Relationship between team age and team strength

I originally thought that I would need individual team age data to get at the question of 'how much strength is a year' equal to.  However a fellow statistician suggested that this could be estimated by looking at how well teams did playing at age versus playing up a year.  Computing the age-effect this would require however cross-age match data and multiple ages.  With help from a fellow poster on washingtonpremiersoccer.com, I compiled match data for the U12, U13, U14 and U15 boys teams in WA and OR.  This analysis required that I had almost all select teams at each age group so that I could assume that 'median' team meant the same thing in each age group (i.e. that I wasn't biasing my samples up or down in any age group).

This new database allowed a joint analysis of team strength using all U12-U16 select soccer team matches in WA and OR for the 2012-2013 season (up to March 3rd, 2013).  Cross-play between age groups in tournaments and leagues (when teams play up) allowed all age groups to be analyzed together.  The following graph shows a boxplot of team strength against age.  The y-axis has been scaled to the median team in this analysis, but the meaning of relative differences remains the same as in my region-specific strength ratings:

	0.0	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4.0
win	34	49	63	76	86	94	98	99	100
tie	31	29	24	17	11	5	2	1	0
lose	35	22	13	7	3	1	0	0	0

A difference of 2 in strength is quite large and the weaker team would rarely win.  A difference of 1 still means a substantial advantage for the stronger team.  The x-axis in the graph is the date of the first age in the age group.  These are US teams and the age brackets start on August 1st.

The graph indicates a striking consistency in the impact of age on team strength.  From age U12 to U16, each year adds 2 strength points to the median team strength.   Thus teams are unable to beat themselves a year later and unlikely to beat themselves 6 months later (if they could enter a time machine and play themselves at an older age).

This suggests that the capacity to increase team strength by selecting older players is substantial, however the spread of team strengths within age is ca 10 (highest team minus lowest team).  Thus age bias on teams is (obviously!) not the only factor affecting team strength.  This also suggests that computing a "age-correction factor" for team strength should be simple.

age adjusted team strength = 
    unadj. team strength - (6.5-mean(birth months of players))/6

where birth month is coded as Aug=1, Sep=2, Oct=3, etc.  6.5 is the mean birth month so this scales the team to "expected strength if team were median age".

Why is an age-correction factor important?  Well if you are trying to understand the strength of a team and how factors other than age affect team strength, then you need to adjust for the team age.  If you want your team to play up in a tournament, then you need an idea of what its strength will be at the higher age so you can choose an appropriate level.  Also if a coach/club happens to have a team made up of summer boys, they might well want to have a sense of the "adjusted" strength of the team if the team were not essentially "playing up".  Or a club might want to compare the strengths of their A and B teams, but for a fair comparison you need to adjust for the age difference between the teams.

What is driving this relationship?  Presumably it is the pattern of physical growth in boys.   The growth curve is pretty linear from U12 (age 10-11) to U16 (age 14-15).  I'll be able to get a better sense of this relationship once I get more U17 and U18 teams and see how the strength levels off.

What next?  An interesting aspect of the age-skew, is that on an age-skewed team, the innate talent is not at its maximum because less talented older players would be chosen over more innately talented, but smaller, young players.  Nonetheless, the strength of the team is higher with the age-skew because age adds greatly to team strength.  As the team ages (U17 and up), one would expect that the age-skew would be reduced as 12-months doesn't confer quite as much advantage.   A question that interests me is how much this age-skew persists in U20+ teams and whether there are other effects of the age-bias, such as positional bias.   The only July boys on an elite (non-academy) team or Dec boys on an academy team would have to be unusually talented (on average).  Are those talents directed to particular positions?  Presumably July (or Dec) goalkeepers would be rare for example.  Another question that interests me is whether Dec professional soccer players have higher valuations than Jan professional players.  Why would that be the case?  In a system with a January cut-off, more Jan born players of lesser innate talent are developed.  The only Dec born players that make it through the system would have to have (on average) higher innate talent.  If innate talent is correlated with valuation, one would expect Dec players to have higher valuations (on average).

Effect of age cut-offs on birth months of Div I college players

Following up on the birth month variations that are seen in the US Soccer Development Academy (USSDA) teams, I was curious to see if we see evidence of these age cut-off (Aug 1 club, Dec 31 ODP, Aug 31 HS) when we look at the distribution of birth months of players on Division 1 college soccer teams.  Participation on USSDA teams and top select (non-USSDA) teams might be expected to increase a high school player's chances of making a Div I college team, thus the deficit of quarter 4 births in the USSDA teams and May-June births on top select teams might carry over to college roster.

