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The Plexiglas Principle – Teams Set To Improve

Imagine, if you will, a world of legwarmers, neon spandex, and hi-top fades. The year is 1983, and New Order’s ‘Blue Monday’ is the must-have soundtrack for your summer.

As a discerning fantasy stathead, however, you have time to savour only one thing: the annual release of Bill James’ Baseball Abstract.

Plexiglas Principle Explained

To overstate the impact of James’ work upon the sabermetric community is a difficult task. Beginning in 1977, his annual compilation of statistics from the previous year of baseball laid the foundation for generations of sports analytics publications to come (this in spite of the first iteration of this booklet selling only seventy-five copies). It was the 1983 edition, though, that introduced the subject of this article: the expectation of regression to the mean, which he dubbed ‘The Plexiglas principle’.

At its heart, the Plexiglas principle simply states that players or teams which exceed expectations one year should not be inherently expected to continue to perform at such a level come the next. Nor should teams which fail to meet their expectations be considered as more likely for failure the next year.

Instead, James argues, we should expect outliers on either end of our distribution of results to regress towards the group average.

Southampton As An Example

Southampton had a poor chance conversion rate in 2016/17. While an average Premier League side converts roughly 10.7% of its chances into goals, Southampton did so at a league-worst rate of 7.5%. Over the course of a season, this cost the Saints a deficit of 10.1 goals relative to the average team.

However, the rate at which a team converts its chances was shown to be essentially random from one season to the next. A comparison of 2015/16 and 2016/17 data for all Premier League teams shows these two numbers to be totally uncorrelated to one another (R2=0.0022).

Indeed, the previous season, Southampton actually registered the fifth-best chance conversion rate in the league.

Over performers and under performers in this category should naturally be expected to regress towards average performance the following year: a prime example of the Plexiglas principle outlined by James.

With this in mind, here are three more teams who under performed their expected chance conversion rate in 2015/16. Those who struggled may offer great potential to the Fantasy manager going into the new season– particularly if last season’s performance leads to drop in price.

Three Potential Improving Sides For 2017/18

Manchester United

After Southampton, the side who struggled the most to convert chances were Manchester United. As anybody who held onto Zlatan Ibrahimovic through September and October can confirm, United’s attackers seemed almost allergic to the act of scoring. Throughout a disappointing season, though, their chance creation numbers remained impressive. In fact, across the entire season, United created a similar number of chances (208 vs 211) to their crosstown neighbours City – and only City the woodwork more times than United’s 13. The key difference between these two sides was the ability to finish these chances: from the same number of opportunities, City created a whopping 80 goals; United produced only 54.

A rebound is almost certainly due. The previous season, United tied for fifth in chance conversion rate (one spot below City) – and had finished above average in finishing rate every season back to 2011 (the first year for which I have data). A revival in United’s attacking fortunes is expected, and should bring with it great Fantasy potential – lifting the already high sophomore-year expectations of players such as Henrikh Mkhitaryan and Paul Pogba.

West Ham United

Another side whose offensive numbers slumped drastically in 2016/17 were West Ham. The Hammers finished as the third-best offensive side in 2015/16, only to fall to the third-worst last season. Hammers fans might feel inclined to blame this slump upon the loss of Dimitri Payet; yet others clearly deserve to shoulder some of this blame. Andy Carroll, in particular, saw his offensive numbers slide last season: despite making two additional starts compared to the 2015/16 season, Carroll produced fewer goals, shots, touches in the box, assists, and chances created.

Come next season, however, fans of West Ham should have hope for an improvement in their side’s attacking fortunes. In particular, much is expected of Argentine playmaker Manuel Lanzini who, having assumed the primary playmaking role for the Hammers, looks set to build on an intriguing past campaign which saw him register 133 FPL  points – top among the West Ham squad.

Watford

The Hornets are perhaps the most speculative of the three sides listed here, but their 2016/17 woes in front of goal are nonetheless due to improve heading into next year’s campaign.

Unlike the other sides listed here, the underlying numbers offer little in terms of optimism: Watford finished 16th in terms of goals scored and big chances created, and 14th in terms of total shots on goal.

Troy Deeney, who produced double-digit goals for the second year in succession, was the lone bright spot in the Watford attacking line – and even he slumped terribly towards the end of the season, without a single goal or assist over the final eight games of the season.

Yet all is not lost for the Hornets. An improvement in chance conversion rate, coupled with the hiring of Hull’s impressive boss Marco Silva, offers some semblance of hope. Despite facing a hopeless task, Silva was able to engineer something of a turnaround in the fortunes of Hull City: accumulating 21 points over his 18 games in charge, after the side earned just 13 points over the first 20 games of the season.

