Accessories useless waste of time

I have just completed 8 desert runs to complete my daily challenge. As I only had one transformer in the desert I just let it run until it was killed. Then I recharged and redid the run. I did this with coconut hat, plus 20% defence, dragon hat,plus 8% defence and with no hat. The transformer was killed at exactly the same spot by a falling tower on every run. The hats made no difference whatsoever. In each case the transformer had one heart left as it was killed. This is the first time I have tested what I have suspected for some time. I am glad I did not pay any money for gems to buy them. Rovio should be as well, otherwise they would be guilty of fraud.