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It seems that my prediction is more appropriate than yours. Aston Villa did have a better performance than Everton, and they dominated the match but one of the things that makes me feel Everton can steal points from Aston Villa is that they have a high fighting spirit, moreover, they play in front of their fans. As we can see, Everton did lose badly in possession of the ball but they have good enough stamina to keep them playing with tight marking.
I hope to be lucky another day, and I have to admit that the analysis you presented proved correct this time. Even though it didn't produce a winner, this match was actually quite entertaining, apart from that, Everton took advantage of the home factor and high enthusiasm to avoid the relegation zone well. A fair result for both, but not for those who bet on one of them winning.
Winning with dominant possession of the ball sometimes doesn't make a difference to the final result, Aston Villa showed that today. On the other hand, for Aston Villa this result paves the way for Manchester City to occupy second place in the standings, while we know that Everton is still one level above the relegation zone, but I believe Everton have the ability to survive in the Premier League next season.