Over recent weeks we have been using a data set of transfers made by Premier League clubs over the last four seasons. From this data, we have been able to give a measure of how good-value a signing has been, which nations have provided the best players, and which players have adapted the best to the Premier League.

Now we will be tying this together by looking at the individual clubs within our data set to see which ones have conducted the best business.

We will look at which clubs have got the best performances from their players, given how much they paid for them. For each club's signings (excluding free and loan deals), we estimate the level they should reach, using our previously-derived formula:

r = -0.00002f^2 + 0.0111f + 6.6776

For each player, we then compare this expected value with the level they did in fact reach. This is then averaged for each player signed by each club. The results are shown below:

It is a huge surprise to see that QPR, a team noted for their misfiring scattergun approach to transfers, tops the pile. However, it should be noted that QPR only had three transfers count for this graph (Caulker, Fer and Sandro), who all performed at a good level. At the other end, Bournemouth are not considered to have performed notably poorly in their transfer dealings, so it is a surprise to see them last. Again, this is primarily caused by a low sample size, with only four players contributing to the average score. Of these, two were notable flops (Murray and Ibe), which was enough to put the club bottom.

Of the clubs with sufficient transfers within the data set to merit examining, the most notable are Arsenal, whose average of 0.22 is more than double that of the next-highest team. Their signings include Alexis Sanchez, whose performance level of 7.80 was the highest of all players in the data set. Signings such as Özil, Debuchy and Gabriel all also out-performed the level their fees suggested.

You can use the widget below to select a team and see how each of its transfers were rated. Just use the drop-down list which appears when you select the team name at the top.

Of the clubs with sufficient transfers within the data set to merit examining, the most notable are Arsenal, whose average of 0.22 is more than double that of the next-highest team. Their signings include Alexis Sanchez, whose performance level of 7.80 was the highest of all players in the data set. Signings such as Özil, Debuchy and Gabriel all also out-performed the level their fees suggested.

You can use the widget below to select a team and see how each of its transfers were rated. Just use the drop-down list which appears when you select the team name at the top.

Needless to say, each club had its own hits and misses, and the greater spending power of the larger clubs means they can absorb the impact of the misses much easier. Next time we will be looking at how a team's performance in the transfer window affected their position in the league.

By analysing transfers made by Premier League clubs over the last four seasons, we have been able to come up with a measure of how good-value signings have been. This method was then used to see where the best-value players have been bought from.

This time we will be considering the past form of signings in order to measure how well they have adapted to the Premier League.

As before, we use all transfers made by Premier League clubs made between the 2013/14 and 2016/17 seasons, where the player has made at least ten appearances for his new club (explained here). As we are considering past performances as well, this time we will only consider players who played at least ten matches for their previous club before moving.

For each player, the average rating (according to WhoScored) from their last three seasons with their old club is compared to the average rating in their first three seasons with their new club. If a player was on loan just before moving, they are counted as moving from the loaned club, since that is where their ratings are for.

The leagues for which ratings are recorded, and therefore can be used, are:

- England's Premier League (153 transfers)
- England's Championship (36 transfers)
- France's Ligue 1 (36 transfers)
- Germany's Bundesliga (33 transfers)
- Italy's Serie A (31 transfers)
- Netherland's Eredivisie (13 transfers)
- Russia's Premier League (5 transfers)
- Spain's La Liga (43 transfers)

For each league, the average difference in ratings is recorded. The results of which can be seen below:

The first thing to note is that for all leagues, the difference is negative. This means that their performance has dropped after moving to the Premier League. This isn't a huge surprise, as we would expect a player who has been bought to have played well enough to merit a transfer, after which regression to the mean may occur (which is explained here). There is also the time required for a player to become familiar with his new club, or indeed for his manager to find the best way of utilising him.

As we would expect, the English Premier League has the smallest difference in performance levels. It is also reasonable to expect La Liga to follow; this is widely considered to be the highest-quality league in the world, and therefore players who play well in that should find that they are of sufficient quality to play in the Premier League.

It is interesting to see that players moving into the Premier League from the Championship play at closer to their previous level than those from Serie A and the Bundesliga, both highly-regarded leagues. In other words, a player playing at a high level in the Championship is more likely to keep up that form in the Premier League than someone from the top leagues in Italy and Germany. Particularly given the recent success of German sides, this is a surprising result.

Significantly behind the other leagues is the Eredivisie, where signings have performed significantly below their level in the Netherlands. This is partly driven by players who have particularly struggled in England since moving, such as Depay at Manchester United, Janssen at Tottenham Hotspur or Henriksen at Hull City. It is also driven by players who was performing at an extremely high level in the Netherlands, whose performances in England have been good, but less spectacular, such as Southampton's Pellé and Tadic or Newcastle United's Wijnaldum.

**Who were the best and worst adapters? **

We can also use this method to look at the transfers in our data set to find the best and worst players at adapting to the Premier League. Click the name of each division below to see the five best and worst adapters from each league. The Russian Premier League is left out, since there are only five transfers in total.

As we would expect, the English Premier League has the smallest difference in performance levels. It is also reasonable to expect La Liga to follow; this is widely considered to be the highest-quality league in the world, and therefore players who play well in that should find that they are of sufficient quality to play in the Premier League.

It is interesting to see that players moving into the Premier League from the Championship play at closer to their previous level than those from Serie A and the Bundesliga, both highly-regarded leagues. In other words, a player playing at a high level in the Championship is more likely to keep up that form in the Premier League than someone from the top leagues in Italy and Germany. Particularly given the recent success of German sides, this is a surprising result.

Significantly behind the other leagues is the Eredivisie, where signings have performed significantly below their level in the Netherlands. This is partly driven by players who have particularly struggled in England since moving, such as Depay at Manchester United, Janssen at Tottenham Hotspur or Henriksen at Hull City. It is also driven by players who was performing at an extremely high level in the Netherlands, whose performances in England have been good, but less spectacular, such as Southampton's Pellé and Tadic or Newcastle United's Wijnaldum.

We can also use this method to look at the transfers in our data set to find the best and worst players at adapting to the Premier League. Click the name of each division below to see the five best and worst adapters from each league. The Russian Premier League is left out, since there are only five transfers in total.