I took all Div 1 teams that made it to post season play (http://www.ncaa.com/interactive-bracket/soccer-men/d1) and took birth months off their rosters.  I was able to get data on 562 players.  I excluded players who did not go to high school in the United States or Canada.  In retrospect, maybe I should have left off the Canadians, but there weren't all that many of them anyhow.  Then I went to the CDC and got the number of births by month for 1990-1994 to come up with expected numbers of players with each birth month.

The blue line shows the actual number of college players with the specified birth month and the red line shows the expected number given the births by month in 1990-1994.

Here are the differences (actual minus expected):

There is a deficit of 16.36 players with birth months in December. Interestingly there is a surplus of almost the exact number of players 16.34 with birth months in January.  Note this is based on a random sample of 562 players from the top Div I teams. If the pattern holds though-out the Div I rosters, then the total deficit of Dec players will be in the hundreds.

We also see that May-June birth months show a deficit while fall birth months have a surplus.  These patterns correspond to what we would expect given the age cut-off affecting US elite soccer players: Dec. 31 for the US Development teams and Aug 1 for select club teams.   Cut-offs for high school will also be important since many players are identified via performance on their high school teams.  School cut-offs vary regionally however.  The difference between percent summer and fall birth month may simply reflect a fall birth month advantage for D1 university students in general and have nothing to do with soccer age cut-offs.  It is well-known that the academic performance of kids born in summer is lower (on average) than that of those born in fall.  The effect is strongest in elementary school but can be seen all the way through high school.  See for example this literature review.

The 95% confidence intervals are about +13 and -13 for this so January and December fall outside of that while the summer months do not.  This suggests that I need to up the sample size a bit. 

I was able to find birth months data for 27 of the Div I teams that made it to post-season play.  When some birth dates were present for some players and others weren't, I collected data for the players I could.  I only took birth dates from the school roster webpages.  If a birth date was missing, but the players was on a US Dev team, I did not look up their birth date from the US Dev website since I assumed that would skew the data to January.  I only included players who went to high school in the US or Canada.
http://www.ncaa.com/interactive-bracket/soccer-men/d1
I got data for
Kentucky, Elon, Louisville, Marquette, UMBC, Boston College, Xavier, Winthrop, Mich State, UAB, U San Diego, UCLA, VCU, Cleaveland State, UConn, Creighton, Dickinson, Old Dominion, Syracuse, UNC, U Maryland, Indiana Univ, Wake Forest, Northeastern, Tulsa, Akron, UNM

The following schools did not have birth months on their websites:
Univ S Florida, Charlotte, St. Johns, Notre Dame, Air Force, UW, Drexel, Georgetown, Niagara, SMU, Cornell, Northwestern, Michigan, Lafayette

Birth Months of Players on the 2012 Olympic Soccer Teams

I looked at the birth month of the 290 players on the rosters of the Men's U23 teams that played in the 2012 London Olympics. This shows that deficit of quarter 4 birth months again.

The actual numbers show the deficit a bit clearer.  There are almost half as many Q4 birth months as Q1 birth months.

Q1 Q2 Q3 Q4
84 79 82 45

Now let's look at birth month for all the players 1989 to 1993 lined up sequentially.  We can compare the number of Q4 (red bars) to Q1 (blue bars) players who are almost the same age.  So we can compare Q4 1989 to Q1 1990, and see if Q1 players, who are slightly younger but born in Q1, are more numerous than the similarly aged Q4 players.

First we see that older players are more common and the frequency drops off steadily by year.  But look at the red and blue bars.  In all of the 4 years, the red bars are lower than the adjacent blue bars---despite the red bar players being a little older than the adjacent blue bar players. 

Note, there is some fluctuation in birth month frequencies.  In the US over the last 10 years, ca. 24% of all births have been in Q1, 25% Q2, 26% Q3, and 25% Q1.  I don't know the frequencies in the 16 countries involved here, but the US data would not make me think that Q1 births are more common than Q4.  Certainly the magnitude of differences seen in the Olympic rosters is much larger than what is seen in natural birth quarter differences.

Next post looks at the deficit of December birth months on Division 1 NCAA (US) male soccer teams. That is a follow up on an examination of Q4 birth month deficits on the US Soccer Development Academy (USSDA) teams.

