Ranglijsten beste prestaties 2015/2016

I made some additions to @SprintMaster's system based on
- how fast the ice rink is
- clap skates or no clap skates
- whether a sporter prefers skating inside/outside rinks and/or highland or lowland rinks.
Furthermore, air pressure has more effect on higher speeds (because of physics), so I changed the correction model to match that.

Those additions are all still in development though.

I have looked at ELO-rankings during my studies (MSc Mathematics). The original system is based on results between two competitors at a time. I would like to know how you adjust this for a competition with many skaters at once; and if you incorporate time differences. I could not find such details on your website, so I would love it if you could point me to the right page, or post an explanation here. (I can probably read Norwegian good enough that I would try reading a Norwegian explanation if you have already written one.)

Toch heb ik het gevoel dat de aanpassingen die ik heb doorgevoerd iets realistischer zijn (die werken inmiddels). Stel je voor, iemand staat net op schaatsen en doet een kwartier over een 1000 meter. In jouw model rijdt diegene als er sprake is van een hoge luchtdruk (zoiets als 1030 mbar) maar liefst 5 seconden harder. In mijn aanpassing rijdt diegene niet harder, omdat de snelheid zo laag is dat de luchtweerstand een verwaarloosbare invloed heeft.
Vervolgens heb je de iets gevorderdere schaatser, die de 1000m in 2 minuten aflegt. In jouw model levert dat bij 1030 mbar een correctie van 0,64 sec. op, bij mij 0,08.
Bij een 1000 meter in ±70 sec. zijn onze correcties gelijk.
Vervolgens gaan we over naar de schaatser van 2100 die op een magneetzweefvliegklapschaats en in een nanotechnologiepak een tijd van 53 seconden rijdt. In jouw model is er toch maar 0,28 sec. correctie. Dat verbaast me. De futuristische schaatser heeft door zijn hogere snelheid veel meer luchtweerstand, maar toch is de correctie bij de beginnende schaatser veel groter! Bij mij krijgt de volgende-eeuw-schaatser een correctie van bijna een seconde.

Natuurlijk, dit zijn uitersten, maar ik hoop dat je mijn idee begrijpt. Bij mij is die 0,34 niet constant, maar een variabele die exponentieel afhankelijk is van de snelheid.

(Dit model zorgt niet voor heel grote wijzigingen. Dat Nuis' Seoulrace nu ineens weer 0,14 achter Kulizhnikovs SLC-race staat, komt voornamelijk doordat ik de baanfactor (hoe snel een baan is) ietsje minder zwaar mee laat tellen. Het gaat waarschijnlijk wel wat uitmaken als ik jaren-80 tijden ga vergelijken met nu, inclusief vasteschaatscorrectie.)

I only became familiar with the ELO system last summer myself, and that was when I decided to use it at the "Skøyteranking" website.

When there are several skaters the original head-to-head system is just about useless, obviously. I read quite a lot about the system, and eventually found out that there is infact a "multiplayer system", which for example is used in chess tournaments (at least, I think it is).

The multiplayer system works like this:

1) Players have different ranking value before a race. Those rankings give them certain probabilities to beat the other skaters that compete in that same race. For example, if skater A have 100 more ranking points than skater B, his chance of beating skater B is 64 %.

2) If you skate against 19 other skaters, your chance of winning against all those opponents are added together. Let's say this adds together to 12,5 for a specific skater in a specific race.

3) Each skater is given a new ranking value after the race. Let's say that a skater beats all his 19 opponents, when he was expected to "only" beat 12,5 of them. The new ranking value will then be (19-12,5) x 15 = 97,5 points higher than it was before the race.

When I began working with the ELO system, I was lucky enough to find an online calculator which makes it possible to do the calculation without much manual work. It seems to have disappeared by now, but I managed to build my own "calculator" (an excel file) which does the tricks for races with up to 40 skaters...

Feel free to ask if you want more information!

I'm still busy with 1000m corrections over multiple years.
If there would be an important competition, with all good 1000m skaters of the last few years, all racing the best races they ever did in that period (2009-2016), this would be the result:
1. Shani Davis
2. Pavel Kulizhnikov
3. Kjeld Nuis
4. Stefan Groothuis
5. Denny Morrison
6. Tae Bum Mo.
This is based on correction for height, air pressure, how fast the ice rink is, whether a skater prefers to skate on highland or lowland, technological development and the average speed of the best skaters over the last few seasons. The ones in bold are the most influencing values when correcting times.

