Baby center released its list of the top 100 baby boy and girl names for 2012. What’s not on the list? Nicole. For most of the eighties Nicole was one of the top ten, but lately it’s been on the decline.

Of my friends who gave birth in the past year, three strived for unique names. I thought they succeeded. If I had to guess, all three picked names less common than ‘Nicole’. In reality each of those names all made the top 100 list. In fact, two of those friends, who don’t even know each other, ended up picking the same exact name (though one used it as a middle name).

This got me thinking. How unique is unique these days?

Babycenter’s list is generated from their members, which isn’t necessarily a representative sample of all babies. To get a broader perspective I turned to US census data. Here’s what I found.

What does the distribution of names look like?

We all know the popularity of given names changes all the time. In 1995 the most popular girls name was ‘Jessica’, but in 2011 ‘Jessica’ was ranked 120th. I wondered if parents looking for rare names may end up like my two friends, and settle on the same “rare” name. Maybe ‘Kendall’ (currently just three ranks below ‘Jessica’, and six below ‘Nicole’) will become the new ‘Emma’.

I looked at a variety of years, but ultimately decided to compare 2011 to 1995 as they have a similar birth rate and 2012 data isn’t available yet.

There are more names to choose from

The US census data only lists names that were given to at least 5 babies. Using the birth rate data I can extrapolate that approximately 7% of babies in 1995 and 8% of babies in 2011 had a name given to less than 5 babies. So in addition to the two years having the approximately the same birth rate, the US census lists for both years represents approximately the same number of babies.

Here’s the interesting thing: In 2011 there were approximately 34 thousand unique names on the US census list whereas there were only 26 thousand unique names on the list for 1995 – for approximately the same number of babies!

The ultra common names are the names on the most decline

In 1995, 44% of girls and 58% boys (or roughly 1 in 2 babies) were given a name that made the top 100 list for that year. For 2011, only 31% of girls and 44% of boys (a little less than 2 in 5 babies) had a name that made the top 100. Thus the use of a name in the top 100 is declining.

Yet, most parents still pick names that in the top 1000. Despite there being over 19 thousand different girl names and 14 thousand different boy names given to babies in 2011, 67% of girls and 79% of boys (or roughly 7 in 10 babies) had a name in the top 1000. If we subtract out the top 100 baby names, we find 3 in 10 babies had a name ranked in the top 101-1000. That’s the same rate as in 1995!

What about Names Collisions?

Parents often state they are striving for unique names out of a desire that their child to be the only child with a given name in school. In other words, they want to avoid a name collision.

How common are name collisions?

Name collisions have been on the decline. Using a Monte Carlo simulation I was able to compute the probability of a name collision for a group of babies. Thirty years ago a group of 40 babies would be 97 to 99% likely to have a name collision. In 1995, there’s a 79.9% probability of a name collision in a group of 40 babies. In 2011, there is only a 56% probability that at least two babies in a group of 40 will have the same name.

The probability of name collisions has actually been on a decline since 1990. (Coincidently the world wide web was created in 90’s.)

Picking a name with low probability of collision

This is actually fairly easy to calculate. Let’s use the name Kaitlyn, the 100 most popular girls name for 2011, as an example.

In 2011, there were 2893 Kaitlyns born (roughly 0.15% of all girl baby births for that year). Let’s say Kaitlyn is going to go to school with just one other girl baby also born in 2011. If we pick that girl baby baby at random, she has a 0.15% chance of also being named Kaitlyn and 99.85% probability of having a different name. Let’s say Kaitlyn is going to go to school with two other girls. Each of those girls has a probability of 99.85% of not being named Kaitlyn. The probability of a name collision is one minus the probability of neither girl having the name Kaitlyn. Mathematically that’s expressed as 1-(1-0.15)x(1-0.15) or 0.3%. The general formula is:

p(name_collision) = 1 – (1 – popularity_of_name)^{number_of_students}

According to the National Center for Educational Statistics the average elementary school has 482 students. According to the US census data, 48.8% of babies born in 2011 are girls. That would mean there are 234 other girls in addition to our Kaitlyn. We compute the probability of a name collision as follows.

p(name_collision) = 1 – (1 – 0.15)²³⁴
p(name_collision) = 1 – (1 – 0.15)²³⁴
p(name_collision) = 29.7%

Thus there is only a 29.7% probability that our Kaitlyn will go to a school with another Kaitlyn.

You would have to pick the 38th most popular girl’s name (Anna) before there’s a 50/50 chance that another child at the same elementary school having the same name. For boys you’d need to pick the 72 most popular name (Ian) to have a 50/50 chance at a name collision. What if you pick a name below the top 1000? Then there’s only a 3% chance of a name collision for girls and a 2.3% chance for boys!

Of course, this analysis is only considering a name collision with another child having the same spelling of the name. There could also be a Caitlyn, Katelynn, etc. According to NameNerds. There are an additional 6938 girls named with a spelling variants of Kaitlyn in 2011. Including these spelling variants, the chance of a name collision increases to 70%.

