As nine of those have now been defeats and the other was a draw, the nature of their plight is clear. It was Everton who launched their slide on Boxing Day - thus preventing Middlesbrough, it seems ludicrous to contemplate now, from moving into second place - and it was Everton who continued it without too much fuss.
There is nothing spectacular about the side which Joe Royle is still fashioning, aside perhaps from the ungovernable dribbling of Andrei Kanchelskis, but they are impressively regimented and combative.
Middlesbrough, initially doing an admiral job of displaying that their recent parlous returns have not affected their confidence, won plenty of possession. But their movement tended to fritter away in the areas that mattered and they failed to provide any sort of examination for Neville Southall.
Jan Fjortoft, whose crosses were careless throughout the afternoon, had perhaps the clearest opportunity when he met the raking cross from Graham Kavanagh, but his swing at the ball lacked precision and so did the resultant shot.
When Gary Walsh made a sterling save to keep out John Ebbrell's header in the 15th minute, it was a sign that all was not as it might be in the Middlesbrough defence. When Everton scored in the 29th minute, the evidence was conclusive. John O'Connor, overlapping down the right, found Graham Stuart with his cross and this time Walsh could merely deflect the header onto the bar whence it rebounded to Tony Grant who decisively thumped home his first League goal.
Seconds before the interval, Everton increased their lead. Kanchelskis went on one of his darting, incisive runs into the box splitting defenders and pursued forlornly by them. He went down under Curtis Fleming's lunge and Andy Hinchcliffe scored from the penalty.
There was never the remotest likelihood that Middlesbrough would pose a lasting threat to Everton in the second half. They had most of the possession and they kept moving forward, but the Everton defence ensured that Southall did not have to work too hard but for one telling save from the hapless Fjortoft. Branco raised hearts, if not immediate hopes. As significant as the South American connection has been to Teesside, it may be more important to their future this season to reintroduce the nous of manager Bryan Robson.