Friday 30 September 2011

Measuring the Fun in Football.

The win probability for each team is tracked on a minute by minute basis throughout each game.At any point in a game a team will have a probability of winning the game outright and an associated probability of drawing the game.By multiplying the probability of winning the game by 3 and the probability of drawing by 1 and adding the results together you will get an expected longterm average for the number of points that team will achieve from that position or Expected Points (EP) for short.

Expected Points graphs do a very good job of illustrating the ebbs of flows of a soccer match and the large swings caused by the relatively rare occurance of a goal is particularly evident.However,they can also be used to quantify more subjective aspect of a game such as entertainment value.

There are a number of factors that contribute towards a game being more or less entertaining and these can be captured by reference to an EP Graph.Swings in fortunes during the game,late winners,spirited comebacks and impressive performances by an unfancied underdog each can contribute towards making a game worth watching and all can be tracked.

While it would be possible to track all of the movements in EP during the match,it's much more useful to be able to simply and quickly get an idea of how eventful a game has been by just looking at the EP graph.One such method is to sum each team's highest EP during the game and divide it by the sum of each teams lowest EP during the 90 minutes.

Under this approach the ManU Basel 3-3 draw scores an Entertainment Value (EV) of around 23.ManU's highest Expected Points Value was almost 3 just after Welbeck's second goal,Basel's was just under 2.6 in the 89th minute just prior to Young's equaliser.United's EP was at a low of 0.24 and Basel's was 0.01.A similarly switchback game where Blackburn came from behind to defeat Arsenal 4-3 earlier this month scores an EV of 14.

Blackburn 4-3 Arsenal,full of incidents and a great come from behind win and a Entertainment Value of 14

By contrast,Tottenham's wide margin all the way 4-0 win over Liverpool scores an EV of just over 3,as does Swansea's 3-0 canter verses WBA.The Welsh side's dour 0-0 draw with Sunderland totals only 1.3.

Little incident in a fairly standard goalless draw for a EV of 1.3

Wednesday 28 September 2011

Manchester United v Basel,Champions League.

The win probability for each team is tracked on a minute by minute basis throughout each game.At any point in a game a team will have a probability of winning the game outright and an associated probability of drawing the game.By multiplying the probability of winning the game by 3 and the probability of drawing by 1 and adding the results together you will get an expected longterm average for the number of points that team will achieve from that position or Expected Points (EP) for short.

One of the most switchback games you'll see his year or any other.Basel were massive underdogs at the start and Welbeck's brace of goals in a minute just after the quarter hour left the Swiss side in a seemingly hopeless position.A Basel win from 2-0 down after 17 minutes against the Champions of England would be likely to happen just once in a 1000 attempts,a draw was about 10 times more likely at 1 in 140.
70 playing minutes and a hat trick of unrelated Frei goals later and we were looking at a one in a thousand occurrence,but Young's last gasp equaliser meant we had to settle for a mere 1 in 140 event.

1-0,Welbeck,16 mins.
2-0,Welbeck,17 mins.
2-1,F Frei,58 mins.
2-2,A Frei,60 mins.
2-3,A Frei(pen),76 mins.
3-3,Young,90 mins.

Defensive Performance and Transfer Window Purchases.

At first glance it seems relatively easy to decide which teams have he strongest defences in the EPL.Goals allowed per game is almost universally used to demonstrate defensive ability.A goal conceded is to a large extent down to a team's defenders,so it stands to reason that the less you concede,the better you are.To add even more weight and justification to this choice is that,unlike say the NFL each team plays all the others twice,therefore the schedule is almost identical for everyone.

However,this approach has problems.Defences will face every other attack in the league twice over the season,but they are stuck with their own forward and midfielders for each game.And the quality of a team's other outfield players can impact on the amount of defending a team must do and this in turn can be reflected in the amount of goals they concede.

