This is the whole point - the "best" player here depends on the base price, a completely random assignation by FPL.

Again, try adding £10m to all base prices and allow yourself an extra £150m - what does that do to your equations?

Conclusion - your measure of value is not accurate, it just "works" for the specific base price FPL have assigned.

FALSE - the "best" player is the one who will earn you the most points for the money. Nothing to do with base price at all.


FALSE - FPL set the base price at the start of the season to the nearest .5M according to the expected mnimum return of any player in that position. This is because, just by turning out for a game, a player can expect to gather points (e.g. appearance points).


It doesn't affect my equations at all. It changes their output values and that's because, as I demonstrated in my previous post and as I keep saying over and over again, adjusting the base price (whether up 10M or down to zero) is the wrong thing to do if you want to accurately calculate a player's relative value.


This does not follow logically from your previous statements. Are you saying it's not accurate because if you pour garbage data in you get garbage data out?


Er...yes.

I think you are confusing baseprice with the linear relationship between price and yield.

If you plot price against yield the trend line passes through the origin (0,0), as it should.

If you plot price plus-or-minus something (like base price) against yield it doesn't because you did something dumb.

Next contestant please!

TRUE


TRUE


TRUE


TRUE


TRUE


FALSE -- You have changed the relative value of cheaper players so they now represent better value-for-money than more expensive players. This makes new previously-unaffordable line-ups affordable.

Your calcs show that if FPL chose a different base price, different players are suggested to be more valuable. If you accept that changing the base price cannot change the value of a player (which you are of course disputing - see the final quote below), then your calculations show that your definition of value is invalid. His logic is fine if you accept that one point.

Have you tried it? I have - and it doesn't go through the origin. In fact, it's wildly different for each position. I don't have stats for minutes played, but I plotted PPG (my preferred metric) for all players who made > 15 appearances. A theoretical £0m GK would score 1 point per game; a theoretical £0m attacker would score -1. We are nowhere near the origin.

In any case, even if FPL did work out base values this way, they would almost certainly use total points. They wouldn't be subtle enough to use points per minute, your preferred metric. And you do a clean up (which obviously I agree with), which is never going to match exactly with whatever clean up they do. There's no chance that points per minute per pound would go through the origin.

Ah, hang on: are you working under the assumption that the base price was chosen to take into account the minimum expected points? Because it isn't. It's just there to make prices look more realistic, with GK < DF < MF < ATT. In fact, if it was based on points, it would go GK > DF > MF/ATT, because cheap keepers score more than cheap attackers.

No, there is no change whatsoever in which lineups are affordable. This was my point 3, which you agreed with.

If a lineup was previously unaffordable in FPL , it costs >£100m. If every player's value is reduced by base, then every lineup has it's value reduced by exactly £64m. Hence, that same lineup costs >£36m in the reduced-price-game, and hence is unaffordable on a budget of £36m.

Conversely, any team that is affordable in the reduced price-game (costs <= £36m) is affordable in FPL (costs <= £100m).

Surely this is the crux of the discussion here - Does FPL set the base price of each player on last season's merit (I know it's not quite as simple as just last season)? For example in Wyld's defense take two almost ever presents last season (which makes an ideal comparison), Ferguson and Lampard; Ferguson is (I'd have put him in at 5.0 personally) just over 1/3 the price of Lampard and surprise surprise he scored just over 1/3 points pro-rata (or ppg pro-rata). So this would indicate they do take into account Ferguson at 2.9ppg last season, or 106pts as being worth 4.5mn.

I think I'm inclined to agree that Ferguson is there at 4.5mn because FPL predicts he will score about 3ppg again, not because of more realism. But maybe it's a bit of realism but more do do with his actual value.

Correct me if I'm wrong but doesn't a 0mn base price player have infinite value (which would send alarm bells straight away) and so the lesser the base value the more inaccurate the 'base price' calculations are? And I may be out on a limb here (probably am) but is it not being proposed that we take base prices of players (Lamp 8.5, Fab 7.5, etc) and use this number to divide into a points total (ppg) because if it is then it's wrong to do so? That is like saying 60/100 is the same as 50/90 because you've taken 10 off each.

