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In figure 1 it looks like we have 50% precision at 100% recall. I don't do a lot of binary classification, but should it be concerning for the model if it is only right half the time (random chance) when we demand it predicts for all data?

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For a binary classifier, recall is defined as the true positive rate: Of all the samples that are actually positive, how often did our model output "positive".

To get this to 100%, the model would simply say "positive" all the time. This means that the precision (the fraction of samples where the classifier said "positive" that were actually positive) goes to 50% (for a balanced dataset).

But it should be possible to get 100% recall with higher than 50% precision if you have a good classifier right?

No. Only if you had a perfect classifier. The only way to have 100% recall is to have absolutely no false negatives. In practice, the only way to have no false negatives is to have no negatives at all.

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