It’s week two, and I’m top of all of my leagues! Like all of them, every single one. Even the Big Scary Monsters one, and that has like 153 folks in. As some of you may remember last year I decided against picking my own fantasy team, and use all of you to help me pick. By using “Crowd Sourcing” I chose the most chosen players to fill out my fantasy team.

Instantly, I found out that my team would be too expensive, and contained 4 players from both Manchester United and Arsenal. I had to be selective, and worked out something their “Fantasy Football Superhero Status!” Basically the amount of teams chosen is normalised to their value. So, to include expensive players they have to be chosen by a large proportion of teams. Makes sense right?

Well it didn’t! My team was terrible, and I gave up. Every week I had to make multiple transfers to get the most popular players. My algorithm predicted that James Collins was becoming the most popular man in football, and I lost faith in my system.

It was your fault! All of you! You changed your minds so often, and kept in terrible players! Your decision to include so many cheap players to keep your costs down crippled me.

So, this year I decided to give it another go. I’m nothing if not a scientist, and I decided to tinker with my algorithm. This post is going to get quite maths, so sorry about that.

Also, sorry to any real maths-folks, as this is very much not proper maths.

First, let’s see how many you lot did at picking. Unfortunately, I’m going to have to use last year’s points as a guide, but have a little look at this mess.

That’s basically looking at how the cost of a player compares to the numbers of points they got last year. There is a significant correlation between how much a player costs, and how many points they got. Let’s see how people choices correlate…

So, what does that look like to you? Almost the same? I’m afraid not. Whilst there is still a significant correlation between the percentage of teams that players are chosen in, the Pearson Correlation Coefficient is lower. This basically means that the slope of the curve is less steep, which generally means that the correlation is smaller.

(In case you were wondering who that fellow with the highest number of points last year, but who has not been chosen in many teams is, it’s Alexis Sanchez.)

Anyway, this should be expected as it’s how they calculate the value of the players, and obviously it doesn’t help me picking a team, as all the highest value players would cripple my £100 million. I guess I should pick players above the line, but just because they did well last year doesn’t mean much for the next one, hey Leicester?

So, I guess, you can ignore all of this so far… quickly now, on to the next thing…

Let’s get rid of chance. As unlikely as it may seem, there is always a chance that a player is randomly picked, so let’s get rid of those players.

At the beginning of the season there were 45 goalkeepers, and 2 opportunities to pick, so the ‘keepers could literally be picked 1st or 2nd, giving us the following equation

Likelihood of being picked = 1/45 + 1/44

This means that just picking a ‘keeper at random would mean that players would be chosen in 4.5% of teams. Pretty high hey? I’m going to call this value the Ederson-Federici Frontier (EFF) as these are currently the goalkeepers which straddle this line.

We want a player that is “significantly” chosen more than chance. But how to determine significance? For the majority of science to become significant a p value of 0.05 or lower is needed. This means that probability of seeing an outcome is 95%. In what is a gross over-simplification I’ve literally decided to just add 5% to the FEC, meaning that for a ‘keeper to be chosen in significantly more teams than chance they have to be in 9.5% of team. This will be called the Heaton-Begovic Line (HBL).

This means that from the 45 ‘keepers in the game, only 8 of them are chosen in significantly more teams that they would be. This are

David de Gea

Ben Foster

Robert Elliot

Thibault Courtois

Joe Hart

Jordan Pickford

Hugo Lloris

Tom Heaton

I think it’s fairly obvious to see which are being chosen as first choice, and which are a cheap back up hey?

So, I’ll save you having to re-read all of that for every position here are the deets

**Defenders**

Starting number (n1) = 164

The Danilo-Yedlin Frontier = 2.5%

The McCauley-Vertonghen Line = 7.5%

Final number (n2) = 20

**Midfielders **

n1 = 198

The Arnautovic-Pedro Frontier = 2.1%

The Mane-Capoue Line = 7.1%

n2 = 17

**Strikers
**n1 = 66

The Vardy-Solanke Frontier = 3.1%

The Aguero-Gayle Line = 8.1%

n2 = 11

That cuts down my options considerably, and stops me from thinking that maybe Capoue will have a good season again.

Now, how else did I waste my time. Let’s have some graphs.

So, on the left hand side we see the average number of points per postion, and on the right how many points the best players in each position got. It seems that overall forwards get more points, defenders and ‘keepers get very similar points. and midfielders are the worst. However, when you look at the players with the highest points, midfielders boss it, and goalies are the worst. Let’s see how good you are at picking.

So, it’s slightly worse, but again that’s to be expected. However, there are a couple of huge differences in the defence and midfield. You lot are terrible at picking two-third of the players. Regardless of whether or not I use FFSS you guys are significantly worse at picking defenders and midfielders. (Obviously the low n number on goalies and strikers could be hiding any significance, but shush!)

Let’s build that in, and work out how good you idiots are. By calculating the ratio between the top chosen players, and the top scoring players, it gives me a good deal of validity of your choices.

Basically, de Gea and Lukaku are definitely in, but there is so much overlap.

The goalkeepers are clearly split into different groups; de Gea wins, and then the second ‘keeper should be chosen from Foster, Elliot, Courtois and possibly Hart. The forwards are similar; 3 out of Lukaku, Kane, Chicarito and Rooney would be the best bet. But Firminho, Lacazette and Defoe are all decent choices.

Defenders and midfielders are a bit tougher, so I think I may have to just make my own choices. These numbers are also skewed by the cheap players. I don’t have anything against him, but I don’t think Rangel will be the highest scoring defender, and I definitely don’t think Crystal Palace should have 3 of the top 10 midfielders.

So I’m just going to wing it. I’ve already cut down 473 players to 56, by removing chance. I can choose more than a quarter of those players, and obviously win the league…

Sorry leagues.

I’m sure this won’t come back to bite me in the ass