Spectators can readily accept that a player can be the recipient of good or bad luck in a single event during a match.The poorly hit shot that bobbles inexplicably beyond the grasp of an already committed keeper or the sweetly hit penalty that crashes against the bar and spins to safety.But there quickly comes a point when skill is thought to overwhelm chance and the best prevail.But when is that point reached.Over the course of a half,over the whole game,a series of games or half a season?
Over the last half dozen posts I've tried to illustrate how many games are required before the team or player observed stats start to be come representative of future performance indicating that repeatable talent is progressively overwhelming random luck.In this post I'm going to try to utilize some of my own models to try to break down all the Group A games from Euro 2012 and demonstrate how the rate of conversion of intermediate stats such as shots gradually trend towards their expected values as sample size increases.
The prediction of goalscoring rates from shooting stats is benefiting greatly from the increased availability of new data.Shot position is by now an obligatory addition to the inputs required to give an expectation value for any attempt.I now have a four figure database that records the fate of shots made in the Premier League primarily over the 2010/11 season and from this data I've produced regression equations that detail how likely a shot is to result in a score,be hit on target or be blocked by a defender provided we know the position on the pitch from where the effort originated.
The model is far from perfect,but the correlations are robust and results obtained from the subsequent regressions should quantify the likely longterm outcome of a given set of shots.Variation between the model's forecasts and what actually happens to a team's small sample sized batch of shots is one possible way of demonstrating the effect that chance plays over single games.A robust model demonstrates what is most likely to occur and sometimes randomness decides what does happen.
I've used Group A from the recently departed Euros as an example.The Euro 2012 Ipad app is a marvelous resource for anyone with the patience to collect any number of in game statistics and I've gathered up the coordinates of (hopefully) every shot attempted by each of the four teams,Poland,Czech Republic,Russia and Greece in the group stages.The expectancy that each shot would be blocked,on target or find the net was then calculated and the cumulative probabilities of each of those three outcomes were compared to the actual outcomes over varying gamespans for both teams and individuals.
How Russia's Intermediate Team and Player Statistics Translated into Results at Euro 2012.
| Russia's 27 Shots vs Greece. | Actual Number of Outcomes. | Expected Number of Outcomes. |
| Shot on Target. | 2 | 9.5 |
| Shot Blocked. | 8 | 5.8 |
| Goal Scored. | 0 | 2.5 |
| Greece's 8 Shots vs Russia. | Actual Number of Outcomes. | Expected Number of Outcomes. |
| Shot on Target. | 2 | 2.7 |
| Shot Blocked. | 2 | 1.8 |
| Goal Scored. | 1 | 0.7 |
| Dzagoev's 11 Group Game Shots. | Actual Number of Outcomes. | Expected Number of Outcomes. |
| Shot on Target. | 4 | 4.2 |
| Shot Blocked. | 3 | 2.3 |
| Goal Scored. | 3 | 1.2 |
| Kerzhakov's 13 Group Game Shots. | Actual Number of Outcomes. | Expected Number of Outcomes. |
| Shot on Target. | 0 | 3.9 |
| Shot Blocked. | 3 | 3.8 |
| Goal Scored. | 0 | 0.93 |
Above I've compared the shot conversion rates achieved by both Greece and Russia in the Group A game and by Kerzhakov and Dzagoev individually over Russia's three game involvement in the tournament.So we are looking at relatively small sample sizes.The shot conversion rates over the course of a single game are often driven by the scoreline,especially in the case of final group games,but this is factored into the comparison because the exact shot position is used to calculate the goal,accuracy and blocking expectancies.
Even in this limited experiment the variation between what would probably happen over larger numbers of trials and what can sometimes happen in much shorter bursts can be seen.Russia,over one game hit the target just twice with their many efforts compared to an expectation of nearly five times that number.They could have expected to score between two and three goals,but came up empty.Greece,by contrast and with less than a third of Russia's shot total managed to perform fairly close to expectations,winning the game in the process with a Karagounis goal that was more likely to be blocked than scored.
