This gist is for my Medium article and is about using linear regression in scoring systems.

scores.py

import numpy as np
import matplotlib.pyplot as plt

def average(lst): 
    return sum(lst) / len(lst)
    
  
def findss(lst):
    # finds the sum of squares
    ss = 0
    mean = average(lst)
    for elem in lst:
        ss += (elem - mean)**2
    return ss

  
def findsp(lst1, lst2):
    # finds the sum of products
    sp = 0
    mean1 = average(lst1)
    mean2 = average(lst2)
    for i in range(len(lst1)):
        sp += (lst1[i] - mean1)*(lst2[i] - mean2)
    return sp


def findscore(lst, size):
    global xax
    slicex = xax[:size]
    slicey = lst[:size]
    meanx = average(slicex)
    meany = average(slicey)
    ss = findss(slicex)
    sp = findsp(slicex, slicey)
    b = sp/ss
    a = meany - b*meanx
    return b*(size+1)+a

xax = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

y1 = np.array([5, 5, 4, 4, 3, 3, 2, 2, 1, 1])
y2 = np.array([1, 1, 2, 2, 3, 3, 4, 4, 5, 5])

y3 = []
y4 = []

for i in range(len(y1)):
    if i == 0:
        y3.append(y1[0])
    else:
        value = max(1, min(findscore(y1, i+1), 5))
        y3.append(value)

for i in range(len(y2)):
    if i == 0:
        y4.append(y2[0])
    else:
        value = max(1, min(findscore(y2, i+1), 5))
        y4.append(value)
        
        
fig = plt.figure(figsize=(18,4))
ax = fig.add_subplot(121)
ax.text(5, 6.5, 'JOE', fontweight='bold', color='white', bbox={'facecolor': 'blue', 'alpha': 0.5, 'pad': 10})
ax.set_xticklabels([])
plt.yticks((1, 2, 3, 4, 5))
ax.set(xlim=(0.5, 10.5), ylim=(0.000001, 7.99999))
ax.bar(xax, y1, 0.5, color="green", alpha=0.5)
ax.plot(xax, y3, color='black', marker='o')
ax.plot(xax, y3, color='red')

ax2 = fig.add_subplot(122)
ax2.text(5, 6.5, 'SUSAN', fontweight='bold', color='white', bbox={'facecolor': 'blue', 'alpha': 0.5, 'pad': 10})
ax2.set_xticklabels([])
plt.yticks((1, 2, 3, 4, 5))
ax2.set(xlim=(0.5, 10.5), ylim=(0.000001, 7.99999))
ax2.bar(xax, y2, 0.5, color="green", alpha=0.5)
ax2.plot(xax, y4, color='black', marker='o')
ax2.plot(xax, y4, color='red')
plt.show()