By Barry Revzin on SwimSwam
With the primary cease of the World Cup in Carmel concluded, we lately posted the present standings by way of each rating factors and cash earned. After Carmel, Gretchen Walsh leads Kate Douglass in rating factors, however solely by a really small margin — 59.1 to 58.9. The dimensions of that margin was very stunning to me, so I wished to take the time to know why.Factors are earned in two methods: by place and by efficiency.
By place: 10 factors for 1st, 8 factors for 2nd, after which 6 pts all the way down to 1 for third by eighth place.
By efficiency: Every time is transformed into World Aquatics factors — primarily based on the components (R / T) cubed, the place T is the time and R is the earlier yr’s world report. This worth is then floored by 10 and divided by 10.
The instance given in World Aquatics’ doc is {that a} lady inserting 2nd within the 100m fly with a time of 55.49 would earn 17.2 factors: 8 factors for the 2nd place end and 9.2 for the 924 factors of the swim.
Solely a swimmers’ finest 3 occasions contribute to their whole every cease. For Walsh and Douglass, they every received 3 occasions, which contributed 30 factors every. Eradicating that, Walsh earned 29.1 efficiency factors to Douglass’ 28.9. Does that appear cheap?
Let’s check out their precise performances (I’m together with Douglass’ 100 IM for completeness regardless that she didn’t win it)
Swimmer
Occasion
Time
Aqua
Gretchen Walsh
50 Fly
23.72
1028
Kate Douglass
100 Breast
1:02.90
974
Kate Douglass
200 Breast
2:13.97
967
Kate Douglass
100 Free
50.83
966
Gretchen Walsh
100 IM
55.91
957
Gretchen Walsh
100 Fly
53.69
946
Kate Douglass
100 IM
56.34
935
This order appears… stunning? World Aquatics factors, as a metric, have some benefits. They’re very straightforward to calculate, because you solely want two numbers (the earlier yr’s world report and the present time). It additionally makes it straightforward to check instances throughout eras, as a type of normalization. Nevertheless, it has some notable disadvantages as a metric as nicely — which is likely to be clear from the ordering above.
Douglass’ 1:02.90 within the 100 breast is the twenty sixth quickest efficiency of all-time and makes her the sixth quickest performer within the occasion, however her 2:13.97 within the 200 breast is the third quickest efficiency of all-time, and solely she has been sooner. I’d take into account the latter to be an objectively higher swim.
On high of that, now we have to go down the World Aquatics record fairly far to get to Walsh’s 100 fly — she solely received 946 factors for an effort that can be the third quickest efficiency of all-time, just because her personal world report in that occasion is so comically absurd. Is that basically a worse swim than Douglass’ 50.83, that ranks because the thirteenth quickest efficiency and would make her the seventh quickest performer (have been she not already larger on the record)? No.
By solely normalizing primarily based on the earlier world report, World Aquatics penalizes nice information (like Douglass’ 200 breast and Walsh’s… every little thing) and rewards occasions which are extra aggressive (just like the 100 free and 100 breast).
What if we did one thing totally different? One other method of normalizing throughout occasions and time is utilizing z-score. What if we calculated each occasion primarily based on first figuring out the imply and normal deviation of the 100 finest *performers* (not performers) within the occasion, after which used these values to compute the z-score of the given swim?
For instance, within the ladies’s 50 fly, the imply is 25.52 and the usual deviation is 0.43, so Walsh’s 23.72 could be a z-score of 4.16 (nicely, it’d actually be unfavourable, however let’s simply flip the signal). If we do the identical calculation for all seven swims and organize them by z-score as a substitute, we get:
Swimmer
Occasion
Time
Aqua
Z Rating
Gretchen Walsh
50 Fly
23.72
1028
4.16
Gretchen Walsh
100 Fly
53.69
946
3.53
Gretchen Walsh
100 IM
55.91
957
3.52
Kate Douglass
200 Breast
2:13.97
967
3.18
Kate Douglass
100 IM
56.34
935
3.04
Kate Douglass
100 Breast
1:02.90
974
2.46
Kate Douglass
100 Free
50.83
966
2.41
This ordering makes considerably extra sense to me. All of Gretchen Walsh’s swims, in addition to Kate Douglass’ 200 breast, are sooner than anyone however them as gone, and Douglass’ 100 IM was the quickest efficiency by any person not named Gretchen Walsh. All of these are *clearly* higher performances than Douglass’ 100 breast and 100 free.
With this metric as-is, Walsh would rating 11.21 efficiency factors to Douglass’ 8.05 (her 100 IM scores extra efficiency factors than her 100 free — but when we account for place, her 100 free offers her 12.41 whereas her 100 IM offers her 11.04).
That hole makes way more sense to me. Douglass had an excellent efficiency in Carmel, however Gretchen Walsh’s was, nonetheless, distinctly higher.
Ought to World Aquatics change to make use of a Z-score-based system as a substitute of World Aquatics factors? We’d nonetheless want to determine the best way to correctly scale the z-scores so that they have the identical stage of influence. However I believe, as a place to begin, I believe such a system would considerably extra precisely replicate the relative performances of various athletes.
Learn the complete story on SwimSwam: Why Is World Aquatics Undervaluing Gretchen Walsh?