Meer resultaten uit het onderzoek: het niveau op de 1000m-mannen was in 2007/2008 belachelijk hoog. Veel verschillende schaatsers konden winnen, en ze reden allemaal erg hard, vooal bij World Cups. Je had van die wedstrijden waarmee je met 1:07.11 (SLC) of 1:08.62 (Hamar) gewoon maar vierde werd. En dat lag niet aan heel lage luchtdruk. Davis, Bos, Spoon, Lee, Morrison, Mun, Koskela... Daarna werd het allemaal minder, begon Davis te domineren en ging het niveau in de breedte hard onderuit.
Twee jaar later had alleen Shani Davis zijn topniveau nog op de OS. Hij was beter geworden. De rest was afgezakt. Pas na Sotsji begon het breedteniveau weer terug te komen. Dit seizoen rijden Kulizhnikov en Nuis op een niveau dat vergelijkbaar is met Davis in zijn beste jaren, al zou je zeggen dat er tegenwoordig harder gereden zou moeten kunnen worden dan 8 of 10 jaar geleden. Achter Kjeld & Kuli BV komt een groep schaatsers die de komende jaren misschien weer voor een hoog niveau in de breedte kan zorgen (Verbij, Yuskov, Kim T.Y., Jorritsma e.d.).
Voorlopige hypothese is dat er een golfbeweging is in het niveau, of voor de wiskundigen onder ons, een sinusoïde.

Mooie analyse.

Gek is wel dat het per afstand heel erg kan verschillen. Ik gok dat het niveau op de 1500 meter in die periode ook erg is gedaald (op Yuskov na), terwijl het niveau in de breedte op de 500 meter wel redelijk doorgestegen is (34.50 rijden is niet meer bijzonder). Op de 5000 meter staat het al jaren stil, en op een paar nederlanders na de 10.000 meter ook.

Omdat ik ook op hoogland /laagland voorkeur corrigeer, kan ik zeggen: Davis zou hem ook op laagland moeten kunnen winnen.

Vat ik het dan goed samen, als ik zeg dat Shani Davis, ondanks zichzelf, de beste schaatser op de 1000m is van de afgelopen jaren?

Nee, want die sporterspecifieke correctie is meestal nooit meer dan een tiende. Ik wil hem niet te prominent maken, zodat uitslagen van wedstrijden niet teveel worden beïnvloed. Het is niet de bedoeling dat je bij deze hypothetische uitslag
Groothuis 1:08.59
Davis 1:08.85
zoveel op laaglandrijder vs hooglandrijder gaat corrigeren dat Davis uiteindelijk sneller zou zijn dan Groothuis...

In sommige gevallen heeft een sporter nog nooit een serieuze wedstrijd op hoogland gereden (Kulizhnikov tot november 2015). Dan werkt die factor niet echt.

Ik zal binnenkort mijn correctiefactoren wat uitgebreider uitleggen, en ook hoe ik corrigeer op "algemene technologische ontwikkeling" en op genormaliseerd jaargemiddelde. Hiermee bedoel ik dat een 1:08.33 in Heerenveen in 2008 meer waard is dan een 1.08,33 in Heerenveen in 2016 bij precies dezelfde luchtdruk.

Soms is het trouwens nodig om je gevoel te gebruiken, en niet blind op cijfertjes te gaan. Mijn model overcorrigeert Erfurt wel eens en de wisselende omstandigheden op buitenbanen blijven ook lastig, vooral als er de ene dag veel sneller wordt gereden dan de andere terwijl het weer niet erg verandert.

As far as I understand the multiplayer system is based on, in your example, one player playing 19 matches and winning all of them. Thus essentially 19 pieces of information. In the case of a skating competition with 20 competitors you still have only data point about a skater. Of course you extract more information from that single data point as you have a clearer indication of the level of the competition than if you have a match between 2 players, but still less information than if the skater had skated 19 head-to-head matches and won all of them. Did you correct for this somehow? (I see you use k=15, which suggests not.)

Of course setting the k-factor is something of an art: A large k-factor creates a quickly responding ranking to changing levels of competitors, but with a large amount of variation once the rankings have settled (and competitors do not change their levels anymore), whereas a small k-factor might become very accurate given enough competitions, but needs many competitions to adjust to a change in level of any one competitor. Considering skaters have fewer races a year than chess players, you'd have to make a relatively larger k to adjust for that. By taking one data point and counting it as 19 you are essentially doing that, so perhaps you got the right mix .

