I think there are a few reasons why our players tend to do better coming on in the last twenty than starting. First of all, the game is typically getting either stretched (if the opposition is losing and *must* attack) or the opposition is falling back to defend a result (Wigan, Swansea, Fulham, Emirates Marketing Project, Chelsea). If they have to come forward, this gives the attacking players like Bale and Siggy and Defoe more space for a counter, and if they are sitting deeper to defend something - as with most teams in our run-in - Huddlestone is then afforded more time and space and his positive qualities outshine his negatives.
Secondly, many teams these days believe, not inappropriately, that they can match up with us so they press us heavily even at the Lane. But like Southampton found out, that means you tend to start flagging and falling back in the last twenty. We struggle to gain control of midfield when heavily pressed because the first touch and control of most of our players are not of the quality of Modric/VdV under pressure, and because we don't move enough to create options for each other when one teammate is trapped. When teams stop pressing us though, we have enough good shooters from range to get goals no matter what kind of game it is.
Finally, we've looked pretty tired as a whole in this run-in. Usually at this point in the season it's a random new player who comes in from the fringes and makes a huge impact with his fresh legs (e.g. remember the contributions of Bale, Pav, and even Bentley and Gudjohnsen towards the end of 2010-11). When nobody comes in from the cold, you get the standard Tottenham Collapse we've seen the last two seasons. Because we've been pressing heavily all the way to the end throughout plenty of games this season, including a grueling Europa campaign that went to overtime, it stands to reason that we've clocked even more miles than we did under Harry. Even if tired, subs who only need to play 20 min can throw everything at the game (I saw Siggy playing RB against Chelsea at one point!), and their urgency lifts up the tempo of the whole team.
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For a starting XI, I think we need a balance of battlers/workhorses and truly classy ball-players. Many PL teams no longer just park the bus at the Lane and wait for a counter - they come here to try to outfight us in midfield, which is another sort of defense. So we have to able to find and create a coherent passing rhythm under intense pressure, and for that I think we need not only toughness but more midfielders who are simply really, really good on the ball and hold a vision of the game in their heads so they can pass swiftly. Teams struggle to press Arsenal and Chelsea because they can just one-touch their way around them. If too many of our players take too many touches or can't pass accurately under pressure (whether due to their relative lack of technique or team movement, I don't know) then we're going to struggle under the kind of press that more and more teams are trying these days.
You can kinda see where I'm going with this. I suspect some of our players are just not comfortable enough on the ball, or intelligent enough footballing-wise to really stamp their name on the starting XI in these sort of pitched battles that only retreat or scatter towards the end. However, they do possess hard work and energy, and more than a few times that's enough to simply overwhelm a tiring opposition if you have a sword named Bale.