoo Search, while a decent standalone business, doesn't contribute much to the rest of Yahoo. Google accounts for far more traffic to almost all of Yahoo's properties. Ah, but perhaps that's where Yang's stubbornness comes from.

If Yahoo just gave up on search, it would be at Google's mercy, like so many other Web publishers. What Google gives, it can take away. And Yang surely knows this, since it's exactly the game he used to play with other websites.

When MarketWatch, the finance-news site, was preparing to go public — this was long before its sale to Dow Jones, of course — Yahoo Finance was linking to its stories for free. As founder Larry Kramer told the tale to me, he thought this was great — free traffic, right? His investment bankers disagreed, seeing this as a big risk, since Yahoo could stop linking at any time. Eventually, MarketWatch struck a commercial deal to pay Yahoo in exchange for a guarantee of continuing traffic.

One of the few Yahoo sites that gets more traffic from Yahoo Search than from Google is Yahoo Maps. When users typed an address into Google, in the early days, Google would link directly to a Yahoo Maps page for the location. And then Google created its own maps site. Links to Yahoo Maps grew less prominent, than disappeared altogether.

The same could happen to any of Yahoo's Google-dependent properties. Yahoo Search is, at the least, a hedge against such a move. Or it would be, if its share of the search market weren't ever dwindling.

The reality: If Microsoft bought Yahoo's search, nothing would really change for Yahoo's valuable, profitable media properties. Traffic from Yahoo Search would continue to decrease — perhaps more sharply, with Microsoft's incompetent Web executives in charge — while traffic from Google would continue to increase. That's where Jerry Yang and Microsoft CEO Steve Ballmer find common ground, in a shared delusion — that either of their search engines, alone or together, amount to anything.