Premier League

Player | Previous club | New club | Old rating | New rating | Difference |

Moses, V | Liverpool | Stoke City | 6.35 | 7.45 | +1.10 |

Townsend, A | Tottenham Hotspur | Newcastle United | 6.76 | 7.35 | +0.59 |

Sigurdsson, G | Tottenham Hotspur | Swansea City | 6.56 | 7.09 | +0.53 |

Benteke, C | Liverpool | Crystal Palace | 6.83 | 7.35 | 0.52 |

Bertrand, R | Aston Villa | Southampton | 6.44 | 6.95 | +0.51 |

Player | Previous club | New club | Old rating | New rating | Difference |

Moses, V | Stoke City | West Ham United | 7.45 | 6.52 | -0.93 |

Ayew, A | Swansea City | West Ham United | 6.98 | 6.24 | -0.74 |

Sidwell, S | Fulham | Stoke City | 7.04 | 6.30 | -0.74 |

Lambert, R | Southampton | Liverpool | 7.03 | 6.33 | -0.70 |

Rémy, L | Newcastle United | Chelsea | 7.15 | 6.45 | -0.70 |

Championship

Player | Previous club | New club | Old rating | New rating | Difference |

Afobe, B | Wolves | Bournemouth | 6.42 | 7.10 | +0.68 |

Grant, L | Derby County | Stoke City | 6.72 | 6.99 | +0.27 |

Phillips, M | QPR | West Bromwich Albion | 6.99 | 7.13 | +0.14 |

Boyd, G | Hull City | Burnley | 6.75 | 6.85 | +0.10 |

Fábio | Cardiff City | Middlesbrough | 6.94 | 6.99 | +0.05 |

Player | Previous club | New club | Old rating | New rating | Difference |

Sako, B | Wolves | Crystal Palace | 7.31 | 6.54 | -0.77 |

Gestede, R | Blackburn Rovers | Aston Villa | 7.56 | 6.83 | -0.73 |

Sandro | QPR | West Bromwich Albion | 6.99 | 6.39 | -0.60 |

Murray, G | Reading | Bournemouth | 6.96 | 6.38 | -0.58 |

Hennessey, W | Wolves | Crystal Palace | 7.01 | 6.48 | -0.53 |

Ligue 1

Player | Previous club | New club | Old rating | New rating | Difference |

Martial, A | Monaco | Manchester United | 6.70 | 7.11 | +0.41 |

Payet, D | Marseille | West Ham United | 7.27 | 7.67 | +0.40 |

Cabaye, Y | PSG | Crystal Palace | 6.68 | 7.05 | +0.37 |

Lovren, D | Lyon | Southampton | 6.95 | 7.32 | +0.37 |

Kanté, N | Caen | Leicester City | 7.36 | 7.61 | +0.25 |

Player | Previous club | New club | Old rating | New rating | Difference |

Thauvin, F | Marseille | Newcastle United | 6.94 | 6.20 | -0.74 |

Manquillo, J | Marseille | Sunderland | 7.06 | 6.41 | -0.65 |

Batshuayi, M | Marseille | Chelsea | 6.74 | 6.16 | -0.58 |

Stambouli, B | Montpellier | Tottenham Hotspur | 7.04 | 6.52 | -0.52 |

Ibrahimovic, Z | PSG | Manchester United | 7.95 | 7.44 | -0.51 |

Bundesliga

Player | Previous club | New club | Old rating | New rating | Difference |

Pocognoli, S | Hannover 96 | West Bromwich Albion | 6.62 | 6.91 | +0.29 |

Fuchs, C | Schalke 04 | Leicester City | 7.04 | 7.29 | +0.25 |

Romeu, O | VfB Stuttgart | Southampton | 6.72 | 6.90 | +0.18 |

Arnautovic, M | Werder Bremen | Stoke City | 6.80 | 6.95 | +0.15 |

Kirchhoff, J | Schalke 04 | Sunderland | 6.78 | 6.88 | +0.10 |

Player | Previous club | New club | Old rating | New rating | Difference |

Schürrle, A | Bayer Leverkusen | Chelsea | 7.53 | 6.79 | -0.74 |

Mkhitaryan, H | Borussia Dortmund | Manchester United | 7.62 | 6.93 | -0.69 |

Schweinsteiger, B | Bayern Munich | Manchester United | 7.47 | 6.78 | -0.69 |

Joselu | Hannover 96 | Stoke City | 7.21 | 6.59 | -0.62 |

Rahman, A | FC Augsberg | Chelsea | 7.37 | 6.75 | -0.62 |

Serie A

Player | Previous club | New club | Old rating | New rating | Difference |

Alonso, M | Fiorentina | Chelsea | 7.12 | 7.51 | +0.39 |

Isla, M | Juventus | QPR | 6.67 | 6.98 | +0.31 |

Kozák, L | Lazio | Aston Villa | 6.44 | 6.61 | +0.17 |

Shaqiri, X | Inter Milan | Stoke City | 6.69 | 6.85 | +0.16 |

Pogba, P | Juventus | Manchester United | 7.71 | 7.72 | +0.01 |

Player | Previous club | New club | Old rating | New rating | Difference |

Cuadrado, J | Fiorentina | Chelsea | 7.61 | 6.37 | -1.24 |

Balotelli, M | AC Milan | Liverpool | 7.59 | 6.54 | -1.05 |

Álvarez, R | Inter Milan | Sunderland | 7.15 | 6.48 | -0.67 |

Jovetic, S | Fiorentina | Manchester City | 7.37 | 6.82 | -0.55 |

Suárez, M | Fiorentina | Watford | 6.91 | 6.38 | -0.53 |

eredivisie

Player | Previous club | New club | Old rating | New rating | Difference |

Martina, C | FC Twente | Southampton | 6.75 | 6.72 | -0.03 |

van Aanholt, P | Vitesse | Sunderland | 7.12 | 7.06 | -0.06 |

Blind, D | Ajax | Manchester United | 7.33 | 7.19 | -0.14 |

Janmaat, D | Feyenoord | Newcastle United | 7.22 | 6.88 | -0.34 |

Wijnaldum, G | PSV Eindhoven | Newcastle United | 7.37 | 6.91 | -0.46 |

Player | Previous club | New club | Old rating | New rating | Difference |

Depay, M | PSV Eindhoven | Manchester United | 7.83 | 6.33 | -1.50 |

Janssen, V | AZ Alkmaar | Tottenham Hotspur | 7.52 | 6.23 | -1.29 |

Pellé, G | Feyenoord | Southampton | 7.97 | 7.05 | -0.92 |

Henriksen, M | AZ Alkmaar | Hull City | 7.14 | 6.22 | -0.92 |

Tadic, D | FC Twente | Southampton | 7.80 | 6.95 | -0.85 |

La Liga

Player | Previous club | New club | Old rating | New rating | Difference |

Sánchez, A | Barcelona | Arsenal | 7.34 | 7.80 | +0.46 |

Llorente, F | Sevilla | Swansea City | 6.59 | 6.92 | +0.33 |

Alderweireld, T | Atlético Madrid | Southampton | 6.87 | 7.07 | +0.20 |

Barragán, A | Valencia | Middlesbrough | 6.83 | 7.02 | +0.19 |

Costa, D | Atlético Madrid | Chelsea | 7.20 | 7.37 | +0.17 |

Player | Previous club | New club | Old rating | New rating | Difference |

Aspas, I | Celta Vigo | Liverpool | 7.14 | 6.21 | -0.93 |

Soldado, R | Valencia | Tottenham Hotspur | 7.10 | 6.39 | -0.71 |

Bastón | Eibar | Swansea City | 6.78 | 6.11 | -0.67 |

Nolito | Celta Vigo | Manchester City | 7.34 | 6.77 | -0.57 |

Bravo, C | Barcelona | Manchester City | 6.87 | 6.35 | -0.52 |