To take an obvious  example.Manchester United defenders at Old Trafford are unlikely to find themselves under the same amount of pressure experienced by their visiting counter parts.United's forward and attacking midfielders will likely have possession of the ball for a longtime,during which there will be little or no defending for United to do.In short overall team quality makes defending easier and not all teams can afford or attract the kind of quality throughout the team enjoyed by Manchester United and the other top teams.

We therefore need to use numbers that initially at least incorporate a team dimension before we try to decide how effective certain parts of a team perform their various tasks.

Average goal difference (AGD) per game is such a stat.It's the difference between the average number of goals per game a team scores and the average number of goals they concede and it is very strongly correlated to success indicators such as final league position.Over the 2010/11 season,Man Utd's average goal difference per game was +1.08,compared to -0.71 for relegated West Ham United.

AGD incorporates both average goals scored and allowed,so it is a genuine team statistic.A team can accumulate positive AGD by scoring goals and although their goal difference will always be eroded by conceding goals it is still advantageous to allow as few goals as possible to be scored against your side.

I've taken each EPL team's seasonal AGD  and plotted the numbers against the average number of goals per game allowed by those teams since the 1999/2000 season.As you can see from the graphic below AGD is strongly correlated to goals conceded.We would of course expect it to be.

From the graph we can derive an equation that relates the amount of goals allowed by a team for a certain level of average goal difference.This relationship gives us an opportunity to see how much of a team's AGD is derived from it's defensive abilities compared to the typical expectation for the EPL.Teams that are overachieving in relation to the norm can be considered to be performing extremely well,defensively regardless of their overall level of talent.

Sunday 25 September 2011

For How Long Will Manchester United be Behind in a Game ?

When Manchester United travelled to Stoke on Saturday they lost their 100% start to the season.Nani's crisp shot from a simple one two on the edge of the Stoke area after 27 minutes was cancelled out by Crouch's first goal for his new club 25 playing minutes later.A cracking game for anyone lucky enough to witness it,but equally interesting from a statistical point of view.

The game was level for the first 27 minutes,United then led for 25 minutes and then the final 38 minutes remained deadlocked,despite the best efforts of Crouch and woeful late finishing from Giggs.But pre game is there some way we can try to estimate the most likely time a team can expect to lead,trail or draw during the game ?

United defending  a 1-0 lead at Stoke.
Expected points calculations rely on the ability to chart the win and draw probability for each team at any point during the match,which in turn are derived from the pre game goal expectancies for each participating teams.Therefore we can use this approach to predict how long a team is likely to be leading,drawing or losing during a game.It seems sensible to initially chart the league's most successful team,as this sets the height of the bar for all other teams.It also helps to give a fan an expectation of how much pleasure,pain or anticipation they are likely to experience during a match.

Probability of course relates to events happening over the long term,so it's not possible to compare predictions generated from those kind of figures over a short time span such as a single game.Therefore to test the methodology I've used all of Manchester United's games from their 2010/11 championship winning season.

Friday 23 September 2011

Individual Player Winning Contribution for Stoke 1 - 0 Liverpool.

Success Probability (SP) is the probability that a team will win a game plus half the probability that a team will draw a game from any chosen point in the game.

1-0,Walters (pen),21 mins.

Wilkinson on for Huth,64 mins.
Jones on for Etherington,68 mins.
Palacios on for Delap,71 mins.

Bellamy on for Henderson,67 mins.
Carroll on for Kuyt,68 mins.
Johnson on for Skrtel,81 mins. 

Only one story here.Liverpool's pre game success probability had fallen from 0.571 to 0.564,before Carragher's unnecessary foul single handedly sent it plummeting to 0.36.Penalties are converted at around 70+% so it was odds on that the penalty would be converted and their SP would fall even further to 0.293.Only a Reina save or Walters miss would restore Liverpool's SP to it's pre penalty levels.

