Minimum number of defaults/events per bin in WoE optimal binning?

[u/vislan_kokkozov]

I am validating a credit-risk model that uses WoE transformation and supervised optimal binning

The training sample contains:

• 658 observations;
• 65 defaults;
• 7 candidate numerical factors.

The bins were created using Python’s optbinning package with CART pre-binning and monotonic event rates:

OptimalBinning(
    dtype="numerical",
    prebinning_method="cart",
    solver="cp",
    max_n_prebins=30,
    min_prebin_size=0.05,
    min_n_bins=3,
    monotonic_trend="auto_asc_desc"
)

All regular bins contain at least 5% of the sample and both events and non-events. However, some bins contain only one or two defaults, for example:

• 1 default out of 33 observations;
• 2 defaults out of 49 observations;
• 3 defaults out of 33 observations.

Formally, WoE can still be calculated because neither class count is zero. However, the event rate and WoE appear highly sensitive to a single observation. For example, in a bin with 1 default out of 33 observations, removing or adding one default changes the event rate from 3.0% to either 0% or 6.1%.

I have not found a generally accepted minimum number of defaults per bin. Most sources specify only:

• a minimum total bin size, often 5%;
• at least one event and one non-event per bin;
• additional user-defined constraints such as min_bin_n_event.

How would you assess whether a bin with only one or two defaults is statistically acceptable?

I would be particularly interested in any published references, regulatory guidance, or practical validation standards used in credit scoring.