In The Ancestor's Tale, evolutionary biologist Richard Dawkins makes the following statement about sexual dimorphism:

Our sexual dimporhism is moderate but undeniable. Lots of women are taller than lots of men, but the tallest men are taller than the tallest women. Lots of women can run faster, lift heavier weights, throw javelins further, play better tennis, than lots of men. But for humans, unlike for racehorses, the underlying sexual dimorphism precludes sex-blind open competition at the top level in almost any sport you care to name. In most physical sports, every single one of the world’s top hundred men would beat every single one of the world’s top hundred women.

I wonder if this has been backed up with proper data.

Expanding on Xen2050's information, the wikipedia List of Olympic records in Athletics page has links to each individual sport, listing the top 25 results by gender. I've compiled the information showing the 25th-best men's result vs. the best women's result. (I skipped the 110m hurdles since they are not directly comparable.) This does not prove the claim (top 100 men vs. top 100 women) but it does give a better feel for the discrepancy between genders in the results:

Sport:              25th-ranked men's result:   top-ranked women's result:

100m                9.87                        10.49

200m                19.80                       21.34

400m                44.10                       47.60

800m                1:42.81                     1:53.28

1500m               3:29.59                     3:50.07

5000m               12:51.00                    14:11.15

10000m              26:49.94                    29:17.45

Marathon            2:04:32                     2:15:25

400m Hurdle         47.67                       52.34

3000m Steeplechase  8:04.95                     8:44.32

4x100 Relay         37.58 (*)                   40.82

4x400 Relay         2:57.87                     3:15.17

20k Walk            1:18:06                     1:23:39

50k Walk            3:36:20 (**)                4:05:56

High Jump           2.38m                       2.09m

Long Jump           8.51m                       7.52m

Pole Vault          5.98m                       5.06m

Triple Jump         17.75m                      15.50m

-- these events use different equipment:

Shot Put (+)        22.08m                      22.63m  (would get 10th place on men's listing)

Discus Throw (+)    69.95m                      76.80m  (would get 1st place on men's listing)

Hammer Throw (+)    82.54m                      82.98m  (would get 19th place on men's listing)

Javelin Throw (+)   89.02m                      72.28m

Decathlon (+)       8663 points                 8358 points

notes:

(*): 20th-place result; lower results not available

(**): 10th-place result; lower results not available

(+): the equipment used is different between men and women. For example, the men's discus weighs 2kg and is 22cm in diameter, while the women's discus weighs 1kg and is 18cm in diameter. The shots, hammers and javelins are also lighter for the women's events. Therefore, these events are not really directly comparable.

On the evidence of the IAAF, the 100th best male athlete is significantly faster and/or stronger than a female. Here are a few examples:

Event     100th Man  1st Woman   Eq male rank

100m          10.15      10.85        3,460th

1500m       3:38.28    3:56.68      > 3,143th (a)

Marathon    2:08:46    2:18:11          797th

High Jump      2.23       2.04        1,085th

Long Jump      7.91       7.05        1,898th

Javelin       77.27      68.92          437th (b)

Note (a): There are only 3,143 entries for the men's 1500m, the slowest being 3:56.00 seconds.
(b) The men's javelin is longer and 33% heavier.

The World Swimming Rankings tell a similar story, but also give one example of an exception. Katie Ledecky's time for the 1500m Freestyle ranks her 72nd among the men. She is clearly an outstanding swimmer, as she is 31 seconds, or one full length, faster than her nearest female rival. She also competes in the 400m and 800m, where she is outside the top 100 men and her times are closer to other women's.

Given that men are more athletic at athletics, they should have the same advantage in team games such as football or rugby, but direct competitions, and therefore comparisons, aren't available.

However, this article has some revealing opinions from champions of both sexes into men's vs. women's tennis.

Extremes

In the fuller quote, Dawkins seems to be talking about extremes, "Lots of women are taller than lots of men, but the tallest men are taller than the tallest women." He also uses the example of racehorses, which don't compete in a team sport, but rather against each other to see which can run the fastest. Finally with "most physical sports" and "the top level in almost any sport," that's almost the literal definition of the Olympics, which Britannica.com says "[t]he Olympic Games have come to be regarded as the world’s foremost sports competition."

Therefore it makes sense to look at the extreme performance records of the Olympic games, specifically events where running times & jumping distances are easiest to compare. Not just the current athletes, but the all time records to really find the best extreme performers.