The foul was entirely down to Carragher,so he's penalised for the entire fall immediately after the penalty award.If Reina had made the save he would have been credited with restoring Liverpool to the pre award state.However,Walters converted,but Reina at least had the small consolation of only being penalised 20% of of the move from the SP immediately following the award and the SP following Walters' goal.A large amount of the negative SP from a penalty is borne by the player who commits the infringement.The rest of the back four were penalised 44% of the shift in SP after the score for allowing the situation to develop initially and so Carragher received a double whammy of negative SP.Short of being sent off as well,which he arguably should have been,it's hard to imagine how a defender could have a more damaging 60 seconds of play.

Walters both scored and created the goal by being the fouled player,so he gets the full 100% credit for the winning goal.


Player. Win Contribution.
Begovic. 0.066
Huth. 0.049
Shawcross. 0.066
Upson. 0.066
Wilson. 0.066
Delap. 0.051
Whitehead. 0.066
Pennant. 0.066
Etherington. 0.050
Crouch. 0.066
WALTERS. 0.337
Wilkinson. 0.017
Jones. 0.016
Palacios. 0.015
Total 1.000


Player. Win Contribution.
Reina. 0.013
Agger. 0.017
Enrique. 0.017
Skrtel. 0.028
Adam. 0.020
Downing. 0.020
Henderson. 0.036
Lucas. 0.020
Kuyt. 0.038
Suarez. 0.022
Johnson. -0.011
Bellamy. -0.016
Carroll. -0.016
Total. 0.000

Winning Contribution in Soccer.

Expected Points graphs are the natural tool to visualise how many league points a team is likely to acheve during certain phases of a game.However,if we are interested in their chances of winning (or drawing) the match then plotting success probability is much more useful.

As the game progresses a team's success probability will ebb on flow dependent upon such things a current score,relative strengths of both team and whether a red card has been shown.By adding a team's chances of winning the match to half it's chances of drawing the game we can chart a teams expected success probability at various stages of the match.

At full time a team will have either won,gaining a success probability of 1.0 or drawn the game and shared the win equally with it's opponent gaining 0.5 wins each or of course lost.

By looking at the changes in success probability from the start of the game to full time,we can start to assign how much success probability should be attributed to the 11 or more participating players.

There are generally four fundamental stages to consider.

1) Change in SP due to time elapsed.

Each team will start a game with a likely success probability (SP) based on their relative strengths compared to today's opponents.This can be calculated by taking a weighted view of both team's recent results.How far you go back in time is a matter for individual taste,but I would suggest the last 25 games as a bare minimum requirement.
Since goals,both scored and conceded determine football games,it's sensible to expess the relative team merits in terms of how many goals each team will on average score in today's game,given the relative merits of both attack and defences.We can therefore use the pre game goal expectancies for both teams to calculate the expected success probability at the start of the game.This is the starting point and it's also team specific for today's game.

As the game develops without any goals occuring,the pregame goal expectancies for each team will start to decay.Thus we can re calculate each team's SP up to the point when a goal is scored.What generally happens is that a much superior team will see it's SP trend downwards towards 0.5 (as the teams are still level) and an inferior oppenent will see it's SP trend upwards.We can assign this change in SP respectively to each team along with any changes that occur in the lulls between significant events such as goals,penalty awards or red cards.

2) Goals scored.

To state the obvious,goals change games.If you score you always increase your success probability.The real bone of contention is how to distribute the credit for the goal between the scorer and the creator,similar to the situation in American Football where the QB throws a TD to his WR.I currently split the credit 80/20 in favour of the scorer.Some goals will be relative tap ins,although as Torres demonstrated recently,there maybe no such thing as a tap in,while other goals may result from a relatively simple pass from a team mate.

3) Goals conceded.

Allowing goals always decreases your SP and again we need to apportion the "blame".Harsh though it may seem,I've given the keepers 20% "credit" for the goal.The remaining 80% I've distributed between the 10 outfielders.55% of remaining fall in SP is divided amongst the defenders.I've chosen this figure because if we use goals scored as a proxy for "attacking play" we find that forwards score 55% of the goals,midfielders 35% and defenders 10%.Therefore it seems reasonable to flip these percentages when  trying to apportion the less transparent skill of defending.Blaming forwards partly for goals conceded may seem strange,but firstly the proportion of fault is relatively small, they do actively defend at corners and goals often develop from failure to maintain possession higher up the field.

