Why was Abel's sacrifice greater?

This is a question that has come up many times, and with many many different interpretations. As I meditated on Hebrews 11, I think I saw one of the main reasons.... correct me if I am wrong!

Genesis 4: ¹ Now Adam knew Eve his wife, and she conceived and bore Cain, and said, “I have acquired a man from the LORD.” ² Then she bore again, this time his brother Abel. Now Abel was a keeper of sheep, but Cain was a tiller of the ground. ³ And in the process of time it came to pass that Cain brought an offering of the fruit of the ground to the LORD. ⁴ Abel also brought of the firstborn of his flock and of their fat. And the LORD respected Abel and his offering, ⁵ but He did not respect Cain and his offering. And Cain was very angry, and his countenance fell.
⁶ So the LORD said to Cain, “Why are you angry? And why has your countenance fallen? ⁷ If you do well, will you not be accepted? And if you do not do well, sin lies at the door. And its desire is for you, but you should rule over it.”
⁸ Now Cain talked with Abel his brother;^{a]" style="font-size: 0.75em; line-height: 0.5em; ">[a]} and it came to pass, when they were in the field, that Cain rose up against Abel his brother and killed him.
⁹ Then the LORD said to Cain, “Where is Abel your brother?”
He said, “I do not know. Am I my brother’s keeper?”
¹⁰ And He said, “What have you done? The voice of your brother’s blood cries out to Me from the ground. ¹¹ So now you are cursed from the earth, which has opened its mouth to receive your brother’s blood from your hand. ¹² When you till the ground, it shall no longer yield its strength to you. A fugitive and a vagabond you shall be on the earth.”
¹³ And Cain said to the LORD, “My punishment is greater than I can bear! ¹⁴Surely You have driven me out this day from the face of the ground; I shall be hidden from Your face; I shall be a fugitive and a vagabond on the earth, and it will happen that anyone who finds me will kill me.”
¹⁵ And the LORD said to him, “Therefore,^{b]" style="font-size: 0.75em; line-height: 0.5em; ">[b]} whoever kills Cain, vengeance shall be taken on him sevenfold.” And the LORD set a mark on Cain, lest anyone finding him should kill him.

I think the answer is in Hebrews 11, where it is said, "⁴ By faith Abel offered to God a more excellent sacrifice than Cain, through which he obtained witness that he was righteous, God testifying of his gifts; and through it he being dead still speaks."

This is because, though Cain's sacrifice was of the ground, I think that even if Cain had offered a lamb it would have had the same results - because if the sacrifice was not done in faith, then it is just dead works, but 'by FAITH Abel offered to God a more excellent sacrifice than Cain". Faith without works is dead.(James 2). I conclude from Scripture too, that Works without faith is dead. It is by FAITH that Abel offered a more excellent sacrifice, for the Bible says,

1 Samuel 16:7 But the LORD said to Samuel, “Do not look at his appearance or at his physical stature, because I have refused him. For the LORD does not see as man sees; for man looks at the outward appearance, but the LORD looks at the heart.”

What do you think about this, after meditating on Scripture?