The Talmud (Shabbat 38a) records the following rabbinic decree:
מאי גזירתא דאמר רב יהודה בר שמואל א"ר אבא אמר רב כהנא אמר רב בתחילה היו אומרים המבשל בשבת בשוגג יאכל במזיד לא יאכל וה"ה לשוכח משרבו משהין במזיד ואומרים שכחים אנו חזרו וקנסו על השוכח
What was the preventive measure?-For R. Judah b. Samuel said in the name of R. Abba in the name of R. Kahana in Rab's name: At first it was ruled: One who cooks [food] on the Sabbath unwittingly, he may eat [thereof], if deliberately, he may not eat; and the same applies to one who forgets. But when those who intentionally left [it there] grew numerous, and they pleaded, We had forgotten [it on the stove], they [the Sages] retraced their steps and penalized him who forgot.
How did the Rabbis know that people were leaving food on the stove intentionally? Isn’t the whole problem that a bystander can’t know what the person intended?
Did they have some specific way that they knew this? Or was it perhaps merely a statistical assumption that there couldn’t possibly be that much unintentional leaving on the stove?