1. Cup runs give Chelsea's season fresh meaning

Manchester City's historic run in the Premier League has done more than kill the title race before the turn of the year; it has sunk their rivals into varying levels of existential crisis.

Chelsea, as defending champions, have found it harder than most. Antonio Conte hasn't enjoyed a victory in weeks, while every defeat has felt like a hammer blow. City are making those below them pay a full price for every mistake, and it is all too easy to dwell on the negatives.

The cup competitions, however, offer fresh opportunities for optimism. Conte has always considered the Carabao Cup to be at the bottom of his list of priorities -- he made eight changes to his team for the visit of Bournemouth -- but it is not in his nature to go through the motions.

Chelsea's starting XI was worth in excess of £200 million despite the inclusion of 17-year-old Ethan Ampadu and they started with purpose, deservedly taking the lead from the first fluid move of the match in the 13th minute.

Michy Batshuayi, challenged by Conte to impress, played a neat pass around the corner to Kenedy, whose sharp back-heel set Cesc Fabregas running through. The Spain international, assists always on his mind, unselfishly squared for Willian to tap in his sixth Chelsea goal of the season.

Bournemouth offered little going forward in a first half that drifted -- their cause not helped by the loss of Jermain Defoe, who eventually succumbed to the effects of a firm early Ampadu tackle -- and Chelsea's dominance was limited only by the disjointed nature of their play.

When the visitors did begin to carry a threat through the direct running of Jordon Ibe early in the second half, Conte's swift response underlined his desire to win the game. On came Eden Hazard and Tiemoue Bakayoko for Willian and Pedro Rodriguez, Chelsea switching from 3-4-3 to 3-5-2.

Alvaro Morata soon followed in place of Batshuayi, but Bournemouth continued to grow into the match.

Chelsea dropped deeper, the influence of their illustrious substitutes badly limited by poor service. In the final minute of regulation it was Dan Gosling who finally found a moment of quality, curling impressively beyond Willy Caballero from the edge of the penalty

But there was one final twist. Chelsea surged forward right after the restart and their substitutes combined, Hazard freeing Morata with a bac-kheel to poke beyond Artur Boruc.

Conte let out a roar of delight, his competitive juices flowing. The Premier League title might be gone, but there are still triumphs to be had this season.

2. Ampadu's rise another worrying development for Luiz

Recent months have offered fresh hope to Chelsea supporters that Conte may be the man to lift the historic roadblock preventing academy youngsters from establishing themselves in the first team -- even if it will have to be on his own strictly defined terms.

Conte is adamant that he will not give "stupid presents" to young players just to appease his critics, and it is this attitude that makes the breakthrough of Andreas Christensen and the rapid rise of Ampadu all the more impressive.

The final six months of 2017 have seen Ampadu go from playing League Two football for Exeter to a full Wales international and a regular in Chelsea's matchday squad, making his Premier League debut as a substitute for Christensen against Huddersfield earlier this month.

Despite playing in midfield in earlier rounds of the Carabao Cup against Nottingham Forest and Everton, Ampadu sees himself as a centre-back and, with his team selection against Bournemouth, Conte confirmed that he does too.

The comparisons with David Luiz can be tiresome, based as they are largely on similarly flamboyant hairstyles. There is, however, something of the Brazilian in the raw aggression -- at times bordering on recklessness -- that imbues the 17-year-old's approach towards defending.

A firm but fair tackle forced Forest defender Danny Fox to be substituted three minutes after Ampadu's introduction in September and Defoe suffered a similar fate, failing to recover from a crunching blow to the ankle that earned the youngster a second-minute yellow card.

Ethan Ampadu has impressed and shown a willingness to tackle in his Chelsea appearances. Photo by John Patrick Fletcher/Action Plus via Getty Images

Adam Smith was wiped out in the penalty area -- fairly, it must be said -- as Ampadu made it clear he would not be intimidated by this stage or his opponents. Between those muscular exclamation points there were plenty of examples of a promising ability to sense danger and deal with it decisively.

You sense it is Ampadu's attitude as much as his attributes that has endeared him to Conte. It is to his immense credit that he finds himself ahead of Jake Clarke-Salter, a defender almost three years older and an Under-20 World Cup winner with England, in his head coach's reckoning.

His convincing display in the centre of the back three, however, should be an even more worrying development for Luiz. The Brazilian already faces a formidable fight to overcome tensions with Conte and the form of Christensen. Ampadu's emergence as another viable option is the last thing he needs.

3. Howe must upgrade Bournemouth

Bournemouth, unlike too many clubs in the lower reaches of the Premier League, know who they are. Eddie Howe has maintained their identity as an expansive passing team in the top flight admirably, maximising every drop of talent from a core of players that powered the club's remarkable rise.

They did their manager and their travelling supporters credit at Stamford Bridge, rallying from a goal down to pin Chelsea back for long periods of the second half and finding an impressive equaliser through Gosling, before Chelsea's luxury substitutes did their jobs.

Yet the winless run now extends to seven matches in all competitions, with City next up at the Etihad Stadium. Bournemouth are certain to go into 2018 with the relegation zone looming large in the rear view and, for all of Howe's good work, it is easy to see why.

A glance at Bournemouth's starting XI on any given matchday leaves the impression of a Championship side playing above themselves, yet this is a club that has always boasted considerable resources and is now enjoying its third consecutive season of Premier League TV money.

Howe appears to struggle to trust players who come from outside, even at considerable cost. Nathan Ake has established himself but Jack Wilshere, a player on a different technical level to anyone else in the Bournemouth squad, too often found himself out of the starting XI last season when fit.

That loan felt like a missed opportunity not just for Wilshere but for Howe, to prove that he could coach and improve a higher standard of player. It is this, you suspect, that might be the reason why there has not been a greater clamour to see him in contention for jobs at Everton and West Ham in recent months.

Bournemouth's core is ageing and their momentum is downward. One way or another, Howe must find a way to upgrade his team, or run the risk that the club where he is so adored might one day decide they have to upgrade him.