4) Red Cards.

It's not harder to play against ten men that eleven,it's easier.Reduced in numbers,a team finds it harder to score and harder to prevent goals being scored against them.A red card reduces that team's SP  and the entire amount by which the SP is reduced counts against the transgressing player.

These are the (very) bare bones of a system to apportion blame and credit for team wins or draws amongst the individual players.So lets use a real example.I've chosen the Fulham Man City game from last week to illustrate the methodology and I've started with a pared down Success probability graph,illustrating the six major incidents from the game.Namely,kick off,two goals apiece and full time.

Significant Events from the Fulham Man City Draw.

0-1,Aguero ,18 mins,assist,Silva.
0-2,Aguero,46 mins,assist,Dzeko.
1-2,Zamora,56 mins,assist,Dempsey.
2-2,Murphy,75 mins,assist,Zamora.

Kasami on for Duff,61 mins.
Ruiz on for Dembele,84 mins.

Zabaleta on for Silva,69 mins.
Johnson on for Nasri,81 mins.
Tevez on for Aguero,83 mins.

A deeper look at some of the SP changing events from the game.

Kick Off).

Man City are the away side,but unsurprisingly given their vast investment are still considered more likely winners.If this game were to be repeated a large number of times I'd expect Man City to score on average 1.9 goals,concede 0.8 goals,win just over 60% of the time and draw just over 20% of the time.
So at kick off Man City have a SP of 0.741 compared to Fulham's 0.259.Just prior to the first Man City goal after 18 minutes,City's SP has declined to 0.722 and that fall is shared amongst the 11 starting players.Fulham's has risen to 0.278 from 0.259 and that is also shared amongst their starters.

Aguero's first goal).

Aguero scores from a Silva assist and Man City's SP goes from 0.722 to 0.902.80% of the credit goes to Aguero and 20% to Silva.By contrast Schwartzer is debited 20% of the 0.18 his team's SP has fallen,another 44% is shared by each member of the back four,28% by the four midfielders and 8% by the the two strikers.

Murphy's equaliser).

His goal raises Fulham's SP from 0.07 to 0.39 of which 80% is attributed to him and 20% to Zamora,who set up the chance.

Last 20 minutes).

Fulham's SP rises from 0.39 at the time of the Murphy goal to 0.5 at the final whistle,this is shared amongst the players on the field at the time of the goal.Man City's players lose the same amount as their SP falls to 0.5 from 0.61 as they were still the most likely winners with the game tied at 2-2.

A summary of each players win shares from the game.


Player. Win Conribution. Comments.
Schwartzer. -0.018 Conceded 2 goals,but benefitted from Fulham being big underdogs and claiming a point.
Kelly. 0.005 Unless they score,assist or are sent off,defenders score identically.Tackles won for example would re distribute the SP.
Baird. 0.005
Hangeland. 0.005
Riise. 0.005
Duff. 0.006 He was substituted while Fulham were still trailing,so didn't reap the
completed comeback rewards.
Sidwell. 0.015
Murphy. 0.271 A late equaliser is always going to be a big SP mover.
Dempsey. 0.030 Assist for Zamora goal.
Zamora. 0.145 His goal could have just been a consolation.Assist for Murphy's leveller.
Dembele. 0.016
Kasami. 0.010 Limited game time,but gained from coming on before the equaliser.
Ruiz. 0.007
Total. 0.5