The most remarkable thing to note is that Victor Moses appears to be the best and worst adapters at a new club for players signed from Premier League rivals, thanks to a freakishly good season on loan with Stoke City. Other notable players are Memphis Depay, whose difference is the largest of any player in the data set, signifying how poorly he adapted to his move to Old Trafford.

**Summary**

After studying the effects of the price tag on a player's performance, now we can consider his previous performance as well to identify which signings have performed above and below expectations. Next time we will be bringing this altogether in order to rate each club's recent transfer activity.

]]>Having collected data on Premier League transfers from the 2013/14 - 2016/17 seasons, we were able to predict a player's level of performance given his transfer fee. This gives us a way of rating transfers on how close to their expected level of performance the player played at.

This time we will use this method to look at the nations where the signings came from. This will allow us to see which nations have supplied the best-value players to the Premier League.

As with our previous article, the data set is made from all signings made by Premier League teams during the given time period. Only players which have played at least 10 matches for their new club are counted, and their rating on WhoScored is taken to give their level of performance.

Only nations which have supplied at least five players are counted. These are Belgium (5 players), France (32 players), Germany (30 players), Italy (28 players), the Netherlands (20 players), Portugal (12 players), Russia (7 players), Scotland (6 players) and Spain (43 players).

Additionally, we include domestic transfers, splitting them into Premiership (138 players) and Championship (40 players, including one transfer from a League One side).

The remaining nations are split into three groups: Western Europe (8 players), Eastern Europe (11 players) and the Americas (6 players). The nations which make up these groups are as follows:

- Western Europe: Austria, Denmark, Norway, Sweden, Switzerland
- Eastern Europe: Croatia, Hungary, Poland, Romania, Turkey, Ukraine
- The Americas: Argentina, Brazil, Mexico

For each nation, we take the average of each player's rating for their new club, and compare it to the rating that should be expected given their transfer fee (using the formula found last time). Below you can see a plot of these ratings:

Nations which appear above the diagonal line have provided players who have under-performed for their new club, whilst those below the line have over-performed.

We can see that the Western Europe and Eastern Europe groups have provided players that have performed significantly poorly for their new clubs. Other nations which appear to provide poor value are the Netherlands and Italy, along with the Championship. There are three nations which clearly have provided the best-value players to the Premier League: Belgium, France and Scotland.

Below is a table showing the full data for each league:

We can see that the Western Europe and Eastern Europe groups have provided players that have performed significantly poorly for their new clubs. Other nations which appear to provide poor value are the Netherlands and Italy, along with the Championship. There are three nations which clearly have provided the best-value players to the Premier League: Belgium, France and Scotland.

Below is a table showing the full data for each league:

Nation/league | Average price | Average rating | Average predicted rating | Difference |

Scotland | £7.95m | 6.83 | 6.76 | +0.064 |

Belgium | £9.11m | 6.83 | 6.78 | +0.057 |

France | £10.56m | 6.83 | 6.79 | +0.044 |

Germany | £13.06m | 6.82 | 6.81 | +0.007 |

Premeirship | £8.08m | 6.77 | 6.76 | +0.005 |

The Americas | £8.99m | 6.78 | 6.78 | +0.004 |

Spain | £14.18m | 6.82 | 6.83 | -0.006 |

Russia | 10.51m | 6.77 | 6.79 | -0.024 |

Portugal | £4.24m | 6.80 | 6.83 | -0.030 |

Championship | £4.24m | 6.67 | 6.72 | -0.057 |

Italy | £11.86m | 6.74 | 6.80 | -0.057 |

Netherlands | £9.44m | 6.72 | 6.78 | -0.064 |

Eastern Europe | £7.06m | 6.57 | 6.75 | -0.179 |

Western Europe | £5.74m | 6.55 | 6.74 | -0.187 |

From this, we can see that it is Scotland which has provided the best-value transfers to the Premier League. This is primarily driven by the excellent signings made by Southampton from Celtic. Of course, this means that the bad news for Celtic is that they possibly could have got more for their exports. Of the major footballing leagues, it appears that France provide better value than alternatives in Germany, Italy and Spain.

**Summary**

By using our previously-identified method for calculating how good-value a transfer is, we are able to identify which leagues appear to be the best for getting new players into the Premier League. We found that the best value was to be found in Scotland, which makes sense - the style of football and culture are similar, and players at Celtic get exposure to playing in the biggest club competition in the world. However, the worst value was found from smaller European leagues, who also have the advantage of the Champions League.

Remember that the data used to create this list only included players who had played at least ten matches. It doesn't include players who were signed but weren't deemed good enough to even play that many - this may change the results, but nevertheless gives a good idea of where the best value is to be found.

Foreign leagues will be the theme of our next article as well, as we use player's past performances to measure how well they adapt to the Premier League.

