Coding and AI classes in Pforzheim

import csv

seasons = []
with open("pforzheim_theatre.csv", encoding="utf-8") as f:
    for row in csv.DictReader(f):
        start = int(row["season"][:4])
        seasons.append((start, int(row["performances"]), int(row["visitors"])))

train = [s for s in seasons if s[0] <= 2016]
test = [s for s in seasons if s[0] > 2016]

def fit(points):
    n = len(points)
    mx = sum(x for x, _ in points) / n
    my = sum(y for _, y in points) / n
    slope = sum((x - mx) * (y - my) for x, y in points) / sum((x - mx) ** 2 for x, _ in points)
    return slope, my - slope * mx

slope, base = fit([(year, v) for year, _, v in train])
print("Trend: visitors change by", round(slope), "a season")
for year, _, visitors in test:
    guess = slope * year + base
    print(year, "predicted", round(guess), "real", visitors)

The trend says audiences fell by about 1,376 a season, and for 2017 and 2018 it is within a few thousand. Then it misses badly: it expects 93,862 visitors for the 2019/2020 season and the real figure is 64,831, and for 2020/2021 it expects 92,486 against 1,869. Something changed that the calendar knows nothing about. The file shows what: the theatre gave 184 performances in 2019/2020 and only 16 in 2020/2021, against 245 or more in every training season. It does not say why, so neither do we.

So Model 2 uses the number of performances instead of the year. That is the more sensible input: fewer shows should mean fewer visitors. If the number of performances is known before the season, this model ought to cope better with the unusual years.

slope2, base2 = fit([(p, v) for _, p, v in train])
print("Each performance brings about", round(slope2), "visitors")
print("With no performances the line says:", round(base2))
for year, performances, visitors in test:
    guess = slope2 * performances + base2
    print(year, "predicted", round(guess), "real", visitors)
print("Fewest performances in training:", min(p for _, p, _ in train))

Model 2 is much better for 2019/2020, within about 6,000. And then it forecasts minus 31,756 visitors for 2020/2021, which is impossible. The reason is in the last line it prints: the model never saw a season with fewer than 245 performances, so between 245 and 300 a straight line fits well, but stretched down to 16 it runs through zero and keeps going. The line even claims that a season with no performances at all would have minus 40,396 visitors.

Data: Stadt Pforzheim, Aufführungen und Besucher (Theater, Oper, Ballett), source Theater Pforzheim, licence CC BY 4.0, downloaded 3 November 2026. Training on seasons starting 2000 to 2016; models, forecasts and the table are our own. For comparison, visitors per performance (also ours) were 421 in 2000/2001, 376 in 2016/2017, 352 in 2019/2020 and 117 in 2020/2021.

Neither model is "wrong" inside its comfort zone. Model 1 assumes the future is like the past; Model 2 assumes a season looks like the seasons it has seen. The lesson for anyone learning AI is the same at 12 and at 50: before trusting a prediction, check whether the question lies inside the range the model learned from, and say so next to the answer.

1. Children, 9 to 12. On squared paper, plot five made-up points that rise steadily and draw a line through them with a ruler. Extend the line far to the left. Where does it cross zero, and does that make sense?
2. Teenagers. Run both models, then train Model 2 on all seasons except 2020/2021. Predict its new answer for 2020/2021 before you run it.
3. Teenagers, further. Write a guard that refuses to predict when the number of performances is below the smallest one in the training data, and prints a warning instead.
4. Adults. Replace the line with "visitors per performance times performances" (a line through zero). Compare its 2020/2021 forecast with the real 1,869 and explain the gap using the per-performance figures in the source note.