Data available for COVID-19 in the USA make it possible to assess the dynamics of disease spread with 20:20 hindsight. Here, we analyze archived data to explain variation among counties and states in the cyclicity and predictability (that is, the extent to which predictions are possible) of disease dynamics, using a combination of statistical and simulation models. For the period after the initial outbreak but before widespread vaccination (May 2020 - February 2021), we show that for half the counties and states the spread rate of COVID-19, r(t), was predictable at most 9 weeks and 8 weeks ahead, respectively, corresponding to at most 40% and 35% of an average cycle length of 23 weeks and 26 weeks. However, there were large differences among counties and states, and high predictability was associated with high cyclicity of r(t). Furthermore, predictability was negatively associated with R0 values from the pandemic's onset. This suggests that a severe initial outbreak induced strong and sustained protective measures to lower disease transmission, and these protective measures in turn reduced both cyclicity and predictability. Thus, decreased predictability of disease spread should be viewed as a by-product of positive and sustained steps that people take to protect themselves and others.