And please let me know if I'm out of my depth here (I feel it) but it appears there is no right answer, just opinion

Before I comment on your post, Relegated_By_Xmas, would you do me the kindness of going through the logic of the previous one I made too? The one that ends, "Please clarify".

(Although I still believe that deducting the base price when calculating value is wrong, it is refreshing to find a fine mind that is willing to argue the contrary, and I'm willing to listen to reason. In the past whenever I have challenged this approach no one clearly argued its case as you are now doing. But I still remain unconvinced -- particularly as we now seem to be heading towards a "it doesn't make any difference" consensus.)

[/quote]
FALSE -- You have changed the relative value of cheaper players so they now represent better value-for-money than more expensive players. This makes new previously-unaffordable line-ups affordable.[/quote]

love this thread. Wyld - I've followed a few of your posts before and liked the way you think about things - but I'm struggling to see how you can agree with the points above and still make that statement. The results of your calculations change, but can you give an example of a player you'd select differently given the base removed situation described?

You are doing the right thing here but coming to the wrong conclusion. Amending the base price to zero (and reducing available money as a consequence) does indeed make base price players infinite in value (judged by points per million, or similar etc) - this shows one is wrong to consider ppm as the correct metric, not wrong to imagine a world where the base price was zero.

PPM would be the correct metric if you could have as many players as you want - in fact you can only pick 15 so being as "efficient" as possible is no good if you don't end up spending your money, that is why ppm is flawed.

Your flawed argument doesn't hold water.

Yes, you have only 15 players to pick, but four of those are expected to sit on the bench at a cost to you of around 18m. That leaves 11 to pick for 82m. Let's say one of those is your captain at around 12m. Then you have 70m leftover for the remaining 10. Assuming "value" players are evenly distributed amongst the field, its pretty easy to acquire most of the ones you need for that budget, and even more so because the best value players in the game seem to lie in the 5-8m range.

Sorry I did actually mean that the smaller (CC-BP) is, the more inaccurate the calculations, not the smaller the BP is as I wrote before: when you are dividing by a price of 0.1 for example (to work out valueBP for a player who has risen by 0.1) you end up with an enormously outrageous number. Taking Ferguson/Lamps example from last season (Ferg at 4.6), we have Ferguson 80 times better value as Lampard. Is this true and what's the Vbp equation based on if it's not = (ppm or ppg)/(Price-BP)? I don't believe there can be an accurate enough equation. The more expensive players at Price-BP become many times more expensive (too expensive % wise) than cheap players and if it doesn't work to an acceptable level for mid vs mid then why should it be trusted to work acceptably for players of different BP/position; that's how I see it anyway unless I have misread some important information on this thread.

Surely for a more accurate comparison of player position value, it would be better to subtract 0 and 0.5 from respective price before continuing calculation instead of 4 and 4.5? I feel really lost now!

You need to be clear on what we are doing here. Let's say you have a 4.5m midfielder who earns 2PPG. You can either upgrade to Ferguson (2.9 PPG @£4.6M, say) or to Lampard (8PPG @£13M). Which should you do? Ferguson is better value, but Lampard scores more points.

The answer is that you should go for Ferguson only if you can use the money you save elsewhere. If you leave that £8.4M sat in the bank, you can 0 points for it. Thus spending £4.6M brilliantly and £8.4M appallingly (i.e. not at all) is a far inferior choice to spending £13M quite well.


I think a money analogy is useful here. A basic measure of investment is "return on investment" (ROI), which is a percentage of how much extra you'll get back. So if you invest £1k and get £1.1k back, that's 10%. Obviously, a higher ROI is better. Perfectly sensible, and hopefully you'll see the analogy with a points return for £m investment.