]]>By using our previously-identified method for calculating how good-value a transfer is, we are able to identify which leagues appear to be the best for getting new players into the Premier League. We found that the best value was to be found in Scotland, which makes sense - the style of football and culture are similar, and players at Celtic get exposure to playing in the biggest club competition in the world. However, the worst value was found from smaller European leagues, who also have the advantage of the Champions League.

Remember that the data used to create this list only included players who had played at least ten matches. It doesn't include players who were signed but weren't deemed good enough to even play that many - this may change the results, but nevertheless gives a good idea of where the best value is to be found.

Foreign leagues will be the theme of our next article as well, as we use player's past performances to measure how well they adapt to the Premier League.

We have spent the last month collecting data on transfers made by Premier League sides, which will help us see which transfer policies have worked. This is the first of a handful of articles which will look at different aspects of this data.

In this article, we will look at how strong the relationship is between the price paid for a player and their level of performance. We can then use this to say which were the best and worst transfers made in recent seasons.

The set of transfers we will be using for this and future articles is all incoming transfers made by Premier League clubs from the 2013/14 season onwards (so covering the previous four seasons). Only players that have played at least ten Premiership matches for their new club are counted.

The problematic part is measuring the level of performance for each player. Due to the nature of football, each player performs a different role and therefore can't easily be compared. For example, counting goals might give a measure of the quality of a striker, but does little to measure other players. In fact, it is not even that easy to measure the performance of strikers this way, since it doesn't take into account the number of chances needed, nor any other factors.

Unfortunately, it is beyond our resources to devise a new method for objectively comparing football players. Therefore, the player ratings given by the website WhoScored are used. For each player in our data set, we calculate their average rating in their first three seasons with their new club. If the club was relegated in that time, we stop counting at the point of relegating, as to avoid inflating a player's score with ratings from the Championship.

In order to see whether spending more on a player returns you better performances, we split the transfers in the data set into £10m-wide bands, with separate groups for free transfers and loans. The average rating for each group can be seen below:

The striking thing is that other than the highest category (over £30m), there is not a huge difference between the groups. In particular, there doesn't seem to be a different between transfers in the range £20m - £30m and those in the range £10m - £20m. Nor is there barely any difference between the under £10m group and free transfers. Meanwhile, the lowest group are loan transfers, albeit not significantly lower than the free category.

This suggests that the only way to guarantee quality is to spend big, something which Premiership clubs are doing; the number of players signed for £30m in our data set started at 4 in 2013/14, moving up to 5 in 2014/15, 6 in 2015/16 before jumping to 10 in 2016/17.

We can plot all transfers in our data set, comparing the price paid and the average rating. This can be seen below. Note that there are two scatter graphs, a standard one and one with a logarithmic scale (explained here). We have excluded free transfers and loans as they can't be shown on a logarithmic scale.

This suggests that the only way to guarantee quality is to spend big, something which Premiership clubs are doing; the number of players signed for £30m in our data set started at 4 in 2013/14, moving up to 5 in 2014/15, 6 in 2015/16 before jumping to 10 in 2016/17.

We can plot all transfers in our data set, comparing the price paid and the average rating. This can be seen below. Note that there are two scatter graphs, a standard one and one with a logarithmic scale (explained here). We have excluded free transfers and loans as they can't be shown on a logarithmic scale.

Unsurprisingly, we can see huge variability in performance, particularly with the cheaper transfers. One thing to note is that the highest-performing players perform at the same level regardless of fee (i.e. the best-performing players signed for under £10m perform at roughly the same level as the best players signed for over £30m - with a rating above 7.4). However, the number of players with particularly low ratings is far lower for the highest transfers fees. This backs up the previous assertion that spending big should at least ensure that you avoid signing a dud.

**Which were the best and worst transfers?**

The regression line on the two graphs above was the best fit for the data, and uses the following formula, where r represents the average rating, and f represents the fee:

The regression line on the two graphs above was the best fit for the data, and uses the following formula, where r represents the average rating, and f represents the fee:

r = -0.00002f^2 + 0.0111f + 6.6776

We can then substitute a player's fee into the above equation, and it will give us an estimate of what level of performance they should have been playing at. By substituting this expected value from the actual rating, we can see the best and worst signings made. Firstly, the ten best signings:

Player | Season | Sold from | Sold to | Price (£m) | Rating | Exp. rating | Diff |

Payet, D | 15/16 | Marseille | West Ham United | 12.75 | 7.67 | 6.82 | 0.85 |

Kanté, N | 15/16 | Caen | Leicester City | 7.65 | 7.61 | 6.76 | 0.85 |

Sánchez, A | 14/15 | Barcelona | Arsenal | 36.13 | 7.80 | 7.05 | 0.75 |

Amavi, J | 15/16 | Nice | Aston Villa | 9.35 | 7.48 | 6.78 | 0.70 |

van Dijk, V | 15/16 | Celtic | Southampton | 13.35 | 7.51 | 6.82 | 0.69 |

Davies, C | 13/14 | Birmingham City | Hull City | 2.25 | 7.37 | 6.70 | 0.67 |

Alonso, M | 16/17 | Fiorentina | Chelsea | 19.55 | 7.51 | 6.89 | 0.62 |

Fazio, F | 14/15 | Sevilla | Tottenham Hotspur | 8.50 | 7.39 | 6.77 | 0.62 |

Antonio, M | 15/16 | Nottingham Forest | West Ham United | 8.08 | 7.36 | 6.77 | 0.59 |

Alli, D | 14/15 | MK Dons | Tottenham Hotspur | 5.64 | 7.30 | 6.74 | 0.55 |

The names on this list are not a huge surprise. Generally, the list is dominated by players signed for modest fees who have put in performances of a far higher level. With this in mind, it is a great compliment to Alexis Sánchez that he makes the list, given that he cost £36.13m. His average rating of 7.80 is the highest of all players in the data set.

It is surprising that two players (Jordan Amavi and Curtis Davies) signed for teams that they were then relegated with. However, this really just emphasises that football is a team sport.

Now, for the list of the worst signings:

It is surprising that two players (Jordan Amavi and Curtis Davies) signed for teams that they were then relegated with. However, this really just emphasises that football is a team sport.

