# Experimenting with new late penalty formula

## Introduction

During my first year of teaching at UC Davis (starting in WQ17), I had no flexible late policy for project submissions. The deadlines were set on 11:59 PM of specified days and late work wasn’t accepted at all. It’s a bit difficult to remember but I imagine that I surely received some pushback from students over time.

According to my archives, I introduced a more flexible late policy in SQ18. Late project submissions were accepted but penalized at the rate of $5\%$ per hour late, and since I didn’t want to penalize (too much) students who were just a few minutes late, this penalty was prorated per minute. So if a group submitted their work ten minutes late, then they would lose $10 * 5\% / 60 = 0.83\%$.

The problem is that if a group was still working on a nasty bug and went over
the deadline by say three hours, they would already lose $15\%$ of their grade (!),
which would de facto limit their grade to a B maximum *(assuming there was no
curve for the project assignment)*.

I kept this late penalty formula for four years until at the end of the last
academic year (in SQ22), a student complained more strongly than usual, which
prompt me to rethink it. *By the way, when professors ask students for their
feedback, please do voice your concerns – if I hear the same complaint over
time by trusted students, it really helps to know what I need to address next.*

## New late penalty formula

The idea of the new late penalty formula I developed is to remove points at an exponential rate instead of a linear one. What is means is that the penalty for late submission will stay reasonably small for a long time, before suddenly shooting up to $100\%$ by a certain time.

The formula that I ended up crafting is $\frac{(1.3471^x - 1)}{(1.3471 - 1)}$, where $x$ represents the number of decimal hours late.

For example, submitting $1.5$ hours late will incur a penalty of $1.62\%$, while submitting $7.2$ hours late (that is, 7 hours and 12 minutes) will incur a penalty of $21.73\%$. It’s only after $12$ hours late, that the penalty exponentially reaches $100\%$.

Overall, the formula behaves as shown on the graph below.

### Excel equation

If one wanted to use this formula in a spreadsheet, such as shown in the
screenshot below, the equation for the late penalty (cell `C2`

) would be:
`=(POWER(1.3471,(A2+(B2/60))) - 1)/(1.3471 - 1)`

## Conclusion

It’s too early to tell, but after using this formula across three project assignments this quarter, I have not heard any complaints from students!

It also appears that the rate of late submission has stayed the same as previous quarters, so the new formula doesn’t seem to “incentivize” late submissions. It only makes them less painful for students. Further analysis on this is required though.