Advanced Micro Devices AMD -0.14% seems poised to have a good year. And it really, really needs to.

The sometimes troubled chip maker has spent the past couple of years improving its finances and preparing many new processors that are now hitting the market. The early buzz on those products has been strong enough to drive AMD’s market value up more than fourfold in the past 12 months. While the stock has come down about 19% from its peak in February, the shares are still trading at a price AMD hasn’t sustained in nearly a decade—which is around 154 times forward earnings.

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That puts a big bill on the chip maker. AMD reports its first-quarter results on May 1. That will include about one month of its new Ryzen 7 processor designed for high-end personal computers. More important, the company’s outlook for the second quarter also should include early sales of its new Naples server chip and a graphics processor called Vega, both of which begin shipping during the quarter.

Analysts are expecting big improvements in its computing and graphics segment following several years of declines. Revenue in that segment is expected to jump 21% this year, according to FactSet.

That target is attainable, especially considering that AMD has less than 10% share in the PC central processor market and essentially nothing in servers, according to Mercury Research. So nowhere to go but up. And the server business in particular should be helped by the fact that big customers there—cloud service operators Amazon, Google and Microsoft —are hungry for an alternative to Intel, which controls about 99% of the market.

But the bigger question is: What happens next? Historically speaking, AMD’s problem has been its ability to compete with the marketing and financial muscle of its much bigger rivals. So the worry is that any share gains this year will evaporate as they have in the past when Intel and Nvidia cut prices.

That is a big risk—one that Goldman Sachs cited when it downgraded AMD to a sell rating earlier this month. On the other hand, today’s server market in particular may be less sensitive to pricing pressure, as big cloud operators prize performance above all. That could help AMD both mount its comeback and make it stick. Its main problem right now is that investors have priced in both outcomes already.

Write to Dan Gallagher at dan.gallagher@wsj.com