Football mathematics

In a comment to the Totti post a few days ago, reader slash commenter Thomas blew everyone's minds, in coming up with a new way to think of Totti and Roma. The gist of it, summed up by this quote:
Let's consider Roma to be the number 1, Totti to be himself and the other 10 players to constitute the letter P. In order for Roma to equal 1, which should be the goal, Totti has to cover the difference between 1 and P.

[...]


If we relate this to the above-mentioned variables, P sometimes has been 0,5, sometimes 0,8 and sometimes 0,7. The need for Totti has varied along these lines, but what everything boils down to is that there always has been different areas in which Totti's presence has been essential for Roma's success. Totti always has been 1-P.
It's a very interesting way to look at it, and certainly a fresh way to think of football and teams' and players' interdependency, and we always welcome and encourage new ways to think about football. But let's consider Thomas' theory, in the changing number Totti has to be in order for Roma to reach balance in 1-P, and how different Roma teams have forced changes in Totti's effort and game. Rather than going through every single one of the teams featuring Totti, I've chosen to look at a selection from this side of the millennium.

Roma 2000/2001 - The best and most successful Roma team of Totti's career. The best co-players he's ever had (and is likely to ever have), there were more to Roma threatening than just attacking through Totti; beside the wing play by Candela and Cafu, Batistuta was an elite striker who based on both reputation and hunger for goals had to be given equal attention from markers. The best team, the best squad of his career equals a P of about 0,8, Totti covering the spread of 0,2.

Roma 2003/2004 - Totti's last season under Capello, in which he and Cassano were given virtually all offensive responsibility. As good as Cassano was that year, Totti still carried the bulk of the weight, both in terms of numbers and leadership towards the younger, more inexperienced Cassano. Given that Roma did have a solid defensive unit that year who allowed Totti the freedom to do what he does, P still equals only 0,5 (I could probably stretch to 0,6 if I see vehement protests, but that's it). Totti's 20 league goals and leadership covers the spread of 0,5.

Roma 2004/2005 - Annus horibilis. Four different coaches, and about as many points away from relegation. Montella's indian summer and his goals helped a lot, but it's scary to think of what would happen if Totti hadn't been Totti. P is 0,3 on this team, and all of that's Montella.

Roma 2005/2006 - The first year under Spalletti, as mentioned and covered in the original post of a few days ago. His importance is hard to overestimate, but at the same time was born a very solid unit, that at least didn't make the team chanceless when Totti was out injured, whereas the preceeding year saw ten players running around without purpose or ideas. Spalletti and the 4-2-3-1 factor raises P significantly: 0,7.

Roma 2006/2007 - A Totti re-born after his injury. Won the Golden boot for being Europe's top marksman with 32 goals in all competitions, and further improved on the role that was created for him the year before, as the striker. It's difficult to grade this particular P, as one have to take into account that by giving Totti a higher number, indirectly it takes away from the rest of the team, and that would be awkward. Final call: P = 0.6.

Roma 2007/2008 - A less spectacular Roma, but a more successful one. Totti was out for a long time in two different stretches, but his importance and quality shone through and always made Roma a much better team whenever he was suited up. But closing so many gaps (from -22 on Inter to being Italian champions for an hour on the very last day of football, knocking out Real Madrid, again winning la coppa) means P needs to be higher: 0.7.

The current season isn't over, so it would be unfair to review it with the same certainty as one can look at those already concluded and written into the history books. But a worse Roma means his quality becomes even more important, if my hand is forced I'd probably estimate P at 0,5. A negative trend, in other words.