Now, for the list of the worst signings:

Player | Season | Sold from | Sold to | Price (£m) | Rating | Exp. rating | Diff |

Batshuayi, M | 16/17 | Marseille | Chelsea | 33.15 | 6.16 | 7.02 | -0.86 |

Bastón | 16/17 | Atlético Madrid | Swansea City | 15.30 | 6.11 | 6.84 | -0.73 |

Juanmi | 15/16 | Málaga | Southampton | 5.95 | 6.06 | 6.74 | -0.68 |

Ayew, A | 16/17 | Swansea City | West Ham United | 20.49 | 6.24 | 6.90 | -0.66 |

Depay, M | 15/16 | PSV Eindhoven | Manchester United | 28.90 | 6.33 | 6.98 | -0.65 |

Janssen, V | 16/17 | AZ Alkmaar | Tottenham Hotspur | 18.79 | 6.23 | 6.88 | -0.65 |

Thauvin, F | 15/16 | Marseille | Newcastle United | 15.60 | 6.20 | 6.85 | -0.65 |

Sordell, M | 14/15 | Bolton Wanderers | Burnley | 0.54 | 6.04 | 6.68 | 0.64 |

Cuadrado, J | 14/15 | Fiorentina | Chelsea | 26.35 | 6.37 | 6.96 | -0.59 |

Aspas, I | 13/14 | Celta Vigo | Liverpool | 9.18 | 6.21 | 6.78 | -0.57 |

This time the list is mainly made up of either highly-priced signings for big clubs which haven't worked out well, or cheaper signings which have been particularly bad. The bad news for Marvin Sordell is that his rating of 6.04 is the lowest across all players in our data set.

It is no great surprise that two of players in the list (Sordell and Florian Thauvin) were signed by clubs which went on to be relegated, whilst Swansea City and West Ham are currently involved in a relegation battle.

Michy Batshuayi might consider himself unlucky to be rated as the most under-performing signing, as he has mainly been playing from the bench so far at Chelsea. However, £33.15m is a very high price to pay for a bench-warmer. He will have time to turn this around though, unlike many of the players on the list who have been sold on.

**Summary**

By analysing past transfers, we can begin to get an idea of what tactics work in the transfer market. This is the first of a series of articles where we will get more of an idea of where the best value is to be found, and which clubs are doing the best at finding it.

It is no great surprise that two of players in the list (Sordell and Florian Thauvin) were signed by clubs which went on to be relegated, whilst Swansea City and West Ham are currently involved in a relegation battle.

Michy Batshuayi might consider himself unlucky to be rated as the most under-performing signing, as he has mainly been playing from the bench so far at Chelsea. However, £33.15m is a very high price to pay for a bench-warmer. He will have time to turn this around though, unlike many of the players on the list who have been sold on.

By analysing past transfers, we can begin to get an idea of what tactics work in the transfer market. This is the first of a series of articles where we will get more of an idea of where the best value is to be found, and which clubs are doing the best at finding it.

Transfermarkt - for a list of all transfers made by Premier League clubs.

WhoScored - for season-by-season ratings of each player's performances.

by Adrian Worton

You may have noticed a dearth of posts on here recently. In fact, the Six Nations model we had been using to track the tournament stopped abruptly. This is due to a remarkably hectic time in my life.

However, upon seeing odds available for all matches of Euro2016 it was impossible to resist the urge to create a new simulator. The simulator can be found in full here.

You may have noticed a dearth of posts on here recently. In fact, the Six Nations model we had been using to track the tournament stopped abruptly. This is due to a remarkably hectic time in my life.

However, upon seeing odds available for all matches of Euro2016 it was impossible to resist the urge to create a new simulator. The simulator can be found in full here.

However, due to the aforementioned time constraints, this article will be light on detail. Simply put, the simulator uses the same method as our first-ever simulator, that of the 2014 World Cup. The only difference is that the formula used to convert odds into probabilities is updated to the one used from the Premiership simulator onward.

**Who will win?**

Using our usual method of running the model 1,000 times to gain an idea of what might happen during the tournament, we get the following result:

Using our usual method of running the model 1,000 times to gain an idea of what might happen during the tournament, we get the following result:

With eerie similarities to the pre-tournament predictions of our World Cup model, we see the hosts have roughly a quarter chance of winning, with holders Spain in a slightly disappointing third place.

With a smaller roster of nations competing, the space is opened for more unusual names, such as Austria, Croatia and Russia, to enter the tournament with an outside chance of causing an upset.

**How will my team do?**

In order to see the exact breakdown for each nation, use the embedded sheet below to select a nation (the top cell will provide a drop-down list), and see how exactly they fared during the 1,000 simulations.

With a smaller roster of nations competing, the space is opened for more unusual names, such as Austria, Croatia and Russia, to enter the tournament with an outside chance of causing an upset.

Using pre-existing methods, it is relatively easy to generate a full tournament from a limited number of odds. The full simulator can be found on the Euro 2016 page.

Now, to my actual work...

Yesterday we introduced the simulator for the Six Nations, and analysed by running multiple simulations. We can now compare the results of those simulations, which are the summation of short-term odds with the long-term odds of various events.

Firstly, we can take the odds from eight well-known bookmakers for the winner of the Six Nations, convert them to probabilities using our usual method and compare with the proportion of times each team won the title in our repeated simulations. These can be seen below:

We can see that firstly, the bookies have largely reached a consensus on each team's likelihood of winning. Each appear to believe that England are the most likely to win the title, followed by Wales, Ireland, France and Scotland, with Italy having a negligible chance.

We can see some slight differences between the likelihoods suggested by the long-term odds and our simulations, but this can be explored easier by looking at the graph below:

We can see some slight differences between the likelihoods suggested by the long-term odds and our simulations, but this can be explored easier by looking at the graph below:

The two diamonds per team represent the minimum and maximum likelihood suggested by the bookmakers' odds. The diagonal line represents the proportion of simulations each team won. Therefore, if the diagonal line passes between a team's diamonds, then the bookies' long-term and short-term odds are in agreement.

We can see there are two teams who this does not apply to:

Scotland - as the line passes below the markers for Scotland, this suggests that the outright odds for them to win the Six Nations are too short given their match-by-match odds. So there is potentially value to be found in betting on Scotland in individual matches.

France - as the line passes above their markers, we can see that the long-term odds give France less chance of winning the tournament than their match-by-match odds would suggest. Therefore, it is unlikely that betting on France in individual matches will provide good value, instead backing them to win the tournament overall might provide better reward (although it is still at best only 17.3% likely to happen).

