Does Vitamin D reduce the severity of COVID-19 outcomes?

There is a heated debate regarding the effectiveness of vitamin D in improving COVID-19 outcomes. While numerous studies show a correlation, many claim it is due to confounding factors. A few controlled trials showed a strong effect, but the most notable one, conducted in Córdoba, Spain, had significant flaws that prevented it from being widely accepted. More studies are underway, and within a year or so we will likely get a more certain answer, but a probabilistic analysis of currently available information can reach a useful conclusion faster, potentially saving hundreds of thousands of lives. Additionally, the conclusion below is included in the Rootclaim $100,000 challenge. Note: this is a simplified analysis; the full version was published in September 2020 on the Rootclaim blog.