As always, we are taking our summer break. We'll be back on Monday 25th of July.

Don't forget our workshop is on Friday 22nd of July in University College Cork. Details on how to register can be found here.

Until then, have a great summer and enjoy Euro 2016! 

By Robbie Butler

Having played competitive sport since I was seven years old, I sometimes reflect on nearly three decades of participation and the thousands of hours spent playing. I'm lucky enough to have accumulated some medals over the years which now mostly gather dust on a mantelpiece at home. Very occasionally, I might turn one over to see what year the medal was won. More often than not, they are anonymous.

Far more frequently, I reminisce about finals won (and lost) and think about how I felt at the time. I'm not sure if others feel this way, but the defeats tend to stick out  (and hurt) more than the elation of success.  That said, the winning feel still remains and can be recalled quite easily. The medals at home don't come close to this. It's not that they don't matter, but the feeling I had when successful is just much more satisfying. Economists attempt to capture this using the concept of utility. Put simply, the utility I got from the winning feeling is far great than the medal.  

Why does this matter? Well, primarily because while medals can be striped, the feeling (or memory) of elation when winning can't be.

Last week's Christy Ring Cup final at Croke Park provides a nice example. For this unfamiliar with the competition, the Christy Ring Cup is the senior championship in hurling for teams that fail to qualify for the All-Ireland Senior Hurling Championship. It is effectively a 'B' Championship.

Last Saturday Antrim (AON) and Meath (MHÍ) took to the field in the final.The game progressed as normal until the 60th minute (matches last a total of 70 minutes). Just after 61 minutes of play the free-to-air broadcaster screening the game, TG4, reported the correct score of AON 1-18  1-14 MHÍ (a difference of four points).

Following another score by Antrim the scoreboard in the stadium incorrectly awarded the point to Meath, and read AON 1-18  1-15 MHÍ (difference of three points), instead of reading AON 1-19  1-14 MHÍ (difference of five points).

With minutes remaining, TG4 continued to report the correct score, now AON 1-20  1-15 MHÍ, while the stadium scoreboard read AON 1-19  1-16 MHÍ. However, the TV channel then decided to change their CORRECT score to match the INCORRECT stadium scoreboard. 

To make matters even more confusing, just before the 69th minute TG4 changed their score again, moving AON back to a correct score of 1-20, but failed to remove the point from MHÍ, whose score continued to read 1-16 instead of 1-15. In the remaining minutes of play MHÍ scored a goal and two points, moving their score on display to 2-18, with AON still on 1-20.

At full-time the scoreboard read An MHI 2-18 AON 1-20 (a one point win for MHI) when in fact it should have read An MHI 2-17 AON 1-20 (a draw).

As one might expect, jubilant celebrations ensued amongst the Meath players, coaches and supporters, followed minutes later by the lifting of the Christy Ring Cup. This feeling can't be taken away now. Since Saturday, the GAA's Central Competitions Control Committee (CCCC) has accepted there was an error in scoring and has ordered a replay. Meath, to their credit, have agreed to this.

By David Butler

​The Cork City Marathon took place today. The male winner was Philip Harty with a time of 02.32.58. The female winner was Nollaigh O’Neill with a time of 3.00.40.

As always, Seamus Coffey (UCC) organised our relay team entry.  ‘Random Walk’ finished 93rd out of 689 relay teams (inclusive of youth and mixed gender teams) with a time of 3.40.40 – we were relatively surprised by this! The winning relay time was 2.24.00. Our relay team included contributors to this website; Robbie Butler, John Eakins, Sean O’Connor and Myself (All UCC). Brendan McElroy (UCC) was the fifth member of our team.

From what I’m told this is the best time Random Walk has recorded over the years. The distribution of finishing times for the 2016 relay race is below. 

By John Eakins

Four years ago, myself and Robbie Butler wrote an article on Ireland’s chances of qualifying from our group in Euro 2012 (see here). We calculated all the possible final points outcomes of a four team group and then identified the points total which would guarantee or close to guarantee qualification i.e. 1st or 2nd place in the group. We reckoned that a win (3 points) was the minimum requirement and 4 points (a win and a draw) would put us in a reasonable position to qualify. 5 points would almost certainly seal the deal. Unfortunately it didn’t quite work out as we had hoped as Ireland lost all 3 games to finish bottom of the group. 