Silva also lifted Hull’s paltry offensive output from 0.85 goals per game to a more respectable 1.1 goals.

Investment in attack is certainly required – with Odion Ighalo now plying his trade in China and M’Baye Niang having returned to Milan, attacking options to support Deeney are scarce. However, the arrival of reinforcements – coupled with the return of creative maestro Roberto Pereyra from a serious knee injury – could signal an improvement for Watford in 2016/17….alternatively, they can always rely on Etienne Capoue to inexplicably score twice every game.

81 Comments Post a Comment
  1. J0E
    • Fantasy Football Scout Member
    • Has Moderation Rights
    • 9 Years
    2 years, 6 days ago

    Brilliant article. I agree re Man Utd and West Ham especially, with the latter also regressed by their new stadium....by the same token I expect Spurs to revert to the mean due to Wembley. Man Utd in Lukaku have a better finisher than the veteran Ibra - that should mean they are bolstered too - and a key reason why I'm keen on both Pogba and Lukaku.

    1. Prokoptas
      • 3 Years
      2 years, 6 days ago

      Thanks, Jonty. United definitely disappointed many last season - I'm definitely expecting that to pick up heading into next season. I'm writing their team preview for WGTA (it's going up later this week), and both Pogba and Lukaku will feature prominently in my thoughts there.

      1. HEADSY
        • 4 Years
        2 years, 6 days ago

        Lukaku will be essential for GW1 squads, he will be in place on Kane for me.

        Really dont see West Ham improving, think they will struggle this season unless they do some serious recruitment. Something the club seems to be in turmoil about atm as they arent signing anyone. If they get Chichartio then he will appeal to me but apparently they arent going to get him because they dont want to meet his wage demands.

    2. statto99
      • Fantasy Football Scout Member
      • 8 Years
      2 years, 1 day ago

      Agree wholeheartedly - excellent article.

  2. Giggs Boson.
    • Fantasy Football Scout Member
    • 7 Years
    2 years, 6 days ago

    Fantastic article 🙂

    I agree with this principle. Which is why I've made tables like these to help:

    Mids who should have scored more: http://members.fantasyfootballscout.co.uk/public-stats-tables/view/19129/

    Unsustainable conversion rates:
    http://members.fantasyfootballscout.co.uk/public-stats-tables/view/18885/

    Sustainable conversion rates:
    http://members.fantasyfootballscout.co.uk/public-stats-tables/view/18884/

    1. Giggs Boson.
      • Fantasy Football Scout Member
      • 7 Years
      2 years, 6 days ago

      Looking at these kinds of numbers helped me choose Mahrez at 5.5m a couple of seasons ago, just a few minutes before the GW1 deadline 🙂

      I'm not saying they will all come as good, long shots need to be accounted for, but they should have some degree of regression.

      1. Prokoptas
        • 3 Years
        2 years, 6 days ago

        Totally agree - there's always a strong degree of randomness involved in small sample size players, but players who have maintained strong expected outputs over longer periods of time are very interesting.

        It's one reason I've been on Pogba so much going into next year...

        1. Giggs Boson.
          • Fantasy Football Scout Member
          • 7 Years
          2 years, 6 days ago

          Same. If United sign a DM he should thrive!

          He hit the woodwork 5 times!!!

          1. Biancazzurri
            • 6 Years
            2 years, 1 day ago

            I keep reading this DM theory, but... it's not like united can't play Fellaini, or technically even Herrera as a DM.

            If Pogba hit the woodwork 5 times, it's more due to luck rather than his midfield partnership.

            He'll be more relaxed and energized playing with his buddy Lukaku, both are in my team.

    2. The Final Touch
      • 2 Years
      2 years, 1 day ago

      Is that Jenna Coleman?
      I miss her in Doctor Who.

      1. Giggs Boson.
        • Fantasy Football Scout Member
        • 7 Years
        2 years, 1 day ago

        Yes. it is.

        Hopefully she returns with Maisie Williams at some point 🙂

  3. Wolves Ay We
    • Fantasy Football Scout Member
    • 3 Years
    2 years, 6 days ago

    So who's going to do well in the Championship? 😉

  4. GreenWindmill
    • Fantasy Football Scout Member
    • 7 Years
    2 years, 6 days ago

    Shot conversion having almost no correlation between seasons is fascinating.

    1. GreenWindmill
      • Fantasy Football Scout Member
      • 7 Years
      2 years, 6 days ago

      Looking at the teams with high conversion rates last year who should therefore negatively revert to mean is interesting...

      1. PvA
        • 2 Years
        2 years, 6 days ago

        Which teams?