**Wooden spoon winners**

We can also apply the same analysis to the odds provided by the same bookmakers for the race to win the wooden spoon - the team finishing last.

We can see there are two teams who this does not apply to:

Scotland - as the line passes below the markers for Scotland, this suggests that the outright odds for them to win the Six Nations are too short given their match-by-match odds. So there is potentially value to be found in betting on Scotland in individual matches.

France - as the line passes above their markers, we can see that the long-term odds give France less chance of winning the tournament than their match-by-match odds would suggest. Therefore, it is unlikely that betting on France in individual matches will provide good value, instead backing them to win the tournament overall might provide better reward (although it is still at best only 17.3% likely to happen).

Unsurprisingly, we can see that both the simulations and the outright odds suggest Italy are strong favourites to finish last, with only Scotland really providing any sort of competition. In keeping with the pro-England theme of the odds so far, we see them as the team last present on the left-hand graph.

On the right-hand graph we can see that the only team discrepancy between the long-term and short-term odds is with Italy, who are slightly below the line, suggesting that the odds provided actually aren't short enough, and might represent value for money.

**Summary**

We can see that overall for this tournament the long-term and short-term odds are largely in agreement, with only minor differences. This is in contrast to the football World Cup, where we found plenty of bets to recommend. This may be because the World Cup simulator involved probabilities created from looking at past odds, whereas the Six Nations simulator has every match already provided with odds.

]]>On the right-hand graph we can see that the only team discrepancy between the long-term and short-term odds is with Italy, who are slightly below the line, suggesting that the odds provided actually aren't short enough, and might represent value for money.

We can see that overall for this tournament the long-term and short-term odds are largely in agreement, with only minor differences. This is in contrast to the football World Cup, where we found plenty of bets to recommend. This may be because the World Cup simulator involved probabilities created from looking at past odds, whereas the Six Nations simulator has every match already provided with odds.

by Adrian Worton

At TGIAF we have created quite a few Simulators, with varying success. Generally, those that have been successful are those where odds for the whole contest is available; such as with the General Election and the Oscars. Our World Cup simulator was built on odds for the entire group stage (75% of matches) whilst our least successful effort, the Premier League simulator, used past results to generate probabilities for the upcoming season, therefore using no current odds.

At TGIAF we have created quite a few Simulators, with varying success. Generally, those that have been successful are those where odds for the whole contest is available; such as with the General Election and the Oscars. Our World Cup simulator was built on odds for the entire group stage (75% of matches) whilst our least successful effort, the Premier League simulator, used past results to generate probabilities for the upcoming season, therefore using no current odds.

Luckily, there are odds available (from a notorious online bookmaker who will remain unnamed; they're perfectly fine at publicising themselves) for the whole tournament. Therefore, there is no excuse (other than my job) not to create a full simulator.

**Method**

Using our usual odds-conversion method, we can easily get probabilities for the fifteen Six Nations matches, which can be seen on the page for this simulator.

One way to see the predictions from this model is to look at the expected points tally for each side. This is calculated by multiply each probability by the number of points it would give a particular team, and summing across all matches.

So for example, say we are looking at France, their opening match against Italy has the following probabilities:

Using our usual odds-conversion method, we can easily get probabilities for the fifteen Six Nations matches, which can be seen on the page for this simulator.

One way to see the predictions from this model is to look at the expected points tally for each side. This is calculated by multiply each probability by the number of points it would give a particular team, and summing across all matches.

So for example, say we are looking at France, their opening match against Italy has the following probabilities:

- France win - 88.4%
- Draw - 2.3%
- Italy win - 9.3%

2 x [probability of win] + 1 x [probability of draw] + 0 x [probability of defeat]

2 x 0.884 + 0.023 + 0

2 x 0.884 + 0.023 + 0

Which equals 1.791. Note that for Italy the expected points tally is 0.209; which is 2 - France's expected score.

Looking at the full tournament we get the following expected tallies:

Looking at the full tournament we get the following expected tallies:

So we can see here that contrary to many pre-tournament predictions of Wales winning, the odds appear to be favouring England.

However, this method does not necessarily mean that England are expected to win. As a stochastic model the only real way to get an idea of its predictions is to look at repeated simulations, as we did with the football World Cup.

**Summing Simulations**

By observing the results from 1,000 simulations, we can get an idea of how the model really works. Firstly, the graph below shows the average points score across the simulations:

However, this method does not necessarily mean that England are expected to win. As a stochastic model the only real way to get an idea of its predictions is to look at repeated simulations, as we did with the football World Cup.

Unsurprisingly, we see no real change from the previous graph; the expected score is really saying what our simulations should have honed in on. The best way to see is to count the number of times each team finished in each position across the simulations:

We can see that the expected points advantage does translate into the higher probability of winning for England, although really it appears a very close fight with Wales, with Ireland and France with not-unrealistic chances of challenging. Despite their excellent World Cup campaign, Scotland appear unfancied, whilst it is no surprise to see Italy with very little chance of finishing outside the bottom two.

Meanwhile at the bottom it appears to be a fight between Italy and Scotland, as it often has lately. However, it is interesting that all six teams finished bottom in at least 1% of simulations.

**Summary**

As with our previous simulators, we can now use this to tease apart interesting facts about the tournament and about the way odds are created for it, which will hopefully appear in upcoming articles.

And you can play with the full simulator yourself on this page.

]]>Meanwhile at the bottom it appears to be a fight between Italy and Scotland, as it often has lately. However, it is interesting that all six teams finished bottom in at least 1% of simulations.

And you can play with the full simulator yourself on this page.

by Adrian Worton

In cricket, reaching 100 runs in an innings (a century) is a major milestone - the number of centuries a player makes in his career is a major statistic which is used in comparisons between batsmen. When Sachin Tendulkar became the first player to reach 100 international centuries the celebrations across India were huge.

In cricket, reaching 100 runs in an innings (a century) is a major milestone - the number of centuries a player makes in his career is a major statistic which is used in comparisons between batsmen. When Sachin Tendulkar became the first player to reach 100 international centuries the celebrations across India were huge.

With this in mind, it would be no surprise that batsmen become nervous when closing in on a century. It is perceived that once a player reaches the nineties, these nerves mean he is more likely to get out before reaching 100.

