Some ASX shares have been hit particularly hard over the past year.
Two on my radar are trading more than 50% below their 52-week highs despite the long-term opportunities remaining strong.
Here is why I would buy them.

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Catapult Sports Ltd (ASX: CAT)
Catapult shares are down more than 60% from their 52-week high.
That is a huge fall, but I still like where the sports technology company is heading.
Catapult works with professional sporting teams around the world, providing technology for areas such as athlete monitoring, video analysis, scouting, and performance management.
What I like is how much more valuable the platform can become as clubs use more of those products together.
A professional team may initially use Catapult to track player workloads, but the relationship can expand into video, tactical analysis, recruitment, or strength and conditioning. That creates opportunities to earn more from existing customers while continuing to add new teams.
I also think professional sport has plenty of room to become more technology-driven.
Teams spend enormous amounts on players and coaching staff. Software that helps them prepare better, make stronger decisions, or reduce the chance of players missing games can therefore have real value.
Catapult still needs to keep converting its growth into stronger profits, and the share price could remain volatile. But after a decline of more than 60%, I think it now offers an attractive risk-reward profile.
Cochlear Ltd (ASX: COH)
Cochlear shares are around 54% below their 52-week high.
The company has faced a difficult period, but I do not think the need for its products has changed.
Cochlear develops implantable hearing solutions for people with severe hearing loss.
One of the reasons I remain positive is that many people who could potentially benefit from a cochlear implant never receive one.
Low referral and treatment rates leave Cochlear with a substantial opportunity to reach more patients over time.
The company is also continuing to improve its products. Its Nucleus Nexa platform gives recipients more personalised hearing technology, while longer-term developments such as drug-eluting electrodes and potentially totally implantable devices could make cochlear implants even more capable.
That does not mean the recovery will be immediate. Cochlear still needs to rebuild investor confidence and demonstrate that earnings can improve after a weaker period.
But with the shares trading at less than half their 52-week high, I think investors are being offered a much more reasonable entry point into a global healthcare leader.
Foolish takeaway
A falling share price is only interesting to me when I still believe in the business behind it.
That is the case with Catapult and Cochlear.
Both have disappointed investors recently, but I think their underlying markets still offer plenty of room for growth. At prices more than 50% below their recent highs, I would be comfortable buying both with a long-term view.