Wednesday, September 29, 2010

Schedule Adjusted Points per Million Spent (aPPMS)

A long distance flight with no TV screens and only a laptop and Excel sounds pretty boring, but for fantasy nerds like me, it provided some time to have a think about better ways to process data to create meaningful statistics (like I said: nerd). The product of the flight - aside from the consumption of a pile of junk food - is a new statistic I plan to refer to over the coming weeks and months: Schedule Adjusted Points per Millions Spent (aPPMS).

Previous readers, or those with some common sense, will no doubt be able to see that Points per Million Spent (PPMS) is simply Points per Game (PPG), divided by the cost of that player. The idea is to try and assess 'value' rather than just points to avoid suggesting that an 9m player who scores 4.5 PPG (0.500 PPMS) is better than a 5.0m player who scores 4 PPG (0.800 PPMS).

For reference, and as a benchmark, assuming most people have budget players on their bench (say, 20m worth) you would need to generate a PPMS of 0.658 in order to generate the 53 points per week needed to hit the 2,000 mark for the season. Any player who can hit this rate is therefore helping you achieve that goal.

Room for improvement
There are a couple of problems with PPMS (that I can see, I'm sure any observant readers will spot plenty more):
  1. A player's value is a moving target and so it is hard to know whether to use their cost at the start of the season, their cost when they scored each individual point, or their price today. Historical cost is clearly not that useful as, taking an extreme example, if a player was averaging 5 points a game as a 6.0m player his PPMS is a very useful 0.833. However, if the subsequent transfers have pushed his value to 9.0m his PPMS is now just 0.556, good but not at a 'must buy' level.
  2. The second issue, especially at the start of the season, is that PPMS fails to account for who points were scored against. For example, after week 2 we might have been ready to crown Ashley Cole the winner of the A.Cole v G.Johnson battle but it seems hasty given that Cole had faced West Brom and Wigan (two sides that may go down) while Johnson had faced Arsenal and City (two sides that may challenge for the title).
To answer the first point; I use the value of the player today as this is what we are hoping to buy at. It means that I will underestimate player's PPMS over a season if their price rises but to be honest we don't really care how good a player was in GW1-9 if we didn't own him. We want to know if he is still good value now and needs to be purchased.

It is the second point that I am trying to combat with aPPMS (that and of course the aforementioned boredom of being on a plane). The basic - perhaps overly so - solution is create a 'factor' for both defensive and offensive players based on the teams they have faced and how many goals that team concede/score. This can then be compared against the average to show if a team's schedule has been easier or harder than other teams in the league. The final wrinkle is to make sure that we apply this factor the right number.

For forwards and goalkeepers this isn't an issue as all their points come at one end of the field (save for the odd goalie assist which I will ignore here). However, midfielders, and particularly defenders, have the chance to earn points both offensively and defensively and so care needs to be taken to not overly inflate/deflate points scored to date. For example, Hangeland managed 7 points against United in GW2 but this should not be included in our adjustment as the fact that United have a strong attacking unit - and are hard to keep a clean sheet against- had no impact on Hangeland's points haul for the week, which were mainly earned due to his goal. Conversely, Kolo Toure's clean sheet against Spurs in GW1 deserves extra credit due to the tough fixture in which it was earned (at Tot). Hence, defensive points for midfielders and assists/goals for defenders will not be inflated/deflated based on the offensive/defensive ranking of the opposition (but will be added back after the calculation to make sure they are counted once only).

At this point in the season, the data is not totally reliable as a big score in one game will skew the results one way or another but either way the results are worth highlighting by way of example

aPPMS - PPMS
  1. Odenwingie (1.417 - 1.320)
  2. Salcido (1.145 - 1.200)
  3. Elmander (1.128 - 1.042)
  4. Ebanks-Blake (1.089 - 0.950)
  5. Carson (1.083 - 0.772)
  6. Carroll (1.081 - 1.111)
  7. Gilks (1.020 - 0.833)
  8. Hart (0.997 - 1.032)
  9. Barton (0.901 - 0.926)
  10. Nani (0.899 - 0.915)
Scott Carson illustrates how big a difference we can get between aPPMS and regular PPMS due to the fact that he has managed 19 points (8th among GK) while facing @Che, @Liv and @Ars already. This would indicate that his current scores are below what he is capable of and is therefore a 'buy low' prospect. Meanwhile, Nani's presence on this list shows just how outstanding his start to the season has been given his relatively high price compared with these other budget options (who will always deliver better value).

Given that the difference between aPPMS and PPMSmay indicate that a player should be a transfer target or put on the block:

Buy low prospects (aPPMS higher than PPMS, difference in parenthesis)
  1. Carson (0.311)
  2. Gilks (0.187)
  3. Ebanks Blake (0.139)
  4. Cahill (0.114)
  5. Pienaar (0.103)
  6. Arteta (0.100)
  7. Rodallega (0.098)
  8. Odenwingie (0.097)
  9. Elmander (0.086)
  10. Tevez (0.076)
I think we can safely say that Everton players are currently undervalued and have played much harder games than are yet to come. In fact, the next three games remain tricky but after that they look good right though GW22. The three noted midfielders will also deserve some consideration at that point. This also suggests that Tevez might have more to come which, along with Drogba's tough fixtures (see below), might cause a bolder blogger to suggest that a switch between the two might be a legitimate option.

Sell high prospects (PPMS higher than aPPMS, difference in parenthesis)
  1. Kalou (0.198)
  2. Malouda (0.188)
  3. Friedel (0.186)
  4. Foster (0.169)
  5. Drogba (0.161)
  6. Young (0.155)
  7. Essien (0.154)
  8. Bale (0.152)
  9. Cech (0.131)
  10. Ferguson (0.131)
Note that I am not suggesting you sell Drogba or Malouda especially if you're sat on a big profit since the start of the game, more that his value has probably been inflated thanks to easy fixtures to start the season (a point observed by Alex Ferguson). But, if you want to make up ground and could use cash elsewhere the Drogba > Tevez move suddenly at least deserves a pause for thought.

I will continue to reference aPPMS throughout the season as well as using the difference between PPMS and aPPMS to suggest buy/sell prospects.

Thanks for reading and I look forward to hearing your thoughts on aPPMS and its usefulness, as well as any potential problems or improvements you can foresee.

    5 comments:

    Mister Sardine said...

    Keep up the good work Chris. Really interesting.
    I am 4th in your mini league just behind you. Carry on and don't look back ;-)

    Chris Glover said...

    Haha. Great looking team by the way. You got on Salcido early - excellent call my friend. I am a bit down on Shawcross but he's a nice option this week for you to fill in for Konchesky.

    Ryan said...

    Wow. I don't mean to be a bootlicker but what are you, a fucking genius? Gotta love your new aPPMS model. It's also pretty neat how the difference between PPMS and aPPMS can be translated to a buy/sell decision.

    Keep on crunching those numbers and stats, Chris! Maybe you should travel around the world more often!

    zorro's brother said...

    Great work Chris.
    Does Al-Habsi deserve some attention given his past schedule (2 of his 4 games have been against TH(A) and MC(H)) and also his next 5 games are pretty decent?

    An Idiot's Complex Life said...

    Will you show the aPPMS before the 2011-12 season kicks off...