          1. PvA
            • 2 Years
            2 years, 6 days ago

            Really interesting, how confident are you that the lower rates will improve?

            1. GreenWindmill
              • Fantasy Football Scout Member
              • 7 Years
              2 years, 6 days ago

              Me? I don't know but some of the numbers definitely do look unsustainable. Compare Man Utd and Chelsea in each column for example...

              1. TopMarx
                • Fantasy Football Scout Member
                • 6 Years
                2 years, 6 days ago

                Looking at your table it caught my eye that Man City had a large number of Big Chances (101). Out of curiosity I thought I would calculate the percentages of Big Chances converted. Man City are 4th worst, only one place above United. Not all bad news for Jesus and Aguero perhaps. Stoke are also set for improvement if they can convert more Big Chances.

                I don't know if the pattern works with Big Chance Conversion, so this data might be useless! Anyway I hope you're having a good summer 🙂

                Team - "Big Chance Conversion"
                CHE - 130.77%
                HUL - 105.71%
                LIV - 105.41%
                BRN - 105.41%
                TOT - 103.61%
                ARS - 100.00%
                EVE - 100.00%
                WBA - 97.73%
                SWA - 91.84%
                WAT - 90.91%
                LEI - 88.89%
                WHM - 88.68%
                SOT - 87.23%
                BOU - 85.94%
                CPL - 84.75%
                SUN - 80.56%
                MCI - 79.21%
                MUN - 77.14%
                MID - 77.14%
                STO - 70.69%

            2. Prokoptas
              • 3 Years
              2 years, 6 days ago

              It depends on the extent of their shortfall, to me. Sides who fall more than one standard deviation outside of the league mean in either direction would make me more confident in their regression. Southampton and United were so far below their expected goal output - more than 10 goals short over the course of the system - that I would expect that to at least more closely resemble the average side going into next year.

              Of course, there's no reason to think that number should over-correct, either; underperforming your numbers one year does not make it more likely that you will overperform the following season. It's best to imagine expected goals as a normal distribution, and assume that any given side will fall close to the mean.

          2. Giggs Boson.
            • Fantasy Football Scout Member
            • 7 Years
            2 years, 6 days ago

            I think sorting by big chances gives a good indication on the potential of a team's attack.

            1. GreenWindmill
              • Fantasy Football Scout Member
              • 7 Years
              2 years, 6 days ago

              I just can't wait for xG 🙂

            2. TopMarx
              • Fantasy Football Scout Member
              • 6 Years
              2 years, 6 days ago

              GB think you might find this table interesting?

              The Next TopMarx Men
              http://members.fantasyfootballscout.co.uk/my-stats-tables/view/8149/

              Players with decent shooting stats but a low goal conversion rate in 2016/17 season.

              1. Giggs Boson.
                • Fantasy Football Scout Member
                • 7 Years
                2 years, 6 days ago

                Yeah, Benteke's big chances stat is very interesting.

                1. TopMarx
                  • Fantasy Football Scout Member
                  • 6 Years
                  2 years, 6 days ago

                  I agree, at £8.0 he's tempting.

                  I hope Aguero gets a price drop, he seemed to be in favour towards the end of last season and surely has to improve his conversion rate.

                  Starting with a front 3 of Benteke, Aguero, Lukaku is my current thinking. With a watchful eye on Lacazette, if he can get close to his 33% conversion rate from last season, and now in a team that likes to create chances, he could be a real bargain.

          3. Doosra - ☭A Noble Grape…
            • Fantasy Football Scout Member
            • 9 Years
            2 years, 6 days ago

            Can we have big chances missed in there, please?

  5. Wolves Ay We
    • Fantasy Football Scout Member
    • 3 Years
    2 years, 6 days ago

    Who were the Plexiglas teams last season Prokoptas and did the theory work?

    1. GreenWindmill
      • Fantasy Football Scout Member
      • 7 Years
      2 years, 6 days ago

      Leicester had the best conversion rate in 15/16 (13.0) and reverted to a mid-table 11.1 last year.

      Crystal Palace had the worst conversion rate (other than Villa) with 8.3 and moved up to 11.4 last year.

      Seems to hold true...

      1. Wolves Ay We
        • Fantasy Football Scout Member
        • 3 Years
        2 years, 6 days ago

        Thanks

      2. Twisted Saltergater
        • Fantasy Football Scout Member
        • 10 Years
        2 years, 6 days ago

        Teams with the worst conversion rate get relegated and are no longer comparable!

  6. Urchin
    • 5 Years
    2 years, 6 days ago

    Thanks, nice analysis and article.... I am almost assured on Lanzini and Pogba in my first team draft after this!!! 🙂

    I had a doubt, in speculating the improvements in the three sides (united, WHU & Watford), you have considered chances created to remain same next season. Especially in case of United....Conversion rate would depend highly on the chances created?

