# Whether and how to bin data beyond a certain threshold

I've seen many admonishments against binning and agreed with them in general, but I wonder it's advisable to do so under certain circumstances.

To adapt an example from my actual project, let's say we're predicting students' failure to graduate college within five years based on their high-school records.

1. One of the statistics is how many times the student has ever received an F. The table below shows the F count, the student count, and the failure rate. Whether the presence of any F is clearly a factor, as is a second F, but I don't feel comfortable drawing inference beyond that. Is it not advisable to group this variable as 0, 1, and "2 or more"? And if it is, should this be coded as three integers or two dummy variables?

.

0   200000  0.05
1     1000  0.11
2       50  0.50
3       20  0.52
4        4  1.00

1. Another statistic is late submissions of assignments. Here, too, the number of late submissions increases the likelihood of failure until it plateaus at 4 or so and becomes erratic. I'm tempted to lump all of the data beyond 4 together, should I?

I would like to learn how to go about making these decisions in a mathematically rigorous manner. Does that depend at all on the choice of learning algorithm (which I haven't made)? Any pointers to materials I can study on my own would be most welcome. Thank you.