A risk threshold is a way of quantifying a runner's tolerance for risk in a speedrun. It usually refers to RNG-based risks, but it applies whenever two conditions are met:

1. The runner is attempting a strat that has a chance to fail
2. The run ends if the strat fails

Risk threshold is expressed with two numbers, formatted like this: 50/24. Read this as "I'm willing to take a risk that has a 50% chance to end my run if it saves at least 24 seconds." There are no limitations to these numbers; you could use 50/10, or 30/24, or 40/15, and so on. It's just preference. Once you've set a risk threshold, you can use logarithms to look up any amount of risk and its required time save. The math is included in this spreadsheet: https://www.dropbox.com/s/oxauinkzsim27nd/Risk%20management%20calculator.xlsx?dl=0

Having a risk threshold is useful because "average time save" calculations don't work when a dead run is a possible outcome. For example, if a strategy has a 50% chance of saving 10 seconds and a 50% chance of losing 15 seconds, the average time save would be (0.5*10)+(0.5*-15) = -2.5. But if the unfavorable 50% ended your run instead, the time could no longer be quantified.

What counts as "ending the run" is also preference. But if you tried to continue after, say, a death to the back end of the Elite Four, you'd lose a massive amount of time because of the extra fights and depleted inventory. Even if the chance of dying was low, the average time save would be very negative. Playing around average time save isn't necessary when you can just reset and try again. (In races or marathons, average time save is much more important, which is why safety strats are favored.)

Risk threshold has one major weakness: It can't measure how far into the run you are. Resetting is a powerful strategy for enabling early-game risks, but you don't want to reset an amazing run on the final fight because you took a risk that could have been avoided. My risk threshold is 50/24, but I'll often take 50/10 risks in the early game, or avoid 50/30 risks in the late game.

Effectively using risk threshold during a run is difficult, and you might perform better by relying on intuition. The main practical benefits of a risk threshold are:

1) Efficiently evaluating a new strat that includes risk (unless you can quickly do logarithms in your head)
2) Putting intuition to a mathematical test (we tend to struggle when evaluating extremely large or small risks)
3) Improving communication between runners ("Oh, your risk threshold is 50/30. Yeah, then that strat might be worth it.")