It's time for Round of 32, the second elimination round out of 5 in our Market Madness series, featured on RealtyTimes by JustRentToOwn. Find the results of the Round of 64 here!

So we've teased out where the stronger economies are located in the first round, pitting some of our favorite cities head to head. For the next round, it's time to take a look at the health and growth of the market: it's time for a little appreciation.

Why appreciation next, instead of home values or something like that? The market you buy in needs to have a strong economy, granted. But if your home isn't growing in value, you're leaving a considerable investment potential on the table. Finding an inexpensive investment means nothing if it doesn't become more valuable. And high value homes don't necessarily mean high growth; if wages for middle income buyers can't keep up, home values slow in growth with lesser widespread demand. Furthermore, buying in a city that is rapidly appreciating early means getting a fair value on your purchase, before you find yourself priced out. Appreciation rates are important!

Nationally, most major cities are expected to grow in value at a rate of between 3.5 and 5 percent under normal circumstances. Higher demand in urban areas will bump up averages, especially in flourishing cities.

Cities that did well in this round aren't just making ground, they're blowing up. Let's go bracket by bracket and check out the best matchups:

Portland (8) over NYC (1): Among some easier-to-pick choices, some bigger upsets came in the form of up-and-coming 18-hour cities taking down larger, higher-priced metros. Portland, a budget-friendly city that is gentrifying faster than any other city in the country, took down the largest city in the nation when it comes to appreciation. And, frankly, it wasn't even close. In many ways, this has to do with the current housing prices in NYC; when you go that high, it hits a point where people can't keep up. Only the wealthy are buying in most of NYC now, which means increasing value is driven by a small set of the population--as well as investors. The market in Portland is driven by good ol' free range organic demand.

Pittsburgh (15) over Seattle (7): Like NYC, Seattle has become a high price metro over the course of the past several years, in large part to the growth of its tech sector--Amazon and Microsoft, namely. Pittsburgh, still a relatively inexpensive place to purchase a home, has also been growing rapidly in tech, but has yet to reach the point where prices are prohibitively expensive. Where there's more wiggle room for upward growth and adequate demand, appreciation happens. Where did the small city winning approach matter less? Major sprawl cities like Houston and Los Angeles, where a wider pool of housing means comparatively lower prices, despite strong economies appreciated at better rates than Seattle and NYC.

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Columbus (4) over Minneapolis (12): Minneapolis is consistently one of the top cities in the country for quality of life: a strong economy, healthy population, low unemployment. Columbus is centered in the heart of the Rust Belt, a region associated with the heartbreak of de-industrialization, but coming back strong. Both are great cities, highly comparable in their super-low unemployment rates and median salaries. Appreciation-wise, Columbus takes the day with a huge 8.9 percent year-over-year rate, while Minneapolis topped out a hair over 5 percent.

Austin (4) over Honolulu (12): Home prices in Honolulu are nearly double those of Austin, despite the fact that Austin is home to one of the fastest growing tech sectors in the nation. A lot of this has to do with location: Honolulu, off in the middle of the Pacific Ocean, features some of the highest basic commodity prices and a limited amount of space to develop. That's the price of paradise, I guess, but it also pushes home prices overvalue and into bubble-watch territory, according to Trulia. Austin is in the heart of flat ol' Texas with plenty of space to branch out, meaning traditionally, prices have been much lower. The popularity of the city, particularly hip neighborhoods, is driving appreciation, which flew to a staggering 9.3 percent putting it on the top of the bubble watch list. Honolulu actually went down a third of a percentage point. The difference? It's very likely in the price point.

Results:

Portland (8) over NYC (1)
Arlington (13) over Miami (12)
Dallas (3) over Omaha (11)
Nashville (7) over Philly (2)

LA (1) over OKC (8)
SF (4) over Tulsa (12)
Cinci (14) over Virginia Beach (11)
Pittsburgh (15) over Seattle (7)

Chicago (1) over Kansas City (9)
Columbus (4) over Minneapolis (12)
San Jose (3) over Colorado Springs (11)
Denver (7) over Aurora, CO (16)

Houston (1) over Albuquerque (8)
Austin (4) over Honolulu (12)
Indianapolis (3) over DC (6)
San Antonio (2) over Mesa (10)