Ranglijsten beste prestaties 2015/2016

There certainly are drawbacks. I should mention that the most important thing for me was to find a better model than the one I used before, which was based on World Cup points.

In fact I have sort of tested the model, but not in the way that you suggest.

I used the different skaters ranking points to estimate their chance of winning the next race, for example at a world cup. The model used to estimate those winning chances came quite close to the actual results (winning probability).

So I think for the moment I will stick to the model. Changing it once again will be a bit more time-consuming than I can afford...

I haven't been able to follow the explanation here, so I have a couple of questions:

Is this the "top level" of those skaters, or is it some kind of "average" level - and if so, which races are counted in?

Sure, I'm not asking you to change your model, just making sure that the drawbacks are clear. As I said, in essence I like the idea.

Testing winning probabilities also seems a good way to test it, I like that. If it's simple to do so, I would still test the winning probabilities against rating differences. Now you only tested the top competitors, but with that test you also check validity for lower to mid-tier competitors. If that test also gives good results, you have more evidence for validity of your model than now.

Top level, not average. I've counted World Cup/WCH/OG races, and sometimes a National Championship.

I'll explain - In English - how Pavel Kulizhnikov's 1:06.70 is corrected (note ø):
In November 2015, Pavel skated 1:06.70 at the Utah Olympic Oval in Salt Lake City. The track is has a height of 1425 meters, and at that height, the average air pressure is 854,2 hPa. At sea level, that value is 1014 hPa. After height correction, you get 1:08.49. Which means, if this race would be at sea level instead of at 1425m, this race would be 1:08.49. Then air pressure correction. The SLP was quite high: 1028 mbar. No, SLP doesn't mean Sverre Lunde Pedersen here, but Sea Level Pressure. That's the air pressure corrected to sea level. With normal (lower) air pressure, Kulizhnikov would have skated faster. @SprintMaster's model corrects it to 1:08.19, my model to 1:08.12 (note 1). Now some different things kick in, such as track speed correction. Comparing to Heerenveen in season 15/16, SLC is 0.18% slower than Thialf if the two rinks would have been at the same height. (note 2). So I have to multiply 1:08.12 with ((100-0,18)/1000). Then you get 1:08.02. Now we still have to correct for two things: the first one is average season speed. That's how fast is skated in the competitions in that season and some previous seasons, based on values as seen in note 2. Here is this value 1:09.28, which affects Kulizhnikov's time with only 0.02. If it would have been 1:10.28, it would affect the time with half a second. This way, you can correct for things like clap skates, as the average season speed was a lot slower back then as skaters were in fact slower. Last thing: skater-specific factor. This is a correction for how much a sporter likes to skate on highland or lowland. For that, I compare uncorrected PRs of the skater to the 5 fastest time on highland and on lowland ranks. Kulizhnikov hasn't really a preference as he skates extremely fast on both, so his value is so close to 1, that it doesn't affect his time anymore. (This factor is almost never bigger than 0.15%. Track factors are sometimes 2 or 3% on outside tracks.) After all the corrections, his time is 1:08.00.

Note ø: I cån't spæk Norwegian, thøugh I'd like to be åble to dø that. / Jeg kan ikke snakker Norsk, men jeg vil det reelt sett. (is that correct?)

Note 1: my model corrects more with higher speeds. If his time was 1:17.70, SprintMaster's model would correct more than mine.

Note 2: this is based on the biased top-10 average (BTA). The formula defining the BTA is
BTA=(100*B4+80*B5+70*B6+60*B7+50*B8+45*B9+40*B10+35*B11+30*B12+25*B13)/535
when the no.1 time is in cell B4, no.2 time in cell B5, etc. I use height correction on the BTA's. When averaging BTA's of multiple competitons on the same track, you can essentially see how fast a track is. By comparing it to other tracks, you can see how much faster or slower track A is than track B. That's how I get my track speed correction factors.

This is truly interesting stuff! It feels like I've entered a club of extreme nerds. A few more questions:

• height corrections and air pressure corrections - are those theoretically calculated? Or empirically? Incidently, in my model a time of 1.06,70 at SLC equals 1.08,65 at Thialf. And if the SLP was 1028 in stead of 1013,25, my models gives an air pressure correction of only 0,15 - to 1.08,50.

• track speed corrections and average season speeds are based on the top 10 times of the tracks / seasons? But wouldn't these results be affected by the fact that some tracks are used more than others to big competitons?

• skater-specific factor. So if a skater normally is better at slower tracks, he gets extra rewarded if he for once skates a good race at a fast track? This doesn't seem logical to me.

My all time ELO lists aren't really published on the Skøyteranking site yet, but it is tempting to give you a sneak view:


fullt navn land tid bane dato
K. Nuis NED 68,24 Heerenveen 29.12.15 2241 (1.08,12)
S. Davis USA 66,91 Calgary 06.12.09 2234 (1.08,15)
P. Kulizjnikov RUS 68,16 Heerenveen 12.12.15 2230 (1.08,16)
S. Groothuis NED 68,39 Sotsji 12.02.14 2177 (1.08,36)
D. Morrison CAN 68,43 Sotsji 12.02.14 2166 (1.08,40)

Fun to see that I have the same top 5 as you, but only PK in the same position!

Nice try... A better version would be: Jeg kan ikke snakke norsk, men jeg skulle gjerne ha kunnet det. Or:

Jeg ønsker virkelig at jeg hadde forstått norsk. Kanskje jeg kan lære noen norske setninger? / I really would like to understand Norwegian. Perhaps I can learn some phrases?