So what about spelling variants?

Using the new counts from NameNerds I found the following names are likely to have a name collision at an averaged sized elementary school. The probability of the name collision is in parentheses.

For Girls: Sophia (97.2%), Isabella (94.1%), Olivia (90.9%), Emma (90.1%), Chloe (88.0%), Emily (87.8%), Ava (86.0%), Abigail (84.6%), Madison (84.5%), Kaylee (81.1%), Zoey (81.0%), Mia (78.9%), Madelyn (78.5%), Addison (78.2%), Hailey (78.1%), Lily (77.3%), Aubrey (76.0%), Riley (75.6%), Aaliyah (74.9%), Layla (74.7%), Natalie (74.3%), Arianna (73.6%), Elizabeth (72.6%), Brooklyn (71.0%), Kaitlyn (69.9%), Ella (69.4%), Makayla (68.6%), Allison (68.1%), Mackenzie (67.4%), Peyton (67.2%), Kylie (67.2%), Brianna (66.3%), Lillian (65.4%), Avery (65.1%), Leah (64.4%), Maya (63.2%), Alyssa (62.8%), Amelia (62.8%), Gabriella (62.4%), Sarah (62.3%), Katherine (62.0%), Evelyn (61.8%), Jocelyn (61.7%), Grace (60.6%), Hannah (60.0%), Jasmine (59.8%), Samantha (59.4%), Alaina (59.3%), Anna (57.8%), Nevaeh (57.6%), Victoria (57.5%), Alexis (57.0%), Camila (56.3%), Savannah (56.1%), Charlotte (54.7%), Liliana (52.9%), Ashley (52.6%), Isabelle (52.0%), Kaelyn (51.4%), Lyla (51.3%), andKayla (50.4%)

For Boys: Aiden (97.5%), Jayden (95.6%), Jacob (92.8%), Jackson (92.3%), Mason (91.9%), Kayden (89.3%), Michael (88.5%), William (87.7%), Ethan (87.5%), Noah (87.2%), Alexander (86.5%), Daniel (84.6%), Elijah (83.6%), Matthew (83.5%), Anthony (83.0%), Christopher (82.5%), Caleb (81.4%), Joshua (81.2%), Liam (80.9%), Brayden (80.2%), James (80.1%), Andrew (80.1%), David (79.9%), Benjamin (79.8%), Joseph (79.7%), Logan (79.7%), Christian (79.7%), Jonathan (78.4%), Gabriel (78.1%), Landon (77.7%), Nicholas (77.0%), Lucas (76.4%), Ryan (76.3%), John (74.9%), Samuel (74.8%), Dylan (74.7%), Isaac (74.1%), Cameron (74.0%), Nathan (73.0%), Connor (72.5%), Isaiah (71.1%), Gavin (68.5%), Carter (67.8%), Jordan (67.1%), Tyler (66.1%), Evan (65.6%), Luke (65.5%), Owen (63.9%), Aaron (63.8%), Julian (63.6%), Jeremiah (63.5%), Brandon (63.4%), Zachary (63.4%), Jack (63.0%), Colton (61.5%), Adrian (61.5%), Wyatt (61.0%), Dominic (60.3%), Angel (60.1%), Eli (59.6%), Austin (59.2%), Hunter (58.9%), Justin (58.5%), Henry (58.4%), Jason (58.2%), Robert (56.9%), Charles (56.9%), Sebastian (56.6%), Thomas (56.6%), Brian (56.4%), Eric (56.3%), Tristan (56.1%), Jose (56.0%), Kevin (55.8%), Chase (55.7%), Levi (55.6%), Josiah (54.2%), Bentley (54.1%), Grayson (54.0%), Giovanni (53.8%), Carson (53.5%), Xavier (52.8%), Ian (51.7%), Jace (51.5%) and Brody (50.0%)

Some obvious ones on the list, but there are definitely some surprises, including two of my three friend’s pick! In 2011, 33% of girls were named a variant of these 61 girls’ names and 46% of boys were named a variant of these boys’ names.

Conclusion

My intuition of what constitutes a common baby name was clearly off. I fell into the trap of thinking names that were common when I was young are still common, and names that were rare are still rare. Even if you made the same mistake I did, the good news is it’s less likely to have a name collision today than 17 years ago.

One last thought. Throughout this analysis there was an implicit assumption that names were rarer because parents were deliberately choosing rarer names. But there are other possible explanations. With an increase in globalization prospective parents get exposed to new names. In the past two years I’ve worked with more Nikhils than Johns, and more Yis that Matts. I know people who picked exotic names for the children purely because they loved the sound of the name, and not because of any ethnicity or ancestry reasons. Perhaps this trend to uniqueness was inevitable, whether intentional or not.

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Update 7/17/15: I’m pleased to announce an interactive web app based on this post. Now you can look up the uniqueness of any name for any year after 1950, see how a name is trending, and what are the odds of meeting another person with the same name!

Posted in Life | Tags: Baby Names, Doing the Math