You must not understand math.
Seriously! Anyone thinking that going for it on '4th and 7 at the Detroit 46 yard line would have given the Cardinals a higher probability of winning doesn't understand probabilities! Even though the game ultimately ended with a tie, the Cardinals actually
increased the number of opportunities for them to win the game by punting in that situation. A turnover (loss of possession on downs) at that point would have swung the probability advantage to Detroit for the remainder of the game.
By punting they kept Detroit in a statistically disadvantageous position.
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With Detroit's posession on first down, FOLLOWING the punt, Arizona still had a 62.5 % probability of winning the game. Upon the pass completion on first down Detroit's advantage was 54.6%; on 1st and 10 at the 24 Stafford was sacked once again giving Arizona advantage, which they kept (increased) until the end of the game.
Had the Cardinals turned the ball over to Detroit near mid-field it would have given Detroit a huge advantage statistically.
The Cardinals made the statistically correct call by punting at that point in the game.