    1. Prokoptas
      • 3 Years
      2 years, 6 days ago

      Thanks, Urchin.

      Conversion rate is independent of chance creation frequency, at least looking at the data from previous years. Sides can produce many chances and fail to convert any of them (like United last year), or exceed their expectations (like Chelsea). I think that United's underlying numbers in terms of chance creation - they basically matched City last year - should provide confidence in them going forward.

      1. Urchin
        • 5 Years
        2 years, 6 days ago

        Interesting, thanks for that clarification.

        And yeah must agree on United point there, especially given that their creative outlet is similar to last year, maybe even better with Pogba more freed up hopefully.
        Cant wait 🙂

  7. Right back Atsu
    • 5 Years
    2 years, 6 days ago

    Brilliant article. Glad it came out after Lanzinis price release. I reckon Alli and Kane will regress this year so may avoid both.

  8. Andy_Social
    • Fantasy Football Scout Member
    • 6 Years
    2 years, 6 days ago

    It is a great and thought-provoking article. What needs further investigation here is to what extent is the plexiglass effect due to the manager, the club and the player.

    You give Watford the benefit due to a new manager - how about Southampton? United have the same manager but new striker. United had a poor conversion rate last year so are due a good one; however Lukaku had a good conversion rate last year, so is he due a bad one?

    Not sure what conclusions to draw, overall!

    1. Prokoptas
      • 3 Years
      2 years, 6 days ago

      Southampton are the ultimate Plexiglass team - more than United, even. They should definitely be due a bounce-back next year.

      You can check out my preview of them, and more data on their attacking failures here: http://whogottheassist.com/posts/844

      1. Andy_Social
        • Fantasy Football Scout Member
        • 6 Years
        2 years, 6 days ago

        Cheers. I'm investing in their defence - currently unclear where their attacking points will come from.

        1. Prokoptas
          • 3 Years
          2 years, 6 days ago

          I'm cautiously optimistic on Tadic this year: he is generally most effective when playing centrally, and less so when out wide. Should be hold down the #10 role, and Southampton start converting the chances he creates at a more normal rate, he could have some really nice value early in the season - particularly given their easy opening fixtures.

      2. Giggs Boson.
        • Fantasy Football Scout Member
        • 7 Years
        2 years, 6 days ago

        They didn't create too many 'big chances' though.

      3. Hotdog
        • Fantasy Football Scout Member
        • 3 Years
        2 years, 5 days ago

        Cracking article. Ward-Prowse could be a great shout for a cheap midfielder

  9. TopMarx
    • Fantasy Football Scout Member
    • 6 Years
    2 years, 6 days ago

    Great read, thank you

    1. Prokoptas
      • 3 Years
      2 years, 6 days ago

      You're welcome - glad you found it interesting!

  10. Puncheon Guly
    • Fantasy Football Scout Member
    • 8 Years
    2 years, 6 days ago

    Great article. So who overacheived and are set for a slump? Chelsea?

    1. Prokoptas
      • 3 Years
      2 years, 6 days ago

      Chelsea are definitely one side due to regress next year - they actually had the highest chance conversion rate of any side (14.7%). Arsenal are the only other big outlier side from last year - they created fewer goal attempts than United, yet still outscored them by 23 goals!

      1. Twisted Saltergater
        • Fantasy Football Scout Member
        • 10 Years
        2 years, 6 days ago

        It's been proven that certain styles of play produce less chances but better quality of chances, such as counter attack where the striker often finds themselves in a one-on-one.

        While Chelsea dominated last season they often played counter attacking football.

        Arsenal meanwhile are shot shy. They create fewer chances due to their possession style and stereotypically like to walk the ball into the net. United struggled to gel with an unsettled first team - that degree of change means it can be difficult for strikers to time runs and be on the same wave length. I'd be curious to see how many of their goal attempts were from outside the box compared with Arsenal?

        1. Prokoptas
          • 3 Years
          2 years, 6 days ago

          There's definitely a difference that reflects their differing styles:

          United took 591 shots, of which 42% came from outside the box.
          Arsenal took 566 shots, of which 33% came from outside the box.

          1. Prokoptas
            • 3 Years
            2 years, 6 days ago

            That's a really interesting point, actually, and it's something which multi-variable measures like xG account for more effectively than chance conversion rate - which is really just a first approximation of under/over-performance.

            Bring on the xG tables!

            1. Twisted Saltergater
              • Fantasy Football Scout Member
              • 10 Years
              2 years, 6 days ago

              Yep, the xG stat is going to be really interesting!

