If we imagine an outdoor race with two obstacles:
- If the participant fails an obstacle attempt they exit the race
- Historical data shows that about 50% of participants will fail each obstacle
- That means that about 25% will finish the race (.5 * .5)
100 people entered today's race with the following current status:
- 75 people have attempted obstacle 1 but only 40 succeeded
- 20 people have attempted obstacle 2 but only 8 succeeded (and have completed the race)
Per the numbers above:
- 25 people are still waiting to get attempt obstacle 1
- 20 people are still waiting to complete obstacle 2
What approach should we use to forecast the number of people who will complete the race?
Here is my thought process, starting with obstacle 1:
success=40 #succeeded fails=35 #failed #prior (50/50 prior) alpha=10 beta=10 x = np.linspace(0,1,100) pd.DataFrame(stats.beta(alpha+success,beta+fails).pdf(x)).plot.line( figsize=(12,6), color='grey', )
The probable success rate therefore lies somewhere between 40% and 65% roughly, meaning that between 10 and 16 of the remaining 20 competitors will pass the first obstacle.
Is that right???
When calculating the same for obstacle 2, does obstacle 1 become a prior or is it completely unrelated???