In my latest Sky Sports Fantasy Football review article, I mentioned about achieving the most matches by using one transfer. The question is, what do you do with two, three or four transfers? It recently dawn on me that I could use a technique called dynamic programming to aid my decision making. Dynamic programming (DP) refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner.
If we have the number of goals each team scores in their remaining matches (can estimate via the prediction tool), then how do we make transfers to optimize the number of goals players play in. I work on the assumption, if a player’s team score more goals, he’s likely to score more points.
To use DP here, we first assume that no transfers are available and so the expected goals for the remaining matches per team is the sum of the projections. The second step, is if we have one transfer, then we select the highest of making a transfer to the highest no transfers table or forgo the transfer and add the goals scored by the team in that match with the optimal transfer in the next matchday. If you have two transfers, your choice is either make a transfer and next step is select from the optimal one transfer matrix or forgo the transfer and add the goals scored by the team in that match with the optimal two transfers in the next matchday, etc.
Though some may be keen to put this into action themselves, I’ve quickly pulled together a spreadsheet that may help given the short time left before the weekend matches.
The DP spreadsheet is HERE
The “Goals” page is the projected expected goals each team is expected to score in their various matches and taken from the prediction tool.
Fixtures & DP – firstly there are some yellow cells which the user can change. These will be explained later.
The first table lists which team plays on each of the remaining 19 matchdays and below this is the expected number of goals the team is projected to score (or matches played if cell B2 is set to games).
Below this are six tables using DP and give the optimum expected goals for starting at each team with zero to five transfers. In column B, it compares the number of goals with if that team had zero transfers. For example, Chelsea with no transfers are expected to score 8.1 (cell D56), if we had a transfer and start at Chelsea we could achieve 13 goals (cell D79) a benefit of 4.9 as shown in column B. If we had two transfers then D102 says we can achieve 15.95 goals an improvement of 7.9 goals (seen in column B) or 3.95 goals per transfer used.
The “Summary”, based on all the calculations above shows the benefit of using one to five transfers for each team and also the benefit per transfer. The highest value seen is TEN for Huddersfield, which you may expect as if you have a player from this team it’s better to get rid!!!!
There are several yellow bits in the fixture & DP page. In column Y, this can be used as a multiplier to a team’s expected goals. For instance, if you have plenty of Spurs plays and don’t want anymore then set the value to zero.
Row 5 is a matchday ratio. If you want to assume more goals are scored in a day then increase this figure. For example, matchday 5 Watford play Arsenal. I don’t have either a player from either team so can increase this to two to reflect possible captaincy.
Assume I have a Watford player, and want to make four transfers with this player. The summary page says I will gain 12.2 goals or an average of 3.1 per transfer. To find out which transfers to make then go to the fixtures & DP page, to the table called 4 transfers (starting row 142). Find Watford (row 160) and move across until you reach the red cell (this indicates you need to make a transfer), move up this column to the table above. Then look for the green cell which belongs to Spurs (who you transfer in). Move along until you find the red cell, column P, then move up this column until you reach the next table and look for the green cell. This belongs to Man City, move to the right until you see the red cell, column T. Then move up the column until you reach the next table and find the green cell which belongs to Man U, reach for the next red cell and move up again. The green cell belongs to Spurs which is the fourth transfer.
I’ve highlighted in light blue in the top table the path we found and it sums to 19.85, which is the 12.2 greater than the 7.65 goals if kept with Watford.
Applying to my team
I have three transfer left. In midfield, I have Newcastle, Leicester (x2), Wolves and Everton players. The first thing I note is that I have no coverage for the upcoming single matchdays. Based on this I change cells G5 and H5 to 2.5
I go to the summary page, I note that Newcastle has the highest value for a transfer used at 9.4 (cell I18). This declines if more are made, so I just need to do one transfer with this player. Going to the DP page I go to the one transfer table and find Newcastle (row 88), the first red cell is in column E, so moving up this column to the next table I find the green cell that belongs to Spurs.
Next team for transfer is Leicester and again the table suggests only one transfer. Going to the DP page and the one transfer table and find Leicester. The red cell is again in column E, which when going to the table above suggests transferring to Spurs.
I have another transfer but don’t want to go to Spurs, so go to column Y and set Spurs to have a zero multiplier (Y23). Even though it says transferring Everton is better, I would no longer be covering a future single matchday. So transferring Leicester is still the option. Now the red cell is in column F. Moving upwards this suggests moving to a Man City player – so despite doubling Arsenal’s goals in one match, they don’t make it into the optimal route.
The issue will be about affordability. For example, can I afford to move from Leicester player to Man city? If not, then I would put Man City to having a zero ratio and continue the process. I’ll work this out in the coming days.
I look forward to using this and think how it can help with planning next season.
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