      2. Deulofale
        • 3 Years
        2 years, 21 hours ago

        Still unsure about how Chelsea are due a regression. Consider 'games won' as a stat. The way Chelsea played last season allowed them to win 30 games. If the season was played 1000 times, let's presume that this is the average (though in reality it could be more or less). If Chelsea, and every team, play the same next year, the most likely games won by Chelsea would be 30. However, you're claiming that the most likely scenario is that Chelsea play worse, relative to all the other teams, simply because they were better last season. But we know they are a better team, and that's why they did better.

        I understand that the concept should work when compared to the own team's history (in principle), since that could be said to be more random. But in reality there's much more going on in terms of personnel change, aging players, club finances etc, that the factors aren't stable enough for it to work.

        The 'chance conversion' stat is no different to 'games won'. Perhaps a stat that was more random, such as throw ins, would suit your analysis better, since this is genuinely more variable season to season. The chances Chelsea create is relative to they way they play, the quality of the team etc etc. So surely the plexiglas principle would only work relative to those factors, i.e. have they converted more chances than is average for them. Though it's still open to the changeable factores mentioned aove. So it would have to be relative to "expected" statistics, which would need to be based on an model that includes the factors of an aging team, personel change etc, which I don't trust that anyone has or can create! haha

        United suit your analysis well because they clerly underperformed, but I can't see the theory holding true for more than half the teams (which is what would make it useful).

        (See post below for more questions from me! 😀 )

        1. Deulofale
          • 3 Years
          2 years, 21 hours ago

          But I would be very interested to find out that I was wrong 🙂 I'm commenting out of curiousity, and I'd like to improve my undrstanding. I hope you don't take offence 🙂

  11. AA33
    • 2 Years
    2 years, 6 days ago

    Brilliant article! Thanks! 🙂

  12. Twisted Saltergater
    • Fantasy Football Scout Member
    • 10 Years
    2 years, 6 days ago

    Wasn't the Plexiglas Principle used on individual baseball players over the course of a season? That's an incredibly large sample size compared with 20 teams in a league.

    The other major point is that an individual's performance in baseball (or tennis, golf etc.) rarely fluctuates massively from season to season unless influenced by injury, contract year etc. In team sports there are many more variables: transfers, new managers, tactical changes, injuries etc. This would explain why your expected shot conversion stat had zero correlation from this season to the one prior.

    We have to be really careful with statistics and I don't think this model can be applied to team sports, imo.

    1. Prokoptas
      • 3 Years
      2 years, 6 days ago

      Yes, the original model was based on individual players. However, the underlying theory is no different than Pythagorean win expectations, expected goals, or any other model that we use to project records or performance on a team level.

      According to Chris Andersen, the average baseball player has 34.16 at bats over the course of a season from which to extrapolate performance data. By comparison, we have 400 to 600 shots per team over the course of a PL season. While there is definitely a higher ratio of noise to signal in the football data based on it being a team sport with less controlled variables, I still think there is strong value in the predictive power of regression to the mean in the case of outliers in any sport.

      1. Twisted Saltergater
        • Fantasy Football Scout Member
        • 10 Years
        2 years, 6 days ago

        I genuinely don't think it can be applied to teams. In any given season, a team can have 3 different managers! It simply isn't stable enough to draw accurate conclusions.

        Taking the simplest thing like an injury to a key player; how does Arsenal perform with and without Sanchez? Spurs without Kane? How does Spurs defence perform when they switch from 5 to 4 at the back?

        Individual performance has many less factors which allows accurate predictive models to be formed.

        1. Deulofale
          • 3 Years
          2 years, 22 hours ago

          I agree. This is also what I'm trying to get at with my post below, and recent discussions.

          People seem to think that poor individual stats predict a positive change in a player's form because they expect a "regression to the mean" within the team or the league. Whereas, even if this where applicable to teams, it would mean change in stats for the individual regardless of whether their individual stats are good or bad.

          However, it's probably much more useful to compare an individual's stats to his own stats of the past, combined with knowledge of extra non-quantified factors, such as how good they look in the penalty area etc.

  13. makaveli123
    • 3 Years
    2 years, 6 days ago

    Great article.

