Blood moons tend to occur more frequently than blue moons, which are relatively rare and happen roughly every two to three years.
blood moons happen more often than blue moons

Blue moon - Wikipedia
Source: en.wikipedia.org
Key Evidence
NASA data and astronomy sources indicate blue moons happen about every two to three years, while total lunar eclipses (blood moons) occur more often, typically one to three times annually. The Royal Museums Greenwich and Wikipedia also support the rarity of blue moons compared to blood moons.
rmg.co.ukrmg.co.ukWhat is a blue moon and how often does it occur?
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What the Evidence Shows
A blood moon is a total lunar eclipse where the moon appears reddish due to Earth's atmosphere scattering sunlight, and these eclipses happen about 1 to 3 times per year on average. In contrast, a blue moon, commonly defined as the second full moon in a calendar month, occurs roughly once every two to three years. This means blood moons are generally more frequent than blue moons.
However, the exact frequency can vary depending on definitions and specific astronomical cycles. For example, some sources note that the term 'blue moon' has different meanings historically, but the modern popular definition leads to a lower occurrence rate compared to blood moons. Community discussions and astronomy sources generally agree on this frequency difference, though some confusion exists due to terminology nuances.