Tuesday, August 21, 2018

How much extra value do premium defenders need to offer? Part I

At this stage of the season, those of us who are statistically inclined face a bit of a dilemma. We know that too much weight should not be placed on the limited data that's available, but yet the alternative is to rely on no data and simply make your picks based on the one or two games of action you've seen, or worse, some voodoo about world class players not being able to score in August.

With this in mind, this time of year offers a good opportunity to explore a couple of other broader topics before the games start coming thick and fast and we get lost in expected goal regressions. Though data in a wider sense may not yet be stable, we can start to take some reasonable confidence from starting lineups and some of the lessons we can draw from there. Specifically here, I am interested in (a) which players offer a discount among their teammates and (b) when would we be willing to pay for the more expensive option. This is typically most useful when it comes to defenders and 'keepers as the substantial part of their value normally derives from clean sheets - which are the same for all starting players - with the difference then being their attacking potential. Two forwards are obviously much harder to compare as while they enjoy the same opponents each week, everything else is different.

What I am interested in then is, if we have a defensive line valued like this:

  • GK: 5.5m
  • DEF: 6.0m
  • DEF: 5.0m
  • DEF: 5.0m
  • DEF: 5.0m
and we expect them all to start essentially every game, what does the premium 6.0m defender need to do in order to justify his price tag?

The big picture benchmark
Looking at the big picture, over the course of the season you'll want to eclipse 2,000 points and probably push into that 2,200+ point range. Without chasing value too much, you should be able to have an average team value of somewhere around 102m (yes it will be higher later, but you're likely to have 8-10 weeks in that 100-101 range unless you hit on some very early risers). However, 17-18m (or more) of that value is going to be sat on the bench each week, meaning you need your ~85m squad to generate those 2,200 points. This means for every million you spend, you need to be earning somewhere around 26 points.

26 points doesn't sound like that much for elite defenders to earn, when the likes of Alonso or Bendy are more than capable of notching double digits in a single gameweek. However, remember that these points need to come from attacking sources only, as their teammates will obviously score clean sheet points at the same rate. This is a slight oversimplification as you may also be paying for increased stability of playing time, and then bonus points further cloud the issue as these can be earned for both defensive and offensive outcomes, but I'm going to put a pin in those questions for now.

If we calculate attacking points as a simple formula of goals x 6 plus assists x 3, then you end up with just six defenders who managed 26 points or more. Not 26 points more than their teammates but 26 attacking points in total. As above, this is an underestimation as we're ignoring bonus points, so if we include an estimate of their full value then you get 29 players who would have notched 26 points or more. The reality is likely then between these two numbers but I have included an estimate of bonus points in the numbers below.

2017-18 cast studies
Let's have a look at a couple of teams from last season to see this calculation in action. Note that I am using starting prices as (a) these are more widely available and (b) it lessens to variety of prices to just seven categories (4.0m, 4.5m, 5.0m . . . 7.0m) rather than having to account for every 0.1m.

Here's an example where I think the top two players are offering not just the attacking bonus but also the playing time stability, as the other centre backs in the team tended to get rotated throughout the season. Ignoring that though, we see that Azpilicueta costs 0.5m more than the pack and would have delivered around 10 more attacking points (if one CB had been consistently deployed). So this is slightly below the 26 point rate noted above but given the extra stability I think a strong argument could be made he was worth it. Similarly, the next upgrade from Azpilicueta to his Spanish colleague Alonso provided an additional 13 points, which for 0.5m equates exactly with our 26 points per million mark. In this situation then, I think it's fair to conclude that Alonso was the best pick, although as fantasy team's became saturated with him, one could make a reasonable case for Azpilicueta too.

Based on these values Harry Maguire was a no-brainer, offering a 24 point premium for just 0.5m. As the season wound on though, his price rose to 5.5m, which seems like about the equilibrium: a 1.0m premium for 24 points (in reality Maguire was worth a little less than this as he earned bonus points at a lower rate than the model suggests, but the general point remains).

Here we can see a team where no one player was able to differentiate themselves and the best selection would likely have been whoever was cheapest (assuming they had a similar chance at playing time). I've shown Watford here but the same logic applies to several teams and the lesson is not to assume that a team's best attacking option is not necessarily a worthy option.

Now we've set the context and defined what we're looking for, in the next post we'll have a first look at this year's team selections and a cautious first glance at the attacking data and see which premium defenders are off to the kind of start that might justify their price tag.

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