Continuing his blog for us, our new resident “statto”

Ewen(@ewen_) does some magic with last year’s Fantasy Premier League (FPL) numbers to look at the ceilings and captain hauls. He’ll be in the “free role” for us this year, looking into issues as and when they arise / take his fancy, as well as appearing on our pods! See his previous postshere.

Rotation – it doesn’t have to be a dirty word. Picking complementary assets, becoming greater than the sum of their parts through careful fixture planning, is squad-based fantasy sport game 101. Resist blowing your beans on your first eleven, and instead, seamlessly segue between class acts across a well-balanced squad. Perhaps it’ll even help you develop a microcosm of empathy for the tinkerman nouveau, Guardiola (unfortunately, we aren’t allowed to have quite the same disregard for player positions as that guy). Let’s begin, slowly.

Rotation policy is at it’s simplest when applied to goalkeepers. The constraints are simple: you have to buy two, but you can only play one each week. This encourages FPL managers to look at a couple of cheaper options that play home & away alternately, for example, rather than lumping for premium products. Which strategy wins out, though?

## Linear Thinking

This problem is nicely suited to a technique called **linear optimization**. In essence, by making a few simplifying assumptions about a situation, we can decide on an optimum solution for it.

Linear optimization is all around us – for example, picking your route to work, lovingly known as “getting from A to B”. The decision is (usually) objectively simple – **which route is the quickest?** By knowing the speed of different modes of transport, and the distance of each possible route, journey times can be calculated. **Constraints** can also be considered – preferred modes of travel, less time walking – and taking these parameters into account, a single best route can be attained.

What does this have to do with your ’keepers? **Everything**. Lets re-frame it as a linear optimization problem:

- Thing we want to optimize = Points scored by the two goalkeepers we pick (ultimately, we’ll introduce cost into the equation to maximise a points/price metric)
- The restrictions (constraints), as discussed:
- Two goalkeepers (no more, no less)
- Only one can play each gameweek

- Other simplifying assumptions:
- We don’t want to make any transfers in this position
- With every possible goalie pair, we always play the keeper who scores the most points that week (in linear world, all of this is possible…)

Seems straightforward enough, right? Let’s see.

## Goalie-Go-Round

Based on the situation outlined above, an implementation of linear programming (the code’s here, if that’s your thing) could do something like the following:

- Cycle through every possible pair of goalkeepers
- For each gameweek, pick the goalie who scored the most points
- Tally up the total points possible for each pair

This task starts with identifying point-scoring patterns at a gameweek-level, so lets start by examining an example goalie pair’s points.

In the above plot, the points scored by week for Chelsea’s** Courtois** and Arsenal’s **Cech** are on show. Not only can we identify the level of points these players scored individually, but how well the patterns of point-scoring complement each other (i.e. do they score well in alternate weeks). It’s *this* complementary aspect that we’ll dive into now, to identify the best match-ups observed so far in the 2017/18 FPL season.

OK, then – what were the top ten combos, if money is no object?

Combinations of Cech/Lossl and de Gea/Pope have had the highest potential so far this season, with a possible points return of 82 points in both scenarios.

This problem is yet to be all the way optimized, though. Let’s examine another top ten – the best *value* pairings i.e. *points per million* (based on the total cost of both ’keepers):

Messrs **Hart** and **Lossl** grab top spot when accounting for both points and cost in our quest for optimization. In fact, Lossl features in the top three best value pairs (alongside **Fabianski** and **Pope**, behind the partner already mentioned).

## Gettin’ Picky

As mentioned in the route-planning analogy, there might be other constraints we’d like to introduce. For example, what if we’ve spent all our cash elsewhere, and have a measly £8 million to spare?

Enter Elliot. This is pretty grim – only Speroni at Palace distinguishes himself from the chasing pack, and barely (I cut out most of them, as nothing is really going on). The return on investment is just sub-par, based on what we’ve seen elsewhere.

How about if we fancy a particular keeper for upcoming weeks, we can identify the best pairings featuring them. What about this season’s pre-eminent underdog, Elliot? We already have an idea who might be top, but perhaps some other promising partnerships will emerge.

Turns out that Pope is the best value partner. Given the fact that Burnley’s current ’keeper has not featured from the season start, this placing is pretty remarkable (hint: this is my current set-up). Still, the #1 match made in heaven (so far) this season, based on points potential per £million, is **Lossl & Hart** edging things.

That’s what you call dovetailing – sign those lads up.

The principles of linear optimization can be applied to many aspects of a game that has such a fundamentally simple goal – get the most points. Watch this space for more linear delights…