Four years on and we have qualified once again for the Euros so it is opportune to revisit our previous work. What makes the analysis particularly interesting this time, is the fact that the competition has expanded to 24 teams, 6 groups of 4, and that four best placed 3rd place finishers also qualify for the knockout round of 16. So this should give us a better chance of getting out of our group relative to Euro 2012. But what does our statistical analysis reveal?

In total, there are 729 possible combinations of wins, draws and losses in a four team group (we do not adjust for quality difference between the 4 teams). If we take just one team in the group of 4 and tabulate the distribution of points arising out of these 729 combinations for this team (assuming 3 points for a win, 1 for a draw and 0 for a loss) we get the following:

For example, a team in a group of 4 can end up with 9 points based on 27 different combinations of wins, draws and losses in the group games, 7 points based on 81 combinations, etc. The distribution is slightly asymmetric because of the higher points weighting given to wins. 

Next we tabulate the position of a team with a certain points total (table 2). As previously stated a team can end up with 9 points from 27 different combinations of wins, draws and losses. But in all of these cases they will be in 1st position in the group. In short, having 9 points always wins the group. Similarly a team who attains 7 points will end up in 1st position in the group 72 out of a possible 81 times and tied 1st 9 out of 81 times.

Let’s work through the other possible points outcomes. If a team gets 6 points there is only a 3.7% (3/81) chance they will not be in the top 2 positions in the group. This occurs when three teams end up with 6 points each and one of the teams ends up in 3rd place because of goal difference/goals scored (so the 3.7% is in itself a conditional probability). But a team is guaranteed a top 3 place with 6 points. Interestingly the same outcomes apply for a team that gets 5 points in a group.

The possibilities become much greater when we get to 4 points. A team on 4 points can win a group (on goal difference/goals scored) by either being tied 1st with two other teams (3.7% or 6/162) or tied 1st with all other teams (3.7% or 6/162). They can be 2nd (27.8% or 45/162) or tied 2nd with one other team (46.9% or 76/162) or 3rd (17.9% or 29/162). So if a team gets 4 points the only possibility that they will be outside the top 3 is if they are tied 1st with all other teams and lose out on goal difference/goals scored (3.7% chance of this happening and that again is a conditional probability). If we apply the same logic to a team that gets 3 points this probability increases to 37% (again this is in part a conditional probability and includes a 22.2% or 24/108 chance of either tied 1st with all other teams or tied 3rd place with one other team and losing out on goal difference/goals scored and a 14.8% or 16/108 chance of finishing in 4th place). For a team that gets 2 points the probability of being outside the top 3 places increases further to 67.9%. A team on 1 or 0 points is almost guaranteed to be in last place in the group.
 
So anything from 4 points up is likely to get us in the top two places in the group and would also almost definitely have us in the top three. Having 3 points would give us a two-third to one-third chance of being in the top 3 while those odds reverse if we were to have 2 points. In short, 4 points or more would be ideal, 3 points might get us there as well while 2 points may not be enough. Anything lower and we are most likely to be out.

There is one final consideration in this analysis and that is the performance of the 3rd place finishers in other groups. It would be next to impossible to extend the analysis done so far to other groups so instead one can look at history for insight. The World Cups of 1986, 1990 and 1994 all used the same qualifying format as what will be used by Euro 2016. Unfortunately, World Cup 1986 and World Cup 1990 are not directly comparable as they used the old points system of 2 points for a win, 1 for a draw and 0 for a loss. Thus only the World Cup 1994 can be used. The table below displays the ranking of the 3rd place teams in that competition. As can be seen, both Argentina and Belgium came third in their group despite earning 6 points. Both teams lost out on goal difference/goals scored in a 6-6-6-0 points group. Italy also lost out on goal difference/goals scored in a group that finished 4-4-4-4 (a group that also featured Ireland). Russia, despite ending up with 3 points in their group, did not qualify.