#4. Brock Lesnar

While Brock Lesnar is better known these days for his work in WWE, his run in the UFC proved he was also a true BMF in MMA. Lesnar made the jump from pro-wrestling to MMA in 2007 when he made his pro debut, winning by first round TKO.
That performance, combined with Lesnar's popularity, led to the UFC signing him later that year. While he would lose his debut, 'The Beast' went on to win the heavyweight title and successfully defend the belt twice before losing in 2010 to Cain Velasquez.
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Lesnar was a freak athlete who clearly did not care what fans, sponsors or anyone else thought about him. He was also very good at getting paid, a trait shared by our more modern BMFs Nate Diaz and Jorge Masvidal.
#3. Tito Ortiz

Should the BMF title have existed in the UFC between 2005-2010, 'The Huntington Beach Bad Boy' would surely have been a prime candidate. While Tito Ortiz's run with the UFC light heavyweight belt took place prior to 2005, he would certainly still have been a worthy contender.
Perhaps the BMF trait that Ortiz showcased the most was his willingness to take on all-comers. Between 2005-2010, he fought Vitor Belfort, Forrest Griffin twice, Ken Shamrock twice, Chuck Liddell, Rashad Evans, Lyoto Machida and Matt Hammill.
This willingness to step up to any challenge, combined with Ortiz's signature bad boy attitude that was on show at all times, made him a fighter who would have definitely been worthy to hold the BMF belt.