I don’t understand what question you’re trying to answer here. e.g., I could imagine questions of the form “If I see someone forecast 39.845%, should I treat this nearly the same as if they had forecast 40%?” Most mathematical ways of dealing with forecasts do (e.g. scoring rules, formulas for aggregating multiple people’s forecasts, decision rules based on EV). But that doesn’t seem like what you’re interested in here.
Also not sure if/how these graphs differ from what they’d look like if they were based on forecasts which were perfectly calibrated with arbitrary precision.
Also, the description of Omar sounds impossible. If (e.g.) his 25% forecasts come true more often than his 5% forecasts, then his 15% forecasts must differ from at least one of those two (though perhaps you could have too little data to be able to tell).
I don’t understand what question you’re trying to answer here. e.g., I could imagine questions of the form “If I see someone forecast 39.845%, should I treat this nearly the same as if they had forecast 40%?” Most mathematical ways of dealing with forecasts do (e.g. scoring rules, formulas for aggregating multiple people’s forecasts, decision rules based on EV). But that doesn’t seem like what you’re interested in here.
Also not sure if/how these graphs differ from what they’d look like if they were based on forecasts which were perfectly calibrated with arbitrary precision.
Also, the description of Omar sounds impossible. If (e.g.) his 25% forecasts come true more often than his 5% forecasts, then his 15% forecasts must differ from at least one of those two (though perhaps you could have too little data to be able to tell).