They beat high-flying Wolfsburg home and away in the group stages. They thumped Young Boys of Switzerland 7-2 on aggregate in the last round, and they face Dynamo Kiev in the next, avoiding the likes of Inter Milan, Roma and defending champions Sevilla. Everton are flying in the Europa League and are realistic contenders to reach the final in Warsaw.
In the Premier League, however, the Toffees are in free-fall: just six points above the drop zone, no wins in their last five and only one in their last 12; Everton are enduring their worst league campaign in 88 years.
Which raises the spectre of a rather unwanted double: could Everton win the Europa League and bag the Champions League place that comes with it, yet still be relegated?
It wouldn’t be the first time Roberto Martinez has combined triumph with disaster. In 2012-13, the Spaniard led Wigan Athletic to their first ever FA Cup triumph, defeating Manchester City in the final 1-0. Just three days later, a 4-1 loss at Arsenal saw the Latics demoted from the Premier League, becoming the first team ever to “achieve” both relegation and FA Cup glory in the same season.
Six points above the bottom three with 10 games to play may sound like a reasonable cushion for the Merseysiders, but it's by no means insurmountable. Last year Norwich had the same margin of comfort with just six games remaining, yet still went down. And as Martinez himself admits, "any team that hasn’t got 40 points in the final third of the season is in a relegation fight."
While on paper the Toffees are comfortably better than at least half-a-dozen teams in the league, “too good to go down” are words that time and again have proven to be empty. They have crucial fixtures against fellow strugglers QPR, Sunderland, Aston Villa and Burnley still to come; however clichéd, each is undeniably a six-pointer.
European triumph and Premier League disaster within the same campaign may be a long shot, but in Roberto Martinez Everton have a manager with a pedigree in bittersweet seasons. If the Toffees continue to shine on Thursday nights only to cave in at the weekend, he may very well be on the verge of an unprecedented double-double.