Now, say you have two options: invest £1k with 20% ROI, or invest £10k with 5% ROI. Which is better? Well, the first one is better value, but the second earns you more money. Ideally you'd like to do both; but what if you were only allowed to do one or the other? Then you'd pick the hard cash. What if you had other decent investment options that you could spend the spare cash on? Then you'd take the £1k option, and invest the £9k elsewhere.

Regarding your infinite point: imagine if I offered to give you £5 right now - you don't need to invest anything. Would you accept? I assume so. Now, what's the ROI on such a thing? Infinite, right? But that doesn't mean ROI is a bad method - you just have to use it right.




That works if you pick Ferguson as your example of a £4.5M midfielder. But then why does De Jong (2.1 PPG) have the same price? Or Muamba (1.9), or Diao (1.7)? Or especially Mark Davies (1.1 PPG in 17 games)? What about Carrick, Babel, Osman, Petrov, Palacios and many other who all averaged less than Ferguson yet cost more?

It just happens to work for Ferguson and Lampard - out of dozens of near-ever-presents, it's bound to work for some pairings. It just doesn't work for the vast majority.

Just to butt in and go back to this Vbp and Y stuff.

What I thought R_B_X had meant and/or said elsewhere before, and what I believe, is that a better comparison of value is obtained via (in your terms)

value = (Y - Y_base) / (price - baseprice)

(where Y_base is the "yield" stat as you described it, for a 'top' base price player in that position - and by 'top' base player I mean the base player that you'd most reasonably consider picking)


Don't you always want to be comparing two players in terms of the extra yield one will obtain over the other for an extra cost?

Ah ha it is all (well some of it) becoming clearer. So we are suggesting for example taking off 2.9ppg (2.9 as an appropriate e.g.??) off midfield Vbp equation, say 2.75 off defender Vbp equation, 3.5 off GK Vbp equation and so on. But we don't know what exact values these are until the end of the season and they will change throughout. So how do we get accurate because: doing the calculations for lesser value players, say 0.5 above base price which I would definitely consider picking by the way at various points during the season, depending on baseYield going up or down 0.1ppg you can have someone's value changing a massive %?? Am I correct?
And also the players mentioned by RBX have potential to do the same as last season (depending on expected injuries, previous seasons) or to do better than Ferguson. I wouldn't argue with many of them as fair prices for expected return otherwise I would find it very easy to pick my team which I didn't

I've done a lame example below and it seems to me, fine when considering expensive players in all positions but when we consider cheap players the Vbp go all over the place. Apologies again if I myself am being lame and not used correct calcs.

A.COLE DANN
5PPG Y (base) Value (base)Value Normal 3.2PPG Y (base) Value (base)Value Normal

2.5 0.71 0.67 2.5 1.4 0.78
2.75 0.64 0.67 2.75 0.9 0.78
3 0.57 0.67 3 0.4 0.78


FABREGAS GUTTIEREZ
7.5PPG Y (base) Value (base)Value Normal 3.5PPG Y (base) Value (base)Value Normal

2.75 0.63 0.63 2.75 1.5 0.7
3 0.6 0.63 3 1 0.7
3.25 0.57 0.63 3.25 0.5 0.7

And Mark Davies/Diao only played bitpart/sub last season and if he started to play regularly (like the others mentioned) FPL would look silly in pricing him at say 2.5mn when he averages 2.8 say; it would skew the game; there has to be some leeway on these types of players. De Jong is playing for an ever changing City side, he could average 2.8ppg this season or not play. Him and many others should almost be disregarded (certainly from our calculations) because they are not going to be in our squads anyway as they are only potential at the moment; we only want value decisions on players who play regularly and return 'decent' points. However Ferguson may be and is a fair comparison as he has played most minutes and will continue to although I wouldn't be surprised if his ppg decreased. Realistically he is the 'poorest scoring' midfielder we'd have, we'd hope. I still say most of the base price players are priced quite fairly according to expected or potential (the ones we generally ignore) return. Also, if Ferguson had base cost of £0 then so would Mark Davies...so taking base off these type of players (inc Carrick, Babel, Petrov, etc) won't work either IF previous calcs are correct format, so no point mentioning them. Carrick scored 4.5 couple seasons back that's why he is priced as he is; last season's total is only part of it. And he plays for a top 2 team. What I'm saying in a roundabout way is that we should only be concentrating on say 250 out of 500 odd players in the prem for these non-BP value calcs and I think the FPL are generally correct in their price assignments based on expected return for these 250.