  14. Bedknobs and Boomsticks
    • 10 Years
    2 years, 6 days ago

    A couple of tables for you; goals per game home and away from last season, corrected to match average conversion rate:

    Home
    ARS ... 1.61
    BOU... 1.63
    BUR... 1.48
    CHE... 2.11
    CPL... 1.19
    EVE... 1.91
    LEI... 1.57
    LIV... 2.08
    MCY... 1.65
    MUN... 1.61
    SOT... 1.28
    STO... 1.41
    SWA... 1.37
    TOT... 2.05
    WAT... 1.48
    WBA... 1.41
    WHM... 1.14

    Away
    ARS... 1.57
    BOU... 0.93
    BUR... 0.74
    CHE... 1.15
    CPL... 1.28
    EVE... 0.91
    LEI... 0.86
    LIV... 1.52
    MCY... 1.92
    MUN... 1.73
    SOT... 1.80
    STO... 1.00
    SWA... 0.91
    TOT... 1.70
    WAT... 0.89
    WBA... 0.83
    WHM... 1.68

    1. Bedknobs and Boomsticks
      • 10 Years
      2 years, 6 days ago

      Pretty tight with regards to corrected home goals, but the way table is very interesting. Note the Manchesters, Southampton and then Chelsea.

      Also interesting to note that it was the teams that got more chances away from home who had the poorer conversion rates.

  15. Catch
    • Fantasy Football Scout Member
    • 3 Years
    2 years, 6 days ago

    Og there is 0 correlation berween conversion rate om season 1 and 2 it means that you can not predict, based on the conversion rate alone, what next years rate will be.

    To say that x team will be better next season due to

    1. Catch
      • Fantasy Football Scout Member
      • 3 Years
      2 years, 6 days ago

      ..A low preformance this season is gamblers fallacy

  16. Catch
    • Fantasy Football Scout Member
    • 3 Years
    2 years, 6 days ago

    Sry for missspelling and dubble post. My phone is awfull

    1. Prokoptas
      • 3 Years
      2 years, 6 days ago

      No problem. I think there is a slight misunderstanding here.

      To say that underperforming one year (relative to the mean) will lead to overperforming (relative to the mean) the next year is indeed a gambler's fallacy. There is no mechanism to overcorrect such that the two-year running average will normalise.

      However, a side which underperforms one year should also not be expected to underperform the second year - those two numbers are entirely uncorrelated. Therefore, we would expect that for any given team, any performance that is an outlier close to the fringes of our distribution (either over- or under- performance) should regress closer to the group average. That is what is meant by the plexiglas principle.

      In the case of the teams listed here, they underperformed their projected goalscoring numbers substantially. That underperformance is not expected to continue into next year, yet prices and ownership is often strongly driven by the previous year's performance. As a result, they could represent bargains in terms of attacking potential per million, which is what this article is trying to get at.

      1. Catch
        • Fantasy Football Scout Member
        • 3 Years
        2 years, 6 days ago

        Thanks! The reasoning is good and I am inclined to agree with the logic. Perhaps it was to harsh to mention the fallacy. =)

        I do still wonder.. is it correct to compare each teams score to the mean score of all teams?

        Should you not insted compare each teams rate to it's own mean over several seasons?

        That way there would not be any confusing between quality in front of goal and randomness(luck).

        1. Deulofale
          • 3 Years
          2 years, 22 hours ago

          Aha! This is related to what I'm saying in my post below.

  17. Individual
    • Fantasy Football Scout Member
    • 5 Years
    2 years, 6 days ago

    Awesome article, mate 🙂

    1. HVT
      • 8 Years
      2 years, 4 days ago

      So much this and a lot of quality contributions given too, thanks Prokoptas.

  18. tm245
    • 7 Years
    2 years, 5 days ago

    I like the approach and am a massive fan of the Abstract, thanks for bringing baseball analytics into the conversation. I'd love for this to work, but Twisted Saltergarter is spot on above -- the sample sizes are not nearly big nor comparable enough to sustain a finding yet.

    One area to think about is the nature of the action being statistically analyzed -- a batter is in the same spot, always, with the same strike zone. The biggest variable is the pitched ball being sent his way, but 600+ at bats per season allows a big enough sample size that expectations can be formed and then applied to future predictions of performance. There are so many more variables to take into consideration for goal attempts that I'm not sure team conversion rates are the best way to look for regression to the mean.

    James also looked at teams from season to season based on run differential as a way for them to exceed or fail to meet expectations. Late inning runs are one of the least predictable performances for teams from year to year, so their overall run scoring and run prevention often provided a better indicator of future performance than wins and losses.

    I think you asked a really important question and I hope your article gives us all more to think about. My response isn't meant to close the conversation down, or to criticize this good exploration.

  19. noquarternt
    • 3 Years
    2 years, 5 days ago

    Really nice article, just the kind of thing I love to read. Thanks for making and sharing.

  20. Triggerlips
    • 8 Years
    2 years, 5 days ago

    Question
    Are individual players conversion rates also unrelated from one season to the next? In other words is conversion rate more down to luck than skill?

