Why do people believe Saban would have built a dynasty if he had stayed at LSU?

The numbers don't bear it out.

At LSU, Saban had at least one game every year where he lost by two scores or more. In fact, he had ten losses of two scores or more and seven losses of three scores or more. At Bama, Saban's had four games where he lost by two scores or more and has never lost by three scores.

At LSU, Saban had at least one game every season when his team was held to ten or fewer points. At Bama, his teams have been held to ten or fewer points three times in ten years.

LSU was never ranked #1 in the AP Poll during Saban's entire time at LSU. There wasn't a single week AP voters believed LSU had the best team in the country.

It's Saban's tenth year at Alabama. He has the same number of conference losses at Alabama that he had during his entire time at LSU (12).

It took eight years at Bama for Saban to match his five year loss total at LSU.

These numbers tell me one of two things. Either it's much easier for a coach to win big at Bama or Saban became a much better and improved coach after his two year stint in the NFL. However you look at it, Saban showed no signs of building this incredible uber-dominant program if he had stayed at LSU. At LSU, his teams had a bad game every year where they either fail to show up offensively (not scoring at least ten points) or lost decisively (lost by two or more scores). Saban lost at least two conference games every year at LSU except 2003. Saban lost at least three games every year at LSU except 2003. His teams never even finished in the top 15 in consecutive years. Where is the proof that Saban would have been able to build this dominant program at LSU?