I'm at a loss to understand your position, Relegated_By_Xmas. Can't help feeling your posts are contradictory and that you are just arguing for the sake of it. What is it, actually, that you are proposing as a measure of value?

Is it:

V = (points/appearances)/price

or

V = (points/appearances)/(price-baseprice)

or

Y = points/appearances
V = (Y - Y_base) / (price - baseprice)

or

what?

Now you seem to be saying that when evaluating the swap of one player for another you also need to take into account the money left in the bank (or the additional funds required to make the transfer).

This is of course true...especially if you are constrained to one transfer that week. Of course you might decide to make two transfers and take a four point hit. Or you might actually have two transfers available because your have carried one forward. Or you might be playing your wildcard. Or it might be the start of the season when you can make unlimited transfers. Or it might be a double-game week. Or you might be carrying multiple suspensions/injuries. Or...

Juggling funds (and avoiding parking them in the bank for too long) is a basic skill in the game. But really this gets away from the point that we just want a simple predictive measure, a measure that can be used to assess the relative worth of one player against another player -- because at the end of the day you want a team packed with high value players. Nowhere do I see baseprice in your argument.

Bump

Relegated's method actually requires comparison to a player who is worth considering in your team at the "base cost". For example: Player C at £4.0m and scoring 40 points.
Now, by Relegated's methods:

Player A costs £1.0m extra and earns 10 points extra (value of 10/1.0 = 10.0)

Player B costs £3.0m extra and earns 50 points extra (value of 50/3.0 = 16.7)

This gives a result of Player A being better (same as you) but a much better indication of what money you have actually chosen to spend rather than taking into account the arbitrary base costs. You can also divide by minutes played if you really want.

I don't know what you want me to comment on. You made two calculations, and noted they were different. You didn't comment on why one was better than the other. Apologies if I'm missing something, but I can't comment on logic unless you are being specific. I'd be happy to comment on anything if you point me in the right direction.

However, this bit:



I'm not sure if that's literally what you mean, but it's wrong when you compare accross positions. Say you've got a £5m keeper and a £7m attacker, both of whom score 5 points per 90 minutes. Using your statement, you "reject" the worst one.

But what if there are a whole bunch of £4m keepers who score 3.9 points per 90 mins, but all the £6m attackers score 2 points per 90? When you decided to pick the defender, you implicitly committed yourself to keeping the cheap attacker. But the cheap attacker is AWFUL; the cheap keeper is pretty good. In fact, the £7m attacker is very valuable, because he saves you from the cheap attacker. (This scenario is, in fact, only a slight exaggeration on the truth - cheap goalies are in fact really good, much better than cheap MFs and DFs)

What you are trying to identify is a quick and easy method of identifying which players are important, and which ones aren't. This example shows where point/cost falls down; it doesn't identify that upgrading the keeper isn't important, but that you desperately don't want to get left with the £6m attacker.



As I've said several times, points over base / divided by cost over base. "Base" is the cheapest player that I would consider, not the cheapest player FPL offers - irrelevent players may as well not be in the game. Essentially, exactly what Triggy said.

Agreed.



Here's a (very rough and ready - sorry about that, don't have time to do it better) graph of PPG (y-axis) against price (x-axis) for every player in this years game who played in at least 25 game last year.



Would you agree with me that at any price point, keepers (basically all of them) are very clearly scoring more points than any other position, that the trend line for attackers is clearly lower than the rest, and that the trend lines for all 4 positions are all clearly different? And would you agree that the trend lines, especially that for keepers and attackers, are not going near to (0,0)?