Player. Win Contribution. Comments.
Hart. -0.021
Richards. 0.015
Kompany. 0.015
Lescott. 0.015
Clichy. 0.015
Silva. 0.097 Supplied an assist and had left the field before the equaliser.
Barry. 0.021
Toure. 0.021
Aguero. 0.259 Two goals.
Dzeko. 0.063
Nasri. 0.056 He wasn't on the pitch at the very end when City's SP was slipping away quickly and,as a forward he wasn't heavily penalised for Fulham's goals.
Zabaleta. -0.039 Appeared when City still led,but couldn't help them protect the lead.
Tevez. -0.007 Appeared with the game stalemated,but couldn't grab a winner.
Johnson. -0.008
Total. 0.5

This initial system rewards or penalises players for being involved in events that are integral to the score and the final result.Consequently,players who aren't involved in game changing incidents tend to score similar shares.As in American Football,it' quite easy to assign a number to depict how influential a quarterback has been to the game,but much more difficult when dealing with a lineman.An improvement to players being scored as a unit would be to re distribute the unit's total by using stats such as tackles made or passes completed.The problem here is that these kind of stats,even if they correlate well with talent,aren't readily available in an easy to use format.So at the moment it's a work in progress and the more obvious contributors to the fore.

Monday 19 September 2011

Expected Points Graphs for EPL Games,September 17th & 18th 2011.

The win probability for each team is tracked on a minute by minute basis throughout each EPL game.At any point in a game a team will have a probability of winning the game outright and an associated probability of drawing the game.By multiplying the probability of winning the game by 3 and the probability of drawing by 1 and adding the results together you will get an expected longterm average for the number of points that team will achieve from that position or Expected Points (EP) for short.

Blackburn 4-3 Arsenal.

The best game of the weekend from a neutral perspective.Arsenal owned the first half and Blackburn's manager,Steve Keane couldn't have been looking forward to his promised showdown with disgruntled fans.The Gunners then self destructed,this time on the defensive,rather than disciplinary front,but a they were a Paul Robinson injury time block away from a second 4-4 all draw within a year.Blackburn managed a goals to shots ratio of more than one after Arsenal's own goals.You get a 4-4 about once every 1,200 games.4-3's are more common,about 1 every 300 generally,but 1 in 500 when the much weaker team comes out the winner.


Aston Villa 1-1 Newcastle.

Villa spent an hour hopeful of a three point haul,but not certain of it.Only home advantage made the Midlands team favoured,pre game and the decrease in EP upon Newcastle's equaliser emphasised how costly drawing from a winning position can be.



Bolton 1-2 Norwich.  

Norwich gained the kind of reward some of their play this season has deserved.They replaced Bolton as EP favourites after the first strike and were greatly helped by the Klasnic red card.They remained much the most likely winners,even when Bolton halved their lead.Bolton still haven't recovered from their semi final mauling last April.

Red Card Klasnic (Bolton),45'

Everton 3-1 Wigan.

Wigan's opening goal was quickly cancelled out and both team's EP were trending towards 1 until Everton's two late strikes.

0-1,Di Santo,31'

Swansea 3-0 WBA.

A fairly unremarkable game statistically as the marginal favourites scored a couple of early goals to nudge the EP within touching distance of three and then comfortably ran the clock down.In reality a massive result at the Liberty against potential fellow relegation candidates.


Wolves 0-3 QPR.

Another comfortable victory curve for the moneyed newcomers as Wolves' start becomes a distant memory and QPR's cash appears to have been well spent.


Tottenham 4-0 Liverpool.

Spurs' early goal split the two equally matched teams,but after that all the damage was self inflicted by Liverpool.Two red cards are fairly rare and by the time of the second one there was very little chance that Liverpool would be able to score and it was overwhelmingly likely that Tottenham would add to the Modric strike.Game over after an hour,even at just 1-0.

Red Card,Adam(Livepool),28'
Red Card,Skrtel(Liverpool),63'

Sunderland 4-0 Stoke.

Another cakewalk for the side scoring first.A game of little interest after the two early goals unless you were a Sunderland fan.


Fulham 2-2 Man City.