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Related work:
 Williams (2009) Relative age effect in youth soccer: analysis of the FIFA U17 World Cup competition
http://onlinelibrary.wiley.com/doi/10.1111/j.1600-0838.2009.00961.x/full 

More on the Relative Age Effect in the US Development program

"For everyone who has will be given more, and he will have an abundance. Whoever does not have, even what he has will be taken from him." Matthew 25:29

In my last post I looked at the birth months for a few of the Academy teams.  This shows that the age-cut is skewing the birth month distribution.  The Matthew Effect says that those players with an advantage, in this case being older for their age group, will advance faster in their skills due to the extra play time and coaching because they would be more likely to be the 'stars' being the eldest on the team.  What's interesting is that US players will mainly have been affected by a different cut-off during their U11-U14 years before they try-out for an academy team at U15/16.  Most US players would have been playing under a system with a August 1 cut-off for their U11-U14/15 years.   If the Matthew Effect is operating, we would expect to see an overabundance of August relative to July birth months on the Academy teams.  August boys were the eldest in their age group while July boys were the youngest---however they are basically the same age.  Now, keep in mind that July boys might have started formal soccer a year earlier (being born in July), so perhaps this extra year (at age 8-10) would offset the disadvantage of being the youngest.

For this analysis, I used all players on the US Development Academy teams whose citizenship was listed as USA.  No players who listed another country or dual citizenship were included.  The following shows the birth month for the U15/16 players born in 1996 (U16).  I left out the 1997's since my previous post suggested that their birth months is strongly skewed to the first quarter.  I also looked at the U17/18 players, broken out for birth year 1997 (U17) or 1998 (U18).

The following plot shows the result.  Y-axis is the frequency of the birth month.  The thin line is the median expected frequency.  It's wavy because the months don't have the same number of days.  The dashed lines are the 95% percentiles.  We see that there is an overabundance of quarter 1 boys, but look at the difference between July and August boys.  They are basically the same age, but July boys are much less frequent than you would expect and August boys are more frequent.   The strange birth month frequency for the U18's (birth year 1994) presumably shows the effect of college.  The boys born in 1994 in Jan-July would be in college while the 1994 Aug-Dec boys are high school seniors.

It matters when you are born: the Matthew Effect

One of the questions I'll be looking at with the strength ratings data for multiple ages is the effect of age on strength of a team. Basically, 'what is a year worth?' and how much can a team potentially gain by being stacked towards kids who are older within the age group.  Note, it is not that coaches are looking at birth month when selecting players.  They are selecting the best players. Age and skill/physical prowess/speed etc. are highly correlated in kids, so the best players will tend to be the oldest in the age-bracket.

This is related to a well-known effect called the Matthew Effect, which you'll be familiar with if you have read the book Outliers. Basically, the existence of age-cutoffs means that kids born towards the beginning of a cutoff have an advantage and are preferentially selected for elite junior teams. These early advantages then translate to an over-abundance of players with birth months near the cutoffs on the most elite teams. So in our Aug 1 cut-off system, kids born in fall are at an advantage and summer kids are at a disadvantage. If the cut-off is Jan 1, then 1st quarter kids have an advantage. Here is a nice blog on the Matthew Effect: The Matthew Effect: Talent ID and sports science application.

Do we see this in soccer? Definitely. The US National Development program is on a Jan 1 cut-off. Here's some pie plots of the birth quarters of the players on the Sounders Academy U16, Crossfire U15/16, and US National U-15 men's teams. For Crossfire, there were 4 players listed as DP. I did not include them as the stats indicated that these players didn't play any games (so presumably DP means 'did not play'). As you can see, there is a clear advantage to being born near the Jan 1 cut-off. Notice the almost complete absence of quarter 4 boys. (The Crossfire team did have a couple qtr 4 boys but they were all "DP").

Does this translate to an over-abundance of players with birth years in the first quarter on the National Team (U-23)? Well, there is an over-abundance of those players on the US National Team.

The Crossfire and Sounders teams are U15/16, which means that some U15s are on the team. Let's look at the distribution of birth year on the teams and the birth months of the U15s:

My next post looks at the birth month effect across all the US Soccer Development Academy teams and shows that we see the '4th quarter' deficit across all team, but we also see a 'May-June' deficit.  The latter would be consistent with an effect of the Aug 1 cut-off on players before they enter the USSDA program.  Another post looks at the birth month effect and the 'December deficit' in the 2012 Olympic rosters and Division I US college soccer players.
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Related work showing that even a 1-month average increase in the team's age has an effect on the team's performance:
Augst and Lames (2011) The relative age effect and success in German elite U-17 soccer teams
http://www.tandfonline.com/doi/abs/10.1080/02640414.2011.574719