An ordinal model would be more appropriate but it might make no practical difference. If you estimate a multinomial model, it is possible you might get something like
That is, greater force might be associated with a higher probability of levels 2 and 3 compared to 1, no increased probability of 4 compared to 1, and a decrease in probability for level 5 compared to 1. This could lead to odd or counter-intuitive predictions (see attached script). More concretely, it does not assume that an increase in force is always associated with an increase in average damage. This is demonstrated in the plot below, which uses the equations above.
Of course, if you have enough data and it truly shows that damage levels 2 through 5 all increase relative to level 1 as force increases, then the multinomial model may perform just fine.
Standard ordinal models assume that the coefficients are the same across all comparisons. This ensures that an increase in force will always be associated with an increase in damage (assuming the coefficient is positive). This is demonstrated in the plot below, where the cumulative logistic regression equation is y = 0 + 0.5 \times force and the thresholds are [-1.5, -0.5, 0.5, 1.5].
The choice between cumulative, sequential, and adjacent leads to different assumptions. As you point out, the cumulative specification makes it the easiest to calculate your target quantity (the probability that damage is 3 or above). Interpretation-wise, it reduces to a logistic regression model where you split the data at 3. I’m less familiar with sequential and adjacent models. I think they are more flexible than cumulative models with the consequence that they can not be reduced as easily to a binary model for your target quantity. But they may have other appealing features you might be interested in.
ordinal_example.R (3.1 KB)