We can test this theory quite simply by looking at the proportion of players dismissed in the 90s, compared to each of the other run-scoring 'decades'.

**Our sample**

We will look at all Test innings from 2000 onwards, looking at each bracket of ten runs from 0-9 up to 200-209.

Firstly, we will just look at innings which end in a dismissal - i.e. ignoring that where the batsman finished not out. We can look at this selected year-by-year to see if there are any overall trends:

We can test this theory quite simply by looking at the proportion of players dismissed in the 90s, compared to each of the other run-scoring 'decades'.

Firstly, we will just look at innings which end in a dismissal - i.e. ignoring that where the batsman finished not out. We can look at this selected year-by-year to see if there are any overall trends:

Note that we have taken the log of each category, in order to make it easier to see the higher-scoring categories.

No distinct pattern presents itself. We can see that the way runs are scored appears to be quite constant, albeit with three years where less runs were scored: 2000, 2007 and 2015.

If we focus on the 90s (in yellow), we see that this section doesn't appear to be abnormally larger than those around it. However, we can get a clearer idea of whether the 90s are particularly significant by looking at the probability of being dismissed in each decade.

**Likelihood of dismissal**

To find the chance of a player being dismissed in each 10-run boundary, we first count the number of players who leave that group - either by being dismissed or by reaching the next decade. We then find the proportion of that group who were dismissed.

By looking at each decade within our sample, we get the following probabilities:

No distinct pattern presents itself. We can see that the way runs are scored appears to be quite constant, albeit with three years where less runs were scored: 2000, 2007 and 2015.

If we focus on the 90s (in yellow), we see that this section doesn't appear to be abnormally larger than those around it. However, we can get a clearer idea of whether the 90s are particularly significant by looking at the probability of being dismissed in each decade.

By looking at each decade within our sample, we get the following probabilities:

The striking thing is that the 90s are in fact the lowest decade until the 120s. So in fact, we can decisively reject the notion that being within 10 runs of a century makes a batsman more likely to be dismissed. If anything, the pressure focuses the mind of the batsmen more, which we would expect from professional sportsmen. And when the pressure is off, when the player has reached the century, then they are more at risk.

**Conclusion**

It's no surprised that received wisdom in cricket isn't always spot-on. You just need to see the antagonistic attitude of many cricket commentators and pundits to the Duckworth-Lewis-Stern method, primarily on the basis that they don't understand it, to get an idea of the lack of faith in numbers that many of the sport's old-boys network have.

]]>by Adrian Worton

Last time we had a look at what the teams in Groups A-C of the Women's World Cup need to do to ensure qualification. Groups A and B will play their final games tonight, but our attention now shifts to the remaining three groups.

Last time we had a look at what the teams in Groups A-C of the Women's World Cup need to do to ensure qualification. Groups A and B will play their final games tonight, but our attention now shifts to the remaining three groups.

Below are the current standings for each group (team name; goal difference; points):

Group D1. USA; +2; 4pts2. AUS; 0; 3pts 3. SWE; 0; 2pts 4. NGA; -2; 1pt | Group E1. BRA; +3; 6pts2. CRC; 0; 2pts 3. ESP; -1; 1pt 4. KOR; -2; 1pt | Group F1. COL; +2; 4pts2. ENG; 0; 3pts 3. FRA; -1; 3pts 4. MEX; -1; 1pt |

Recall that the top two sides progress to the next round, with the four best of the six third-placed teams getting through. However, as with last time, we will just focus on finishing in the top two.

Below are the possibilities for each group, including the probabilities of each outcome suggested by odds:

Below are the possibilities for each group, including the probabilities of each outcome suggested by odds:

The interesting thing is that unlike Groups B & C, all three of the groups we've looked at today see all four teams with a chance of qualification.

Using the same method as last time, we can work out the probabilities of each side progressing:

Using the same method as last time, we can work out the probabilities of each side progressing:

Group DUSA - 94.9%AUS - 57.7% SWE - 41.1% NGA - 6.0% | Group EBRA - certainESP - 44.6% KOR - 29.0% CRC - 26.4% | Group FFRA - 84.5%ENG - 62.1% COL - 48.9% MEX - 4.4% |

We can see how open the three groups are. Group D is likely to see USA through, and Nigeria out, so the main interest lies in the Australia - Sweden fixture. Whilst Sweden are favourites, Australia are more likely to go through simply because a draw would suit them.

Group E sees Brazil already winning the group. Therefore, we see a three-way race between Spain, South Korea and Costa Rica. Even though Costa Rica narrowly lead this race, they face Brazil in their final match, meaning they are actually the least likely to progress.

And in the final group we see an even more curious phenomenon, where group leaders Colombia, who can go through in eight of the nine possibilities, are still more likely to fail to make the top two. Although it is not hard to think that the bookmakers have underestimated their ability, given how well they played against France.

**Long-term vs short-term odds**

As we did with Groups A-C, we can compare our probabilities for a top-two finish with those suggested by odds:

Group E sees Brazil already winning the group. Therefore, we see a three-way race between Spain, South Korea and Costa Rica. Even though Costa Rica narrowly lead this race, they face Brazil in their final match, meaning they are actually the least likely to progress.

And in the final group we see an even more curious phenomenon, where group leaders Colombia, who can go through in eight of the nine possibilities, are still more likely to fail to make the top two. Although it is not hard to think that the bookmakers have underestimated their ability, given how well they played against France.

As we did with Groups A-C, we can compare our probabilities for a top-two finish with those suggested by odds:

Curiously, there are odds available for Brazil finishing in the top two of Group E, despite the fact it is a foregone conclusion. So even at 1/100, this represents a good value bet. Costa Rica also appear to be good value for money.

Colombia being given odds of qualification of 3/1 is quite high, given that we showed they can progress with eight out of the nine possibilities. Although given that 4 points is likely to be enough even if they finish third, there is a chance Colombia take their foot off the pedal in their match against England.

But the most significant difference is in Group D. We commented earlier that it was slightly surprising that Sweden were less likely to finish in the top two than Australia, given they went into the match as favourites, and this shows in the long-term odds. This means that either betting on Sweden to win the match is good value for money, or betting on Australia to win the group is. In fact, these two outcomes trade off against each other perfectly, since if Sweden fail to win, then Australia will qualify (unless this match is a draw, and Nigeria beat USA by 2 in a high-scoring match - but such a situation is exceptionally unlikely).

