Mike Smith's 4th and Inches: The Right Play?

Mike Smith is one aggressive head coach

In today's Saints/Falcons game, Mike Smith was faced with a 4th and inches decision on his own 29 yard line in overtime. He chose to go for it. The run play he chose was stuffed, the Saints took over on downs, gained a first down, and kicked a game-winning field goal. Without being results-oriented, I wanted to figure out if Mike Smith's decision was the incorrect one. I checked out another site regarding some calculations regarding this play, but I don't really agree with all of them. So, here's my take on this play:

There are two choices here for Smith: punt, or go for it. The league average on 4th and less than 1 is a 74% conversion rate. Assuming that a conversion gives them a 1st and 10 around their own 30 yard line, the Falcons would then have about a 57% win probability (WP). If they fail on the conversion, the Saints would get the ball around the Falcons' 29 yard line. In this situation, the Saints may gain a first down before trying a field goal or may just run three times and kick it. John Kasay is a very competent kicker, and we can assume (if they run 3 times and kick the field goal) that a field goal attempt would be somewhere around 40 yards (the league average for this distance is around 83%).  If the very potent Saints offense decides to try to move the ball closer, gains a first down, and kicks a shorter field goal (say a 30 yarder), the league average goes to somewhere near 91%. Let's assume that there's a 50/50 chance of first down or no first down (the Saints don't go 3 and out often and Sean Payton is a VERY aggressive play-caller). This makes the percentage of losing ON THAT DRIVE around 87%. Now, let's assume that you miss the field goal. The Falcons now have the ball back around the 30 yard line in the exact situation you had before (about 57% WP).  Taking all outcomes into account, by going for it, you have a 44% WP.

For the punt decision, the league average for punts is about a net of 40 yards. The game did take place indoors, so let's add an additional 5 yards to that, giving the Saints the ball at their own 25 yard line. According to a combination of 2 minute drill stats and scoring probability calculations (I think both apply here. It's not a pure scoring drive or 2 minute drill, so I decide to combine probabilities), the Saints have somewhere around a 52% WP. Conversely, this means that a punt would give the Falcons a 48% WP.

So, by expanding a little bit on the other site's calculations, I believe that punting is a better play in this situation. The Saints hadn't exactly been moving the ball that well in the game and had gone 3 and out in their first drive of overtime, so it's not out of the question that they could be stopped again. I enjoy Mike Smith's aggressive onside kicks and 4th down attempts, but I don't think he's exactly a good coach. He made a slight mistake here and needs to punt that ball on balance.