When we look at sorting algorithms, it's interesting to see how different things affect how fast they can sort. Here are some important points to think about:

1. Choice of Data Structure: For example, quicksort can be really slow, with the worst time taking $O(n^2)$ if the way we pick our "pivot" (the number we use to split our data) isn’t good. This usually happens when the data is already sorted or nearly sorted.

2. Type of Algorithm: Some algorithms that compare values, like mergesort and heapsort, keep a worst-case time of $O(n \log n)$ no matter how the data is arranged. On the other hand, easier sorts like bubble sort can slow down to $O(n^2)$.

3. Characteristics of the Input: The kind of data we are sorting matters a lot. Some algorithms work better with certain patterns. For instance, insertion sort does well with data that is partly sorted but really struggles when the data is all mixed up and random.

Knowing these factors can help you pick the right sorting algorithm for what you need. Each algorithm has its own strengths and weaknesses depending on the situation. This shows how important it is to be flexible in designing algorithms.