    1. Johannes
      • 4 Years
      2 years, 4 days ago

      Over 30-40 games I would say it’s more down to skill, but surely some luck involved as well.

  21. Captain Choice - Ag imirt &…
    • 10 Years
    2 years, 2 days ago

    This article is about 'regression to the mean' where a person/team having performed above average one season will regress back to the average.
    Which explains the American Sports illustrated 'curse'

    There is a good book on this type of thing and decision making which may/may not help fpl players.

    'Thinking fast and slow' by Daniel Kahneman,

    https://www.amazon.co.uk/Thinking-Fast-Slow-Daniel-Kahneman/dp/0141033576

    1. Andy_Social
      • Fantasy Football Scout Member
      • 6 Years
      2 years, 2 days ago

      A bit of intellectual rigour on the site. I like it!

    2. MTPockets
      • 10 Years
      2 years, 1 day ago

      Smart guy, although some cited studies (esp social psychology, priming) found to have sample-size & replicability 'problems'. Should be careful about having too much faith in the book's conclusions, something the author's since conceded on.

      1. Captain Choice - Ag imirt &…
        • 10 Years
        2 years, 1 day ago

        Did not realise that. Half of the book was an entertaining read anyway.
        Makes you think while you read it

  22. MTPockets
    • 10 Years
    2 years, 1 day ago

    Love it. Need to look through some of the tables listed above.

  23. Deulofale
    • 3 Years
    2 years, 22 hours ago

    @PROKOPTAS, GREENWlNDMILL and everyone. I really like the article and it's really piqued my interest in projections as I start to get to grips with the stats area. Since everyone's like "tl;dr" on the most recent article, I'll post this where it belongs, so maybe I can get some answers/discussion going. 🙂

    The idea of Plexiglas is very strange to me in this article. The "uncorrelated" stats are only looked at between the last two seasons. Yet we all know Leicester's season was the strangest season in a while.

    Whereas if you look at GW's table below, and roll back the years, you can actually see that the top teams usually have the top conversion rates. http://members.fantasyfootballscout.co.uk/my-stats-tables/view/19269/

    I think it would be a mistake to assume that the Plexiglass Principle is applicable to conversion rates in the Premier League on the basis of this non-correlation alone. Do you really believe that the top 6 teams for conversion rates last season (CHE, ARS, TOT, MCI, EVE, LIV) will have have a decreased conversion rate on average? My guess is that this is relatively stable: it will go up and down each year, but the best teams are usually at the top, just like for 'goals scored', and 'games won'.

    In fact, is there any other evidence that the Plexiglass effect is actually at work in football at all? I'm no expert, but I truly wonder whether it is only applicable to MLS (to some degree) and draft systems, and only for specific statistics, which you would need to test first. I feel like this represents our urge to jump on some secret formula that simplifies the decision-making process, and give us an edge over others with a nice, neat, though probably mythic story about how stats work.

    Likewise, the definition of over- and under-performing in the article seems to be conflated into the comparison of performance with the mean AND by comparision with "expectations". However, these concepts are far from the same, and I'm not sure by what measure our expectations can be quantified, nor what the definition of expectations is either. In this way, we are conflating the principle of conversion with the mean and how good we think a team (or player) should do, which is a mistake.

    Which brings me to the final point that this principle applies to the team. As I said to Giigs Boson, the starting XI and positions and all sorts of things are variable, whereas the team name, 'Arsenal' is not (hense the "non-correlation". If I was in that team and never scored goals, Arsenal's conversion rates would go up and down each season, but my conversion rate would stay on 0. So the question is, how can we use this to predict individual performances. Surely if the team is expected to do better, then so is the player. But if a player has low stats, there is no basis to assume he is going to improve (without the application of team stats, other stats, and the eye test!).

    If anyone could give us any more insight into this, it would be much appreciated. PROKOPTAS, what do you think? I'm genuinely interested, and I might be very wrong, so I certainly don't mean any offence by questioning the article. However I do value scepticism, criticism and discussion. There's more discussion on stats and trends with Doosra and Giggs Boson here, if anyone is bored and interested. http://www.fantasyfootballscout.co.uk/2017/07/15/scout-notes-pre-season-3/?hc_page=7#hc_comment_15873024

    1. tm245
      • 7 Years
      1 year, 12 months ago

      This is a great post. I have the same inkling as you so I'm glad you posted it. As for Bill James, the Plexiglass Principle was one of several indicators he would use to measure teams and try to project their future performance. This article from 10 years ago is a decent overview I found online:
      http://www.hardballtimes.com/the-bill-james-indicators/

      A few takeaways pertinent to your questions: the Pythagorean approach is invested in analyzing runs scored and allowed, whereas the Plexiglass is basically just looking at wins and losses to see which teams might have been lucky or unlucky.