I agree with you about goalkeepers and defenders being better value than midfielders and forwards. That's why I usually spend my money at the back, rather than in midfield or at the front.

Er, I think I mentioned that one a few years back in some other posts...

But now you have clarified your position re how to calculate V I will come back to you in a while.

YES, YES, YES, and ...

NO. The trend lines are pretty close to 0,0. Thank goodness you didn't need to deduct that baseprice or you would be nowhere near it!

(By the way, you can easily add a trend line in Excel. Its on the Chart menu.)

It seems to me that the main difference in these two arguments is that one is focused on optimization theory while the other is more focused on application. The optimal selection of 15 players would have to factor in base price, but in practical terms, the complexity of this calculation leads to managers using analyses basically void of base price considerations (as well as minimizing the number of player options, both things a theoretical model wouldn't do).

Given that only 11 of 15 players can play each week; and considering home and away advantages, rotation risks, and incremental value from one position to another, how many base-price players will you have on your team (if any)? In theory, a model could be built to answer this, but for all practical purposes, most will start with a "best guess" and modify as necessary (likely in some iterative fashion).

The theoretical "best" solution (traveling-salesman model?) is an interesting academic problem, but the more practical approach of comparing any two players for their relative value seems more relevant.

Regardless of the approach, it will get weaker the more inaccurate your predicted points, and it’s here where the very best players seem to excel (what's the caveat of all investors? - past history does not necessarily predict future earnings). You can be a genius of optimization, but if your predicted points are hooey, so too will be your team.

Yes, we base calculations on 250 players but of these how many are base players we would consider in our starting xi during a season, not many; I'm saying that FPL have the base player prices roughly correct for these handful of players. In practical terms we can't really use any specific approach because of all the transfers, wildcards, rotation, etc.

Isn't one reason for strikers being terrible value compared to defs/mids because you have a transfer (transfers) each week and top strikers have the potency to score way more in one go? They have to have slightly skewed value, so even though A.Cole may outscore RVP in the season it may not be correct to choose Cole because you can 'continually' swap RVP for Tevez, Bent, Torres, etc and get massive hauls which you wouldn't really be able to do properly if you'd spent £45mn on GK+defs. This is not true of cheap strikers on the whole which is why I stick to one at most, it's cheapo Carroll atm. The most flexible squad is IMO the best, says he at 897,000th.

I said cheap goalkeepers and defenders are better value. My conclusion on where to spend my money is the absolute opposite of yours, for the reasons I outlined in my other post - the points gap between a £6.5m goalie and a £4.5m goalie is very low, and not worth the upgrade.

This is exactly the point that is being made - a decision to spend £7m on a defender should mean it's better to spend £7m than £6.5m, or £6m, or £5.5m (and spend the rest of the cash elsewhere), not just that it's much better than leaving an empty space in your squad.

Your method suggests that Van der Saar is amazing value at £6.5m with 4.6 PPG, one of the best in the game. But the likes of Sorensen, Hahnamann, Robinson etc all scored about 4 PPG for £4.5m/£5m, so you are paying an extra £1.5m to £2m for an extra half point per game. The game, as you identify, is about spending every £ as efficiently as possible - the first £4.5m you spend on goalkeepers is incredibly efficient. The incremental £2m to go from £4.5m to £6.5m is very inefficient.

So... where are you two overall in the current FPL league?

I tend to not look at stats too much and just do the obvious thing... Watch football matches on a very regular basis...

I get less of a headache that way.

So many assumptions here - I thought you were looking a method that works in general. No wonder best value players are 5-8: That is pretty much the full rnage for Defs and gks.

I'm assuming you are trying to find one metric that, when you sort players into order of the metric tells you who to pick. It does not exist. There are useful measures, but no "holy grail".

Ask yourself one question - IF you added £10m to ALL prices and had £150m more to spend, should your method still pick the same team?

And another: IF you deducted £4m from ALL prices and had £60m less to spend, should your method still pick the same team?