Therefore, if you place a bet on:

**Summary **

It may be a result of there being less public attention on the Women's World Cup than in the men's tournament last year, but we have seen some very surprising slip-ups from the betting companies. Given the disaster of the bets placed on the 2015 General Election, this presents a chance to recoup some money.

With all six groups looked at now, our articles should provide some clues as to what to expect in the next few days.

]]>Colombia being given odds of qualification of 3/1 is quite high, given that we showed they can progress with eight out of the nine possibilities. Although given that 4 points is likely to be enough even if they finish third, there is a chance Colombia take their foot off the pedal in their match against England.

But the most significant difference is in Group D. We commented earlier that it was slightly surprising that Sweden were less likely to finish in the top two than Australia, given they went into the match as favourites, and this shows in the long-term odds. This means that either betting on Sweden to win the match is good value for money, or betting on Australia to win the group is. In fact, these two outcomes trade off against each other perfectly, since if Sweden fail to win, then Australia will qualify (unless this match is a draw, and Nigeria beat USA by 2 in a high-scoring match - but such a situation is exceptionally unlikely).

Therefore, if you place a bet on:

- Sweden to beat Australia (5/4)
- Australia to finish in the top two (9/10)

With all six groups looked at now, our articles should provide some clues as to what to expect in the next few days.

by Adrian Worton

The Women's World Cup started in Canada a week ago, and we have seen some great football so far.

With the second round of group fixtures underway, we will look ahead to the final round of games, and look to see what each team needs to do in order to qualify. Today, we look at Groups A, B and C. Below are the current standings for each group (listed as: team; goal difference; points):

The Women's World Cup started in Canada a week ago, and we have seen some great football so far.

With the second round of group fixtures underway, we will look ahead to the final round of games, and look to see what each team needs to do in order to qualify. Today, we look at Groups A, B and C. Below are the current standings for each group (listed as: team; goal difference; points):

Group A1. CAN; +1; 4pts2. CHN; 0; 3pts 3. NED; 0; 3pts 4. NZL; -1; 1pt | Group B1. GER; +10; 4pts2. NOR; +4; 4pts 3. THA; -3; 3pts 4. CIV; -11; 0pts | Group C1. JPN; +2; 6pts2. SUI; +8; 3pts 3. CAM; +5; 3pts 4. ECU; -15; 0pts |

In each group, the top two teams progress to the knockout rounds. Additionally, the four best-performing third-placed teams progress. We will concern ourselves with the top two in each group, since teams will want to avoid the lottery that comes with finishing third. However, teams that finish third with at least 4 points are all but certain to progress, and finishing with 3 points is likely to be enough.

Below are the outcomes from all nine possibilities for each of our groups. We have also shown the probability of each result, converted from bookmakers' odds.

Below are the outcomes from all nine possibilities for each of our groups. We have also shown the probability of each result, converted from bookmakers' odds.

We can now work out the probability that each team progresses by summing the probabilities of all outcomes that sees them progress. In scenarios where two teams are tied on points and goal difference is needed to separate them to send one through (such as in Group A, where wins for New Zealand and the Netherlands sees Canada and New Zealand level), we just assume each side has an equal chance of progressing.

Applying this to all three groups gives us the following chances of qualification:

Applying this to all three groups gives us the following chances of qualification:

Group ACAN - 87.5%CHN - 74.1% NED - 20.0% NZL - 18.4% | Group BNOR - 99.9%GER - 97.0% THA - 3.1% CIV - zero | Group CJPN - certainSUI - 82.9% CAM - 17.1% ECU - zero |

Note that we use "certain" and "zero" to denote foregone conclusions. These are separate to "100.0%" and "0.0%" as the latter values might be situations where there is some possibility of an alternate outcome, but the chances are so small that they disappear with rounding.

Also, it should be noted that whilst Ivory Coast and Ecuador are listed as having "zero" chance of progressing, they could still quality as a third-placed team. Although with their horrific goal differences, it is extremely unlikely they will progress.

We can see that Group A appears to be the most open, whilst Group B is a lot less close than its table suggests. And Group C will be entirely decided by the result of the Switzerland - Cameroon fixture, making that one to watch.

**Long-term vs short-term odds**

As we did with the Men's World Cup last year, we can compare our probabilities with the probabilities suggested by the bookmakers' odds for teams finishing in the top two of their group:

Also, it should be noted that whilst Ivory Coast and Ecuador are listed as having "zero" chance of progressing, they could still quality as a third-placed team. Although with their horrific goal differences, it is extremely unlikely they will progress.

We can see that Group A appears to be the most open, whilst Group B is a lot less close than its table suggests. And Group C will be entirely decided by the result of the Switzerland - Cameroon fixture, making that one to watch.

For Group B no odds are available, leading us to assume that the bookmakers have already decided that Germany and Norway progressing is a certainty. Our probabilities are slightly different, but not by much.

For Group C we shouldn't see a big difference, given that who qualifies out of Switzerland and Cameroon is entirely dependent on one match. However, there is a slight difference, which is surprising.

Group A is where we see the biggest discrepancy, as New Zealand have no odds listed, leading us to assume that the bookies don't think they can progress. However, we have seen that they have a decent chance of progressing (higher, indeed, than Cameroon). The result of this is that we can say that the odds for the other three teams are bad value for money.

**Summary**

Even with a very limited number of odds, we are able to judge long-term bookies' odds by using their short-term odds as a measure.

But the most important aspect is that ahead of the final round of games, we can put the chances of each team into perspective.

Next time we will go through the chances of the teams in Groups D-F!

For Group C we shouldn't see a big difference, given that who qualifies out of Switzerland and Cameroon is entirely dependent on one match. However, there is a slight difference, which is surprising.

Group A is where we see the biggest discrepancy, as New Zealand have no odds listed, leading us to assume that the bookies don't think they can progress. However, we have seen that they have a decent chance of progressing (higher, indeed, than Cameroon). The result of this is that we can say that the odds for the other three teams are bad value for money.

But the most important aspect is that ahead of the final round of games, we can put the chances of each team into perspective.

Next time we will go through the chances of the teams in Groups D-F!

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