      To me the power of the large sample sizes that baseball provides us is not in regression to some overall mean for the entire sport, but rather to a personal mean: a team or an individual player will, over the course of a long stretch of time, inevitably find his or its level. Batters on how well they hit, and pitchers on how well they pitch.

      As you so aptly pointed out, the changes in personnel and coaching in the PL mean that so much changes from season to season it would be incredibly difficult to apply a regression-based approach, imo -- what is Man United's level? How is that defined, or measured?

      1. Deulofale
        • 3 Years
        1 year, 12 months ago

        Hurray! A reply. I've been trying desperately to get answers without having to actually do any work to figure it out! Haha

        It seems to me that the answer lies in common sense. The claim that Man United underperformed last season is implied, by many, to be apparent in the stats. But until somebody demonstrates otherwise to me, I'm inclined to believe that the stats only reflect that they did well on some metrics and badly on others, and the 'fact' that they underperfomed is an assessment based on personal opinion and common knowledge of their history (rather than their history statistically-speaking).

        Chelsea decline one year, then won the league the next. Leicester won the league and then declined. Hurray the theory works! But how do you explain teams that go down 2 divisions in 2 or 3 seasons?

        There must be a better way to make projections using stats. Most likely it comes out of an assessment of individual players' levels, as you say, and some assessment of other factors (relavant to James' indicators), such as the age of the team, incoming players etc, which can be based on stats or personal opinion or both.

        I'm certainly taking all the veteran's knowledge on here with a grain of salt until I gain a better understanding. If you're interested in any further reading and opinions (very few facts), then there's a small amount of discussion to be found in these links. Perhaps this is the best place to have that conversation, though!

        http://www.fantasyfootballscout.co.uk/2017/07/15/scout-notes-pre-season-3/?hc_page=13#hc_comment_15873834

        http://www.fantasyfootballscout.co.uk/2017/07/15/moving-target-kyle-walker/?hc_page=11#hc_comment_15877073

        1. tm245
          • 7 Years
          1 year, 12 months ago

          Interestingly, one of the most criticized strategies on here --- "he's due" -- is the simplest version of this. In baseball, over the long haul, it is actually correct more often than you might expect. Over the course of a season, a player finds his level: if he has been hitting poorly for two months after being a strong hitter in previous seasons, you try to buy low on him in a trade because you anticipate the second half of the season to be a rebound in which he gets hot.

          We often mock it in FPL, but I wonder if it is really that simple for individual players with proven track records. As for teams, I think it becomes a bit more difficult to predict what their level is since any changes in style and personnel will result in needing to recalibrate the level.

          As for United, though, I believe that they underperformed offensively: tons of new personnel, no developed style of play, an aging striker whose larger than life personality and early season explosion might have compensated for some truly donkey level performances as the season wore on, and plenty of unconverted chances.

          With not as much change this offseason (and the biggest one being a younger, faster version of a proper talismanic striker), I think they are set to explode in attack.

          1. Deulofale
            • 3 Years
            1 year, 12 months ago

            I think the 'he's due strategy' on here is about keeping a player because he's more likely to score now, because he didn't score recently. However, we all bought the players at a particular price expecting them to score a particular amount. If he's only going to perform back at the expected level, then he's only worth the price we paid for him, and there's no telling that he's likely to return to his level in the next match. Moreover the fixtures and form of other players have changed by this point.

            The 'he's due stragety' I would say is akin to the gambler's fallacy of expecting a heads because you got tails 10 times in a row. It's the same in that it will eventually reach the level of 50%. But it's no more or less likely in the next game.

            However if you stick with the player long enough (fixtures and other factors permitting), he will return to the level, as you say. The he's due thing doesn't seem to be a long term strategy to me haha.

            'finding your level' doesn't fit with 'being due' for me anyway. Being due is about the underlying stats suggesting they will score in the coming games, which they always had anyway, but they have been 'unlucky' not to recently. In baseball, as you say, you try to buy low when someone hits a run of bad form, you don't try to buy them for the value of their expected outputs, when you have other players already hitting that output in your team or for a cheaper price in other teams etc.

            I'm getting all confused now. The he's due thing is definitely something to be wary of at the same time as being wary of dismissing it. At the end of the day, if depends on who's saying it and how they're using it, since it can be both true and false to varying extents! 🙂

            1. Deulofale
              • 3 Years
              1 year, 12 months ago

              New community article by Speadsheet about the Plexiglas principle

              http://www.fantasyfootballscout.co.uk/2017/07/18/from-cant-hit-a-barn-door-to-scoring-sensation/