We can't judge West Ham United as small team but in realistic they can't consistent on top performance actually last end primer league games where they have chance for finish on 4th standing position place but at least they can't play with top performance. After defeating by Tottenham Hotspur exactly still have chance for West Ham United as finish on 4th position but several match left have waiting by Arsenal, Chelsea and Manchester City. Still have another option for getting champion league spot maybe become the champion on UEFA Europe League where West Ham United success on quarter final right now.
West Ham have been having an extraordinary season. But at this stage of the championship, I think it will be very difficult for them to reach 4th place. Mathematically it's still possible, but it would be necessary for the teams in front to start losing several games.
In the best case scenario, they may even manage to stay in 6th place, if Man United continues to play very irregular games.
Westham United still have a chance to make the top four this season. The title challenge is still very open and they’re just 6points below Arsenal. They are still competing in the Europa League which is their primary focus right now not having the squad depth to withstand this pressure that comes with competing for both titles is what might or will sink them in the EPL. They have made it through to the quarter-finals, while they are currently in seventh place in the Premier League. Even though Arsenal are the favorite to finish in the top four ahead of Tottenham Hotspur, Manchester United, and West Ham, I still believe that anything can happen before the end of the season.