As soon as you put Amex in the mix, that's an impossible question to answer. Amex says that they post transactions on the date that they occur and use that day or the previous day's rate. I had a paper (click-clack machine!) Amex transaction at a restaurant recently on a weekend. It is clear from how long it took to get onto my online account that they did not receive it until days later, but it is still dated with the original transaction date on my account. In that situation with a Chase card, the transaction date would be days later and they would use the rate prevailing at the time of posting.

This makes comparison hard. Over the long term, what matters is how far away from the mid-rate our transactions' rates are. Pairing transactions seems like a good idea. It's ideal when the transactions are calculated in the same way. However, when we include Amex, whose date calculation methods differ from the others, it makes the Amex data vary wildly.