Comeback performance runner up of the week award goes to Fulham,who were very impressive in recovering from a two goal deficit against markedly superior opponents.The Cottagers' EP had hit the floor after almost an hour and that's where it was heading again until Murphy's late leveller.


Man Utd 3-1 Chelsea.

A seemingly comfortable Man U win concealing a hand full of "what ifs".To take the most obvious one,if Torres had scored instead of missing an 83rd minute open goal,the score would have been 3-2 to United.About 12 minutes remained and Chelsea's EP would have increased over tenfold from 0.01 Expected Points to 0.13 EP.However, Man Utd would still score around 60% of any subsequent goals,it was odds on that there wouldn't be any anyway and the home side's EP would still have been 2.75.In a nutshell,if Torres had scored,Man Utd would still go on to win 9 times out of 10.Of course Sir Alex would argue that Chelsea should have been down to 10 men by then anyway.


Saturday 17 September 2011

Derby County's 11 Point Plan.

When Billy Davies took over at Derby midway through the 2006-2007 season,he came armed with a three year plan to make the team credible contenders for promotion to the EPL.Unfortunately for both himself and Derby he secured Premiership membership a bare 6 months down the line.

Promotion through the playoffs is never ideal for teams.Firstly,they are about a fortnight behind the automaticly promoted teams in terms of squad strengthening.The semi knockout nature of the playoffs also means that the strongest team from season long campaign is far from guaranteed to progress.60% of previous playoff winners had failed to breach the 40 point barrier usually considered the benchmark for EPL survival.

Derby at least ensured that the Championship's third best side followed Sunderland and Birmingham into the top flight,but their squad strengthening was restriced to two forwards,Rob Earnshaw during the close season and Kenny Miller a month into their EPL career and a defender,Claud Davis.The combined cost,just over £9 million.

The Rams,fielding 8 players from the playoff win over WBA led 1-0 five minutes into their opening EPL match against Portsmouth.Pompey had finished top ten the previous year and as such presented a good benchmark for where the East Midlands team stood.The fans could be forgiven for thinking that "things don't get much better than this". Unfortunately,things were going to quickly get worse......alot worse.

That first game ended 2-2,was followed by a narrow defeat at Manchester City and a much more comprehensive one at Spurs.By the time Liverpool's six goals inflicted their 4th defeat in five games,Paddy Power's marketing department had smelt blood and promptly paid out on Derby's relegation.

A solitary win came 16 days later,by a single goal over Newcastle.The game was played on a Monday,meaning that Derby went the entire season without winning on a Saturday.Davies was sacked in mid November,followed rapidly by the departure of a fair proportion of the board.His replacement was Paul Jewel,battle hardened at Wigan,but incapable of pulling Derby out of a death spiral that became steadily steeper as 2007 progressed into 2008.

Every undesirable record was etched into the Rams' record books.Least EPL points,11;least wins,1;least goals scored,20;most defeats,29,worst goal difference,-69;first team to be officially relegated before April and they only escaped conceeding the most goals because Ipswich's 94/95 side played a 42 game season.

To help understand why Derby failed so abysmally to cope with their brief Premership existence I've charted their Expected Points tally for a point during each of their EPL games that season.I've chosen the scoring of the first goal as the reference points and calculated the expected number of points Derby on average should have gained from that position.As a reminder,Expected Points for any game situation are derived from the win and draw probability associated with each team at that particular moment in the game.

Expected Points where Derby Opened the Scoring in 2007/2008.

