Modelling a race

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:

1. 75 people have attempted obstacle 1 but only 40 succeeded
2. 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?

update

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???

Many thanks

• Since you are given no historical information at all about people who are "still waiting to get through" various obstacles, why do you suppose any forecast is possible? – whuber Feb 17 at 20:05
• thanks @whuber - based on my knowledge thus far, a Bayesian approach allows us to assign a 50/50 prior and we now have data on 75 competitors who have attempted the obstacle – DrBorrow Feb 17 at 20:09