[A quick disclaimer, I have played soccer all my life, am a devoted fan of the sport (and pretty good judge of teams - see my amazingly insightful prediction of Spanish success in the European Championship in June) and personally would welcome an MLS team in Portland.]
There has been quite a bit of economic research on the effects of new stadia and new teams and the results are in general agreement that there is little measurable net positive impact of teams and stadia to overall investment or economic activity. This research has done a lot to change the public debate about such projects, ten years ago, you would probably have heard about stadia being economic engines driving the city forward. Now, there is little in the way of overblown promises about being a boon to overall economic activity and, I think, Paulson and the City of Portland are to be commended in keeping the rhetoric subdued: with reasonable patronage, the teams could service the debt. Portland would carry the risk and the reward is an MLS team and a nicer place to watch baseball.
Though overall investment and economic activity are not seen to be increased by stadia construction, there is some agreement that such projects can serve as focal points for investment. In other words they can attract investment to an area that might not otherwise see it. This comes form the fact that there are positive externalities that comes from gathering people together in new or improved stadia: you bring custom to areas that would not normally see it. This custom is not totally captured by the teams themselves and thus there is a positive benefit that can be captured by those interested in opening up shops, restaurants, bars and even new housing.
Anecdotally, Denver is a good example of this. Before Coors field, Lower Downtown in Denver was a run-down warehouse district, with the new ball park it is now a thriving entertainment and shopping district and many, many new apartment projects have sprung up around the park advertising their proximity to the park and the district. [A caveat: we will never know the counter-factual - would LoDo have had the same renaissance without the stadium? This problem plagues economic research and we do the best we can to try and deal with it, but all of this evidence on the impact of stadiums is, at best, strongly suggestive.]
So, while there does not seem to be evidence of overall increases in economic activity (e.g., we should not expect the Portland tax revenue to increase), it is reasonable to talk about creating a focal point for local investment. Whether the small minor-league park envisioned for Lents is enough to drive enough investment to really create a change in the area is an open question, but I suspect so (it will also, hopefully, be small enough to avoid the other side of the externality: noise, trash and traffic). Open to debate, however, is whether there is another way to create a self-funded way to create a focal point (e.g., BIDs).
So is it a good idea? Well, people derive happiness from having sports and cultural attractions (we often see survey evidence of such attractions being a prime reason people choose to live where they do) but it is a very hard thing to measure. The point is that the benefits of having sports teams is more than just the measurable economic activity that they create, but the utility people derive from their presence. Whether it is worth the risk to the City of Portland to finance the stadium projects ultimately depends on how much these sporting attractions matter to Portland residents.
The Oregonian also published today an Op-Ed piece that argued that the City should not invest in stadia but rather green jobs. In it the author points out, rightly, that there is no evidence of overall net increases in economic activity or tax revenues from such investments, but wrongly suggests that we should, therefore, expect no local investment in Lents. These two things are not the same. What is worse is that the author presents a false dichotomy: invest the $75 million in energy improvements for housing. I have nothing against such a proposal in principle - but it has very little to do with the sports stadium proposal. The $75 million for stadia is intended to be self-funded, the green housing proposal is not self-funded. The fact that the city would borrow $75 million could impact their ability to raise more funds as cheaply in the future, but should not prevent them from investing in green housing or other such proposals in any significant way.