Considering this though, it might be interesting to use a smaller value of k for the 500m compared to the 10000m, as there are more races in the 500m (and also adjusting it for the number of competitors in the race). Have you tried adjusting the value of k and looking what happens? The one time I tried to implement Elo, this was quite revealing (and considering I did it for my chess club with me as one of the competitors, some people thought I had alterior motives in changing the rankings based on adjusting some constants...).

Still, if you look at your list, it seems that they perform quite well overall. I can basically believe all rankings, except for Mantia's score for the 1500m. That he beats Yuskov for the no 1 spot surprises me, but then again Mantia did also get the best result of the season according to Sprintmaster. But that he is 200 points ahead of the rest of the field (and thus should beat everyone 75% of the time) seems not quite right.

Based on seasons 2006-2007 till 2015-2016.
5 Dutchies in top-12, but none of them on the podium.

Davis' best race is his WR, Morrison's best race is the WC final 2007, Kulizhnikov's best race is World Cup 2015 SLC, Nuis' best race is Dutch Sing. Dist. Champ. 2016, Groothuis' best race is his Olympic gold race, Lee's best race is one in Harbin were he skated a quick track record on a not so quick track.

Mo got a bit lower than in my previous setup, because I decreased the influence of rink speed as it was too... well, influencing.

I again changed some things, removed some settings as they were kind of replaced by another setting, and balanced some things out.

Sadly for our Scandinavian friend @Skøyteranking, there's no Norwegian guy high in the rankings. That might change though when I go further back in time, to Søndrål and Strøm.
There's Heerenveen in the title, as I corrected it if all the races were on Thialf ice rink in 2016 with normal air pressure and decent ice quality. As you can see, the best five skate theoretically faster than the track record.

Edit: Kjeld Nuis liked my tweet about this.

I can see that you have been confused by my links...

The socalled "ELO-toppen" is in fact what I (or rather my calculation system) see as the best results of last season. In deed, Mantia's 1.44,26 seem to be on top also in SprintMaster's view.

But this does not mean that Mantia is ranked as the best 1500 m skater at the end of last season. The distance lists as of March 2016 can be seen here:

(men) http://www.skoyteranking.net/45500107
(ladies) http://www.skoyteranking.net/45500110

For the 1500 m, Yuskov is by far the best skater on the list of March 2016. Nearly 400 points more than Mantia means he should the American in 9 out of 10 races. But it should be mentioned that Mantia has dropped from 2076 pts after his win in December to 1848 pts at the end of the season. Which brings me over to your other point...

I was quite a newcomer to the ELO-system, so I must admit that I just used what I thought would be the "concervative" choice when it comes to the k-factor:

• I use k=25 for the new skaters. (Everyone who has skated against less than 30 opponents is considered "new")
• I use k=10 for skaters who has more than 2400 points on a particular distance.
  
• I use k=15 for all the rest

I haven't done any experiments with higher or lower k-factors, but you could certainly have a point about more races on the short distances. But the tight competition on the 500 m also makes it very difficult to be constistantly producing good results, which is needed to climb higher and higher in the rankings.

A couple of excamples from last season:

Both Kulizjnikov (500 m) and Kramer (5000 m) are winning almost every race they compete in.
Kulizhnikov's ranking was 2374 at the start of the season. With a lot of wins and one disqualification, his ranking was 2378 at the end of the season...
Kramer's ranking was 2409 at the start of the season. He won every single World Cup and also the Wch, and so he is at 2470 at the end of the season. The climb is quite impressive, when you consider how high he was already when the season started.

But when (not if!) Kramer begins to lose, he will move downwards very fast, because he has such a high rank right now.

I like the idea of using ELO ratings in skating, but there are some important drawbacks compared to chess.

-The number of competitors and the number of observations per competitor are much lower in skating than in chess, leading to very volatile ELO estimates.
-There is a large correlation between observations since when you win in skating, you beat many players at once, rather than just one (as Celebithil indicated).
-The influence of mistakes in skating are much larger than in chess (you will lose against many players at once, rather than just one).
-A major drawback is that it is challenging to empirically test the validity of your model due to the limited number of observations per year. Maybe you can test whether skaters with differences of approximately 100 ELO points have the correct winning percentages against each other; there may be enough data points to test that. You could use that to test the values of k.