@Skøyteranking
To add in some confusion, my model is different than @SprintMaster's model.

This is my model:


E3: corrected time=H3^0,8*L3*R3*(1-((((1000/M3)^4/(120376))^1,1*((((K3-1014)/1014))))))*(M3*((((-J3+1014)/1014)*100*0,17)/100+1))
L3: sporter specific factor=((S3*I3+3+T3)/4)
O3: highland sporter factor=(N$2/N3)
Q3: lowland sporter factor=(P$2/P3)
R3: season speed value=((1+((69,16+0,075)/S1))/2)
S3=(O3-Q3)/900
T3=(Q3/O3)

With
H3=rink factor
I3=rink altitude
J3=average rink pressure
K3=sea level pressure
M3=not yet corrected time
N3=highland PB
P3=lowland PB
N$2=average of five best highland times in the world (that's for 2005/2006 of course a different value than for 2015/2016)
P$2=same as N$2, but fot lowland


E3 Formula explanation:
I multiply the not corrected time with
(rink factor)^0,8
originally, the rink factor was too influencing, so I added in that ^0,8
sporter specific factor
that's that thing whether a sporter prefers highland or lowland
season speed value
how fast usually was skated back then when the time was skated, explained in previous post
(1-((((original time)^4/(120376))^1,1*((((SLP-1014)/1014))))))
this is my air pressure correction model. Corrects more at higher speed, and gives imho more plausible results. I'll explain it more clearly if you want, and if I'm able to. It took me a few hours to get to this thing...
((((-average rink pressure+1014)/1014)*100*0,17)/100+1))
same as in @SprintMaster's model, but with 0.17 instead of 0.166.

It's understandable. Anyway, this goes far above my head already...!

But to summarize, it seems to me that your model(s) gives more credit to times from high altitude than mine, which of course is embarassingly simple compared to yours. But just like you, my correction factor for altitude is higher for the 1000 and 1500 m than for the other distances:

(500) 3,032
(1000) 3,345
(1500) 3,797
(5000) 2,16
(10 000) 2,011

(ladies 500) 2,936
(1000) 3,37
(1500) 3,17
(3000) 2,562
(5000) 1,63

This sounds reasonable. Håvard Bøkko has been the national champion six times, but never really give his full "attention" to the 1000 m.

Pavel Kulizhnikov 1:08.10 Stavanger
Pavel Kulizhnikov 1:08.10 Stavanger
Kjeld Nuis 1:08.12 Stavanger
Kjeld Nuis 1:08.13 Stavanger
Pavel Kulizhnikov 1:08.16 Heerenveen

1: that's the BTA for Heerenveen for season 15/16 (I've used 11/12 till 15/16 BTAs to calculate that). It's used for determining the track speed factor. I've explained the BTA in a previous post, which I'll quote again
2: no idea . Removing that makes all times ±0.04 faster, but doesn't change a lot.
3: that one is speed dependent.
(1-((((1000/M3)^4/(120376))^1,1
The values resulting from this formula are around (1-0.34) as in your old model on which I based mine, the air pressure correction value was 0.34 instead of 0.243.


BTA explanation incoming!

So the 1000m men BTA for Heerenveen for 15/16 = (1*(BTAs of all 1000m men competitions in 15/16)+0.75*(BTAs of all 1000m men competitions in 14/15)+0,55*(BTAs of all 1000m men competitions in 13/14)+0,38*(BTAs of all 1000m men competitions in 12/13)+0,25*(BTAs of all 1000m men competitions in 11/12))/(1*(amount of 1000m competitions in 15/16)+0,75*(amount of 1000m competitions in 14/15)+0,55*(amount of 1000m competitions in 13/14)+0,38*(amount of 1000m competitions in 12/13)+0,25*(amount of 1000m competitions in 11/12))

I have accepted your challenge! But I'm a little bit confused (or should I say depressed) about the results:



I have used rankings as of December 2015, and tested how skaters with 10, 20, 30 etc. points more than certain opposing skaters did against those skaters in races throughout the 2015/16 season. The winning probability was ecpected to follow the blue line, but in fact was observed to be quite a bit higher (orange dots). The number of observations aren't very high for each level - mostly from 20 to 30. But I'm troubled by the facts that it (almost) consistantly lies above the blue line of expected probability.

This was a test using rankings as of Dec'15. I will do a new test using the newest rankings (March'16), and this time only with 100 points difference. I'll get back to you!

- A sigh of relief!

At least, the result of this new test was more convincing than the first one.

94 observation of "duels" where the best skater is ranked 100 points better than the weaker skater (post-season ranking).

100 points better ranking equals winning probability of 1/(1+10^((-100)/400)) = 0,64. The observed probability of 0,66 is reasonably close, so I guess the system goes on without any corrections next year.

Thanks for carrying this out.

With that last test you check the March ratings against races skated before March. Since the March ratings are highly correlated with those races, the winning probabilities should be almost correct. Clearly, something would be wrong with the model if it is unable to predict the historic observations with which it has been estimated (I expect that the same will also hold for lower differences if you test it like this).
That by itself does not imply that the model is valid, by the way.

I do find the bias when predicting future observations, as you showed in your first test, rather troublesome and I'm wondering what causes this. Will the estimates be better if you update the ratings after every race rather than taking the December ratings?

I will do some further testing. It's off season, anyway...

That would be awesome. If properly tuned, the ELO-method can be a strong tool for predicting winners. That is something that cannot be done with the corrected times of Sprintmaster and EenBrabander, so it would be a very welcome addition to the set of available tools.