Which are the fastest (and slowest) running countries in the world?

As running becomes more and more popular around the world, the need to rank countries by the speed of their runners is clearly needed. Why should I care you ask? It's a good point you're making I'd retort, but we seem to like ranking of all sorts of things so why not? We rank countries by feelings of love, Cities by bike-friendliness, and even professions by right swipes.

(Note: Just scroll down to see the maps and lists of fastest countries without going through the explanations.)  

To get some data on running speeds I decided to look at the New York City Marathon, one of the largest and most international marathons in the world. I collected results from 2011, 2013 and 2014 -- about 150,000 runners all together. A simple way to find countries' speed is to take the average speed of the runners of each country and compare. The problem with this approach is that it is somewhat naive. Different countries may be represented by different compositions of runners. A country with more female runners may appear slower than a country with more male runners. In a poorer country, it may only be the highly motivated, faster, runners who choose to make a pricey trip to New York. 

To construct an adjusted rankings of countries' speed I follow the insights supplied by the gravity model in Economics -- a model originally developed to analyze trade flows between countries and regions. Analogous to the manner gravity is determined by objects' mass and the distance between them, this model predicts that the strength of trade between two countries is affected by their distance from each other and the size of their economies. The closer are countries and the bigger their economies, the stronger is the predicted trade.

For a runner to decide to compete in the NYC marathon she must consider how much she wishes to participate in the run (and enjoy a visit to NYC) against the price of the trip and the time it takes. If the runner lives in NYC than the price is quite low and the time is negligible. Even a runner who is not highly invested in marathon running, and is slower than average, may still decide to participate. On the other hand, for a runner who lives in Delhi, the cost is substantial and the trip's duration is likely to be a number of days at least. A runner incurring the cost of the trip is someone who is possibly more motivated and hence a faster runner than average. As a result, we would observe that Americans run the NYC marathon slower than Indians, and could incorrectly conclude that average speed of all American runners is slower than all Indian runners.

By controlling for age, gender, distance from NYC, and GDP per capita, I find the average marathon adjusted 'pseudo'-times of countries with more than 20 participants. You can see below two world maps colored according to countries' NYC marathon running times (in number of hours to complete the marathon). The upper map shows the adjusted times and the lower one the original times.

So which countries are the fastest? Below is the list of countries ranked by their adjusted average running time. You can also see their ranking according to the original, non-adjusted, average running times on the right.

Rank	Country	Adjusted time	Original time	Original rank
1	Kenya	3:39:10	2:37:52	1
2	Slovenia	3:40:24	3:51:21	2
3	Norway	3:46:58	4:18:29	22
4	Luxembourg	3:47:56	4:16:29	18
5	Switzerland	3:48:53	4:17:39	20
6	Portugal	3:49:57	3:54:50	3
7	Denmark	3:52:20	4:13:49	14
8	Austria	3:53:59	4:14:20	15
9	Belgium	3:55:11	4:12:56	12
10	Sweden	3:56:07	4:19:45	25
11	Czech Republic	3:57:04	4:00:22	5
12	Iceland	3:58:08	4:19:32	23
13	Spain	3:58:52	4:07:12	8
14	Latvia	3:59:24	4:02:29	6
15	Bermuda	4:00:10	4:12:11	11
16	Slovakia	4:00:25	3:55:31	4
17	France	4:01:01	4:19:50	26
18	United States of America	4:03:09	4:35:30	46
19	Poland	4:04:55	4:03:45	7
20	Netherlands	4:05:31	4:25:46	33
21	Germany	4:07:12	4:29:22	38
22	Croatia	4:07:41	4:07:48	9
23	Canada	4:08:53	4:24:53	31
24	Finland	4:10:22	4:35:16	45
25	United Kingdom	4:10:42	4:28:04	36
26	Costa Rica	4:12:53	4:14:36	16
27	Italy	4:13:39	4:27:34	34
28	Greece	4:14:37	4:18:24	21
29	Russia	4:16:37	4:13:16	13
30	Chile	4:18:08	4:17:31	19
31	Colombia	4:18:16	4:16:22	17
32	Israel	4:20:36	4:09:54	10
33	Brazil	4:25:20	4:25:20	32
34	Hungary	4:25:51	4:19:40	24
35	Panama	4:27:32	4:33:45	43
36	South Korea	4:27:33	4:48:01	52
37	Mexico	4:29:08	4:31:26	41
38	Dominican Republic	4:30:47	4:27:41	35
39	Argentina	4:30:54	4:29:49	39
40	Peru	4:31:01	4:24:34	29
41	Ecuador	4:32:54	4:24:43	30
42	Australia	4:32:58	4:22:49	27
43	Japan	4:33:48	4:53:25	57
44	Uruguay	4:34:27	4:33:10	42
45	Ireland	4:35:58	4:34:37	44
46	Venezuela	4:38:40	4:37:01	47
47	Hong Kong	4:41:29	4:24:13	28
48	Guatemala	4:42:06	4:28:41	37
49	United Arab Emirates	4:42:39	4:50:53	54
50	Singapore	4:47:53	4:30:55	40
51	Turkey	4:48:21	4:43:36	49
52	The Bahamas	4:51:05	4:53:01	56
53	Paraguay	4:53:43	4:42:32	48
54	New Zealand	4:54:53	4:52:28	55
55	China	5:00:03	4:47:01	50
56	South Africa	5:20:13	4:47:56	51
57	India	5:42:24	4:48:47	53
58	Philippines	5:54:54	5:08:41	58
59	Indonesia	5:57:59	5:26:36	59

It is easy to see how factors like average age and gender composition affect the country rankings in the list by checking some of the highlighted countries in the scatter plot below.

Countries by average age and fraction of female runners

Kenya, the fastest country in the world by far is represented by much younger runners than any other country. For that reason, the adjusted rankings, while still showing Kenya as the fastest country in the world, reduce the gap between it and the second fastest country considerably. Slovakia, represented by somewhat younger runners and by a very low fraction of female runners is relegated from being the 4th fastest country in the original running times to the 16th fastest in the adjusted times.

On the other hand, Canada is represented by a high fraction of women and South Korea is represented by much older runners than any other country. For those reasons both these countries' rankings are higher using the adjusted running times.