Method to identify the point where numbers fall off sharply

I have a series of numbers:

numbers = [100, 101, 99, 102, 99, 98, 100,  97.5, 98, 99, 95, 93, 90, 85, 80]

It's very to see by eye that the numbers start to fall sharply roughly around 10, but is there a simple way to identify that point (or close to it) on the x axis?

This is being done in retrospect, so you can use the entire list of numbers to select the x axis point where the dropoff accelerates.

Python solutions are preferred, but pseudo-code or a general methodology is fine too.

Solution

Ok, this ended up fitting my needs. I calculate a running mean, std deviation, and cdf from a t distribution to tell me how unlikely each successive value is.

This only works with decreases since I am only checking for cdf < 0.05 but it works very well.

import numpy as np
from scipy import stats
import matplotlib.pyplot as plt

numbers = np.array([100, 101, 99, 102, 99, 98, 100,  97.5, 98, 99, 95, 93, 90, 85, 80])

# Calculate a running mean
cum_mean = numbers.cumsum() / (np.arange(len(numbers)) + 1)

# Calculate a running standard deviation
cum_std = np.array([numbers[:i].std() for i in range(len(numbers))])

# Calculate a z value 
cum_z =  (numbers[1:] - cum_mean[:-1]) / cum_std[:-1]

# Add in NA vals to account for records without sample size
z_vals = np.concatenate((np.zeros(1+2), cum_z[2:]), axis=0)

# Calculate cdf 
cum_t = np.array([stats.t.cdf(z, i) for i, z in enumerate(z_vals)])

# Identify first number to fall below threshold
first_deviation = np.where(cum_t < 0.05)[0].min()

fig, ax = plt.subplots()

# plot the numbers and the point immediately prior to the decrease
ax.plot(numbers)
ax.axvline(first_deviation-1, color='red')