Home Team. Away Team. Time of Goal. Derby's EP
after Goal.
Actual Points.
Portsmouth. DERBY. 4 1.318 0
DERBY. Portsmouth. 5 2.062 1
Newcastle. DERBY. 6 1.069 1
DERBY. Fulham. 10 2.017 1
DERBY. Bolton. 19 2.166 1
Blackburn. DERBY. 19 0.984 0
DERBY. Blackburn. 27 1.911 0
DERBY. Newcastle. 39 1.945 3
DERBY. Man City. 47 1.910 1
15.382 8

Derby opened the scoring in just 9 of their 38 league games that season.An average team,scoring first will avoid defeat in around 80% of those games,Derby did so just 66% of the time.Only once did the actual points they gained from the match exceed the EP the opening goal had taken them to.Evaluating Derby from their Championship results and increasingly their EPL results as the season progressed,they should have been able to gain about 15 points when leading in those 9 games,instead they got only 8.Not a season defining difference,but an indication of how Derby just kept on deteriorating with time.They rarely scored first and they almost never used the advantage that scoring first imparts to a team to kick on.Only Newcastle failed to retrieve at least a point when they fell behind to an opening goal scored by Derby.

Expected Points When Derby Conceded the Opening Goal. 2007/08.

Home Team. Away Team. Time of Goal. Derby's EP
after Goal.
Actual Points.
DERBY. Birmingham. 1 0.787 0
Tottenham. DERBY. 2 0.208 0
Arsenal. DERBY. 10 0.051 0
DERBY. Liverpool. 12 0.078 0
DERBY. Reading. 15 0.298 0
DERBY. Chelsea. 17 0.048 0
WestHam. DERBY. 20 0.174 0
DERBY. AstonVilla. 25 0.231 0
DERBY. Arsenal. 25 0.055 0
DERBY. Everton. 26 0.441 0
Liverpool. DERBY. 27 0.061 0
Chelsea. DERBY. 28 0.062 0
Middlesbro'. DERBY. 32 0.135 0
DERBY. Middlesbro'. 38 0.457 0
Man Utd. DERBY. 40 0.048 0
DERBY. WestHam. 42 0.415 0
Man City. DERBY. 43 0.243 0
Everton. DERBY. 56 0.119 0
AstonVilla. DERBY. 57 0.157 0
Wigan. DERBY. 60 0.176 0
Reading. DERBY. 63 0.221 0
Birmingham. DERBY. 68 0.182 1
DERBY. Tottenham. 68 0.167 0
DERBY. Man Utd. 76 0.073 0
DERBY. Wigan. 82 0.074 0
Sunderland. DERBY. 90 0.070 0
Bolton. DERBY. 90 0.060 0
Total Points. 5.091 1

If Derby's record when scoring first was below par,their record when conceding was dreadful.They fell behind on 27 occasions,allowing opening goals ranging from the first to the last minute,but they managed to peg back just one team,namely Birmingham.Yet again their decline was so precipitous that historical results couldn't factor their true awfulness with any degree of accuracy.They should,on average have claimed a feeble 5 points once they fell behind from a possible 81.They got only 1.

Derby's horror year saw them produce a goal difference of -69 or -1.8 per game.A Championship team usually sees it's goal difference decline by around a goal a game when making the jump in class to the Premiership.So Derby's goal difference from their previous Championship season of +0.35 should have only declined to -0.65 indicating a likely points haul of about 40 points.They should have been likely relegation candidates,but they shouldn't have slumped as badly as they did.

Their only win also gives a hint at where they failed to give themselves the best possible chance to survive or at least avoid humiliation.Any Derby victory in 2007/08 would have been considered an upset and if you're going to see an upset it's most likely to occur in a low scoring game.Over the last 5 EPL seasons in games where only one goal was scored,the average Expected Points for the winning team at kickoff was 1.6.By contrast the average starting EP for winning teams where 5 or more goals were scored was 1.9.In short,poorer teams are more likely to win low scoring games than they are higher scoring ones.If Derby wanted to give themselves the best possible chance in the EPL they should have spent more of their limited funds on defenders and less on strikers.

To summarise,the Rams made poor use of their admittedly limited finances before making their squad strengthening purchases.They should have bought defenders instead of forwards,both for immediate results and for better resale value.But ultimately their poor Expected Points record after a game's opening goal and their large average goal difference per game disparity compared to the previous season,indicates that they were one of the few professional teams to throw in the towel,both during games and over the season as a whole.