The same wide spread between expectation and reality is seen in the individual efforts of to Russian forwards.Dzagoev hit an expected 4 shots on target from his 11 efforts,but got lucky and out performed his expected goal tally by a factor of nearly three in this limited run.Thus ensuring that he'll be an over priced addition to the EPL in 2012/13.Team mate Kerzhakov,enjoyed no such luck,failed to hit the target once and was derided as "historically wasteful" in the press.Fortunately his manager Dick Advocaat seems to appreciate that a player's last 20 games are more relevant that his last 90 minutes and backed his striker and acknowledged the role of luck in his "historical wastefulness".
How Group A's Intermediate Defensive Stats Began To Trend Towards their expected Values.
| Czech Republic's 36 Defended Shots. | Actual Number of Outcomes. | Expected Number of Outcomes. |
| Shot on Target. | 10 | 12.9 |
| Shot Blocked. | 8 | 8.0 |
| Goal Allowed. | 5 | 3.4 |
| Greece's 51 Defended Shots. | Actual Number of Outcomes. | Expected Number of Outcomes. |
| Shot on Target. | 8 | 16.8 |
| Shot Blocked. | 11 | 12.5 |
| Goal Allowed. | 3 | 3.9 |
| Poland's 30 Defended Shots. | Actual Number of Outcomes. | Expected Number of Outcomes. |
| Shot on Target. | 9 | 11.5 |
| Shot Blocked. | 7 | 6.4 |
| Goal Allowed. | 3 | 4.0 |
| Russia's 36 Defended Shots. | Actual Number of Outcomes. | Expected Number of Outcomes. |
| Shot on Target. | 12 | 12.8 |
| Shot Blocked. | 5 | 7.9 |
| Goal Allowed. | 3 | 3.6 |
How Group A's Intermediate Attacking Stats Began To Trend Towards their expected Values.
Czech Republic's 33 Shot Attempts. | Actual Number of Outcomes. | Expected Number of Outcomes. |
Shot on Target. | 13 | 12.1 |
Shot Blocked. | 3 | 7.2 |
Goal Scored. | 4 | 3.3 |
Greece's 20 Shot Attempts. | Actual Number of Outcomes. | Expected Number of Outcomes. |
Shot on Target. | 5 | 7.3 |
Shot Blocked. | 5 | 5.3 |
Goal Scored. | 3 | 1.8 |
Poland's 44 Shot Attempts. | Actual Number of Outcomes. | Expected Number of Outcomes. |
Shot on Target. | 14 | 7.6 |
Shot Blocked. | 9 | 5.1 |
Goal Scored. | 2 | 2.0 |
Russia's 54 Shot Attempts. | Actual Number of Outcomes. | Expected Number of Outcomes. |
Shot on Target. | 9 | 18.4 |
Shot Blocked. | 14 | 11.7 |
Goal Scored. | 5 | 6.0 |
If we now take a look at every shot attempt made or faced by every Group A side,resulting in an average sample size that is twice that of the Russian strikers and the Greece Russia match,the actual outcomes start to gravitate towards the expected rates.Goals,both scored and allowed particularly in this larger sample set approach their expected levels.
In all Group play,Russia actually scored 5 goals where the cumulative probability over their 54 attempts suggest they should have managed 6.Armed with the knowledge that they were unlucky to remain scoreless against Greece,this also highlights another aspect of randomness in sport.Over extended trials a team's actual rate statistic tends to approach their expected average,but this may happen in uneven lumps.In Russia's case a random bunch of bad luck may have coincidentally followed a random piece of good fortune,resulting in a large win and a narrow defeat instead of the preferred two routine wins.It's certainly not a given that good luck is immediately followed by bad,but it does happen.
Luck plays a massive,but largely unacknowledged role in deciding sporting contests and the rate at which teams convert their chances,coupled also with the fluctuating rate at which these chances arrive is just one aspect of this reality.It's part of the reason why Blackburn can win at Old Trafford,but over a season Rovers will finish well adrift of their hosts and why assessing a team or player over a limited timescale often leads to extreme and inaccurate evaluations....and an overpriced post tournament signing.