Comparing the very top record performers would show the very extremes of performance, as Dawkings was at least partially partially talking about. Here's the Olympic events & their all time records from Wikipedia's List of Olympic records in athletics, I'll try formatting them by sport, with the mens & women's records side-by-side for easier comparison:

                              Records

Event                   Men's       Women's

=====                   =====       =======

100m                    9.63        10.62

200 metres              19.30       ♦21.34

400 metres              ♦43.03      48.25

800 metres              ♦1:40.91    1:53.43

1,500 metres            3:32.07     3:53.96

5,000 metres            12:57.82    14:26.17

10,000 metres           27:01.17    ♦29:17.45

Marathon                2:06:32     2:23:07

110 metres hurdles      12.91       12.35

 * only 100m hurdles for women

400 metres hurdles      ♦46.78      52.64

3,000 m steeplechase    8:03.28     8:58.81

4×100 m relay           ♦36.84      ♦40.82

4×400 m relay           2:55.39     ♦3:15.17

20 km walk              1:18:46     1:25:02

High jump               2.39 m      2.06 m

Long jump               8.90 m      7.40 m

Pole vault              6.03 m      5.05 m

Triple jump             18.09 m     15.39 m

(♦ denotes a performance that is also a current world record.

 Statistics are correct as of 19 August 2016.)

The following events differ in the weight of the item thrown so aren't directly comparable, but given the drastic difference in weight of the items (usually half as heavy for women) yet still similar records, it seems worthy of inclusion:

Shot put                22.52 m     22.41 m

 * men's shot weighs 16 lb, women's 8.8 lb

Discus throw            69.89 m     72.30 m

 * men's weigh 2kg/4.4 lb, women's 1kg/2.2 lb

Hammer throw            84.80 m     82.29 m

 * men's weigh 16 lb, women's 8.82 lb

Javelin throw           90.57 m     71.53 m

 * men's weigh 800g/1.76 lb, women's 600g/1.32 lb

It appears that the men's records are quicker/faster/further for everything except the incomparable item throwing events. This strongly supports Dawkins' statement.

What about the next 99 athletes?

_{I would ask Dawkins why he chose the seemingly arbitrary number of the top 100 men & women, it could've been with the idea that there are only a few extreme performers, but the Olympic records seem to indicate that there's not only a dozen or even a hundred, but thousands of very closely performing athletes.}

Looking specifically at the (arbitrary) 100th best vs the very best, using the IAAF source for Wikipedia, similar to Boodysaspie's good answer but not just looking at current athletes but all time records (or at least since electronic timing ) and not just the Olympics, gives results with usually far more than 100 men's records faster than the fastest woman, so it looks like Dawkins' statement holds water:

• For the 100m the top performing women's all time record is 10.49s (that's faster than the Olympic record), but the 100th fastest men's record is 9.97s. In fact there are at least 1686 male athletes with times faster than the women's record (they are 10.30s or faster) (the IAAF website doesn't have records beyond 1686 for the men's 100m).




• 200m, women's record is 21.34, there are 1544 men with records 20.70 or faster




• 400m, women's record is 47.60, there are 709 men's records 45.50 or faster




• 800m, women's record is 1:53.28, there are 657 men's records 1:46 or faster




• 1,500m women's record is 3:50.07, there are 938 men's records 3:38 or faster




• 5,000m women's record is 14:11.15, there are 1262 men's records 13:30 or faster




• 10,000m women's record is 29:17.45, there are 1085 men's records 28:09.98 or faster




• Marathon, women's record is 2:15:52, there are 1883 men's records 2:12:00 or faster




• 400m hurdles, women's record is 52.34, there are 889 men's records 50.00 or faster




• 3,000m steeplechase, women's record is 8:44.32, there are 809 men's records 8:30 or faster




• 4x100m relay, women's record is 40.82, there are only 73 men's records in total, all 38.48 or faster




• 4x400m relay, women's record is 3:15.17, there are only 87 men's records in total, all 3:02 or faster




• 20k walk, women's record is 1:23:39, there are 546 men's records 1:23:00 or faster




• High jump, women's record is 2.09, there are 625 men's records 2.25 or higher




• Long jump, women's record is 7.52, there are 818 men's records 8.00 or longer




• Pole vault, women's record is 5.06, there are 655 men's records 5.50 or higher




• Triple jump, women's record is 15.50, there are 516 men's records 16.80 or longer