The answer should be "yes", but I'm not sure you see it.

Agree, this question is key - Once you recognise it, the logic on cost and points over base to make a decision follows on. Despite a lot of posts on here I've not seen anyone try a refute it with anything more substantive than 'it's obviously not true'

Anybody who thinks it isn't true might want to play around with the attached spreadsheet.

(can somebody confirm it works - I made it in Openoffice but saved it in Excel format because I assume more people have access to that)

Earlier I said...


At the time the logic seemed obvious to me, so I didn't bother to think it through.

Later I said...


Again, unforgivably for someone with a background in the sciences, I didn't bother to check the logic of my statement fully.

And more recently benwildman (no relation ) said...


which is enough to force me to re-evaluate my earlier statements.

Fortunately I have good test data to check to establish the veracity of the plus-or-minus-the-baseprice-makes-no-difference theory. So I will go and do that now....

[time passes]

So now I have done that. First I ran my analysis on my cleaned data* for the 09-10 season, using my normal value calculation, i.e V=Y/P.

where P = total points in 09-10 season
Y = total points in 09-10 season/minutes played in 09-10 season
P = price at start of 10-11 season
*minimum playing time = 1000 mins

Selecting the best players in each position by V gives the team:

Sorensen SC
Hahnemann WW
Higginbotham SC
Kyrgiakos LI
Neville MU
O'Shea MU
Samba BR
Tuncay SC
Bale TH
Dunn BR
Giggs MU
Johnson MC
N'Gog LI
Keane TH
Bendtner AR

This team has a low value of 85m simply because the best value players in the game are found in the low end of the market. That isn't the team I'm going to play with eventually, it's just the starting point for further considerations.

Now, if the plus-or-minus-the-baseprice-makes-no-difference theory holds water, shifting the value of each player up 10m should have no effect on my value calculations in each position. If I pass my data through the V = (points/minutesplayed)/price equation I should end up with the same output because according to the theory "it is impossible for any strategy to become more or less successful as a result".

However, if I run the calculation again, I get the following result:

Gomes TH
Sorensen SC
Cole A CH
Kyrgiakos LI
Johnson LI
O'Shea MU
Higginbotham SC
Fabregas AR
Bale TH
Giggs MU
Arteta EV
Dunn BR
Van Persie AR
N'Gog LI
Drogba CH

with a team value of 259m slightly over the bank balance available in this imaginary game.

Now I'm not sure that proves that the plus-or-minus-the-baseprice-makes-no-difference theory is a load of tosh (in fact, I'm sure it doesn't), but what it has done, is suggests a solution to a conundrum I have been grappling with for some years: How do you use the information from V to optimally pack your team up to the 100m limit?

As shown in the first squad above, raw V gives you a cheap team with 15m left in the bank, but this new calculation -- adjusting the baseprice way way up, not down, note -- actually takes you just over the theoretical spending limit for the new imaginary game. It turns out that if you set the baseprice adjustment somewhere between 7m and 8m UP, you end up with a team packed with high-value players that's pretty much right on the button when it comes to spending:

Gomes TH
Sorensen SC
Cole A CH
Kyrgiakos LI
Johnson LI
Higginbotham SC
O'Shea MU
Fabregas AR
Bale TH
Giggs MU
Arteta EV
Dunn BR
Van Persie AR
N'Gog LI
Keane TH

This solution packs in as many high-value players (as calculated by my V) as possible with a minimum amount of wastage. I won't go into the maths here because there is not room, but the proof is quite elegant.

So chuffed am I at discovering this solution to my packing problem, I think I am going to modestly call it Wyld's Optimal Packing Solution.

Of course this is just the starting point for further tweaking. Some players would be downgraded to lower cost bench warmers, injured/likely-to-be-rotated/suspended player would be replaced, and there are stategic issues of optimum formation and upcoming fixtures and tactical issues of home advantage and opposition strength to be looked at. But I think it is a solid basis from which to proceed.