How do I calculate average mortgage balance to determine how much interest I can deduct if I refinanced my purchase mortgage?

For example, if my purchase mortgage was $1 million and I refinanced the loan, the ending balance for the purchase mortgage would be $0 with an average balance of $500k which would make all interest deductible for the purchase mortgage. And then calculate the average balance for the refinancing separately. In essence, doing each 1098 separately.

Or should I calculate the average balance using the beginning balance from the purchase mortgage 1098 and the ending balance from the refinancing 1098?

The two methods yield very different results.