Does the birthday paradox actually hold in sports?

The math says: in a group of 23 people, there's a 50.73% chance two share a birthday. We checked against 38,228 real team lists across 93 sports and 289 countries.

Real team match rate

47.5%

vs expected 44.8% (+2.7 points)

Why it matters: The real team lists come in slightly above the clean model, which suggests birthdays are not perfectly random once selection systems and team-building enter the picture.

Team lists analysed

38,228

avg team size 22.9

Why it matters: This is enough sample size for the headline result, but sports with only a few team lists still need caution.

Player entries

971,027

from 10 datasets

Why it matters: Player entries are not unique people; repeated seasons intentionally show what real team lists looked like over time.

Sports covered

leagues + Olympic disciplines

Why it matters: The variety lets us separate universal birthday math from sport-specific selection effects.

Countries represented

289

primarily via Olympics & football

Why it matters: Country patterns mostly reflect team sizes and available datasets, not national biology.

Real team lists vs birthday math

Share of team lists where at least two players share a birthday. Top 15 sports by number of real team lists in the dataset.

Why this matters: The main pattern is reassuring: real rates usually track the math. The interesting exception among these high-sample sports is Football (Football), which sits +6.3 points from the same-size random team-list baseline.

Probability vs team size

Expected curve (yellow) vs real rates at each team size. Individual sports are plotted only where at least 3 real team lists exist at that size.

Why this matters: This is the paradox in one curve: by team size 23, the theoretical chance has already crossed 50%; by 41, it is over 90%. Most big rates on this site are team-size effects first, sport effects second.

Where real teams beat the math

Sports where real team lists have the biggest gap from what random same-size teams would predict. Minimum 50 team lists to avoid tiny-sample noise.

Surprise: The big misses mostly go upward: real teams share birthdays more often than the clean birthday-problem model predicts. Artistic Swimming (Aquatics) is the standout at +15.5 points.

Popularity vs paradox rate

Each point is a sport. X = player entries in the dataset (a rough size proxy, log scale). Y = share of team lists with shared birthdays.

Surprise: Popularity itself is not the magic ingredient. Football (Soccer) has the most player entries here, while American Football has the highest shared-birthday rate because its teams are much larger.

Sports closest to clean birthday math

Sorted by gap from same-size random teams. Smaller is closer to the math. Minimum 20 team lists per sport.

#	Sport	Team lists	Avg players	Real	Expected	Gap
1	Cycling Road (Cycling)	349	6.7	5.4%	5.5%	-0.1 points
2	Swimming (Aquatics)	682	14.6	25.8%	25.9%	-0.1 points
3	Snowboarding (Skiing)	113	11.0	15.9%	15.7%	+0.2 points
4	Basketball (Basketball)	334	14.0	23.7%	23.2%	+0.4 points
5	Weightlifting	331	7.2	5.7%	6.3%	-0.6 points
6	Short Track Speed Skating (Skating)	100	7.7	8.0%	7.4%	+0.6 points
7	Football	28	19.6	39.3%	40.0%	-0.7 points
8	Alpine Skiing (Skiing)	341	10.1	14.4%	13.6%	+0.7 points
9	American Football	2,416	55.0	91.8%	91.0%	+0.8 points
10	Bobsleigh (Bobsleigh)	264	8.3	9.8%	8.8%	+1.1 points
11	Baseball	3,591	34.9	75.6%	74.3%	+1.3 points
12	Tennis	157	7.3	8.3%	6.8%	+1.5 points
13	Rowing	585	16.7	32.0%	30.5%	+1.5 points
14	Beach Volleyball (Volleyball)	47	7.0	4.3%	5.7%	-1.5 points
15	Artistic Gymnastics (Gymnastics)	392	11.3	17.3%	15.8%	+1.6 points
16	Cross Country Skiing (Skiing)	359	9.6	13.4%	11.8%	+1.6 points
17	Volleyball	24	12.9	20.8%	19.2%	+1.6 points
18	Freestyle Skiing (Skiing)	127	10.5	16.5%	14.8%	+1.8 points
19	Judo	335	8.4	11.0%	9.1%	+2.0 points
20	Canoe Slalom (Canoeing)	76	7.3	9.2%	7.1%	+2.2 points
21	Diving (Aquatics)	174	8.0	5.7%	8.0%	-2.2 points
22	Rugby Sevens (Rugby)	30	19.9	43.3%	41.0%	+2.3 points
23	Canoe Sprint (Canoeing)	338	9.7	14.8%	12.3%	+2.5 points
24	Cycling Track (Cycling)	286	7.7	10.1%	7.5%	+2.6 points
25	Equestrian Eventing (Equestrian)	52	5.3	5.8%	3.1%	+2.7 points
26	Shooting	563	10.0	16.2%	13.5%	+2.7 points
27	Ski Jumping (Skiing)	101	5.7	1.0%	3.8%	-2.8 points
28	Table Tennis	125	6.1	7.2%	4.3%	+2.9 points
29	Curling	81	8.1	11.1%	8.2%	+2.9 points
30	Archery	113	6.3	8.0%	5.1%	+2.9 points

What to notice: The closer a sport gets to a zero gap, the more it behaves like simple birthday math. Road cycling and swimming are almost textbook cases here, which is surprisingly satisfying.

Gender split: rate vs team size

Real shared-birthday rates compared with same-size random teams, where the source records gender.

Why it matters: The gender gap is mostly a team-size story. Men have the larger average team size here (25.2 athletes), so their birthday-match rate naturally rises.

Countries where teams share birthdays more than expected

Countries with enough team lists, sorted by the largest positive gap from same-size random teams. Minimum 50 team lists.

Careful: Treat country rankings carefully: high rates often mean larger teams, not a country-specific birthday effect. The useful signal is the gap from the same-size-team baseline; here NEPAL runs +21.9 points above expectation.

When are athletes actually born?

Share of athletes born in each calendar month, vs the share you'd expect if birthdays were evenly spread across calendar days. The orange line adjusts for month length, so February gets a lower fair-share baseline.

Based on 298,568 unique athletes across all loaded datasets. Records with missing or year-only DOBs are dropped at ETL time, so what you see here is real signal.

Surprise: Jan has the most athletes by raw count, but Feb is furthest above its fair share after month length is accounted for. Dec is the lightest month relative to expectation.

Want more?

The birthday paradox is just the headline. Once you have 298,568 athlete birthdays in one place, you can ask a lot of other questions: relative-age effect, leap-day athletes, the single luckiest team-up of all time, youngest and oldest sports, and more.

What to notice: The weirdest story is not a single birthday. It is the repeated early-year tilt: January and February keep showing up as heavier than a calendar-only model would predict.

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