Elo-like ratings for ZakStunts: The Folyami Project

[Duplode]

Here are the ratings after ZCT277! In a round of big point swings, race winner Alan halved the gap to the second place. Mortimer McMire reached a personal best, while satanziege has returned to the current ranking. This is the updated evolution chart:

[Duplode]

Here is the ZCT278 update of the ratings! Resting champion Argammon has ceded the first place of the current ranking, after ten months in the lead. Mortimer McMire has attained a personal best rating, while HunterBoy344 has joined the rankings for the first time. Below is the updated evolution chart:

[Erik Barros]

I'm trying to make a triangle waveform 

[Duplode]

Here is the ZCT279 update of the ratings! Personal best ratings were attained by the Am League title contestants, Mortimer McMire and Ryoma, who also had the two biggest positive rating changes in the round (+70 and +29 respectively). We also had two new entries: Alecu and Stein Viterbo. Below is the updated evolution chart:

[Duplode]

I have the feeling there is rating inflation going on.

It Would be nice if you could look into the issue more thoroughly then I did. 

Sure! Later I will rerun some diagnostics involving global properties of the ratings. These can be tricky to interpret given how the pool of pipsqueaks is always changing, but they might provide some signal on whether there's something unusual going on.

I've finally managed to get back to this. Inflation can be a tricky thing to diagnose, as there are so many ways to slice the data, so here are a few different ways to look at the global evolution of the ratings.

The most intuitive thing to check, perhaps, is the mean rating at each race of everyone in the current ranking (which covers those pipsqueaks with a included race entry over the previous four rounds):



While closer analysis could be merited, at first glance there aren't obvious signs of systemic inflation or deflation. The long-term shifts that do exist can be attributed to the evolution of the competition as a whole:

• Once the ratings stabilise in the first few seasons, the mean rating initially settles around the upper 1600s, and for the most part stays there up to 2007.
• After that, somewhere around 2008 we enter what I like to call The Middle Ages, an era of few newcomers and relatively small scoreboards, mostly occupied by experienced pipsqueaks that under today's rules would have already graduated from the Am League. To pick just one example, ZCT133 in August 2012 featured twelve pipsqueaks, all of them already having reached the podium by that time. Under such circumstances, the mean rating went up to the 1700s and at times even beyond, mostly due to a shrinking pool of newbies and upcoming competitors.
• A long transitional period follows in the late 2010s. Once we reach the current decade, things have settled down again, and the mean rating is back to the 1600s range.

Another way of looking at the evolution is focusing on a specific position in the current ranking. For instance, below is the rating of the sixth-placed pipsqueak (starting from 2003 so that the unrepresentative low values from the first few races don't mess up the chart):



This gives us a different perspective, which has more directly to do with the depth of the field. Still, there is no continued growth of the sixth-place rating, which typically oscillated around 1900 (up to the Middle Ages) or 1850 (in the current era).

Looking at the current ranking probably gives us a perspective better attuned to the action on the racetrack at any given moment. What about the overall pool of pipsqueaks, though? Below is the evolution mean rating of all pipsqueaks, including those that haven't made it to the ranking due to having fewer than five included races:



Rating changes in the Folyami system don't add up to zero because of provisional status, which makes ratings change faster for pipsqueaks with less than twelve races. The direction of the global change depends on which share of those newcomers succeed in getting strong results and improving their ratings. That being so, a slow decrease of the global mean is expected.

Lastly, for something of a compromise between looking at the current ranking mean and the global mean, we might try looking at the mean rating across pipsqueaks that have made it to historical ranking (that is, which have at least five included races and thus made it at least once to the current ranking):



That looks remarkably stable, with the mean having remained pretty much static throughout the Middle Ages, and seeing only a very mild downward shift in the last few seasons.

[Duplode]

Time for the November update of the rankings! Before that, a feature announcement: as promised a few months ago, an interactive full history graph is now available! You can also download the CSV with the ratings from the same page.

On to the ZCT280 rankings themselves: by flying on an Indy to the top of the podium, Argammon has not just retaken the current ranking lead while setting another personal best, but also taken the second place in the historical ranking! The previous change of positions in the historical podium had been in 2016, and the last time someone had newly reached it was in 2009. That's not something you'll see every day. Congratulations Argammon!

It was a busy race elsewhere in the current ranking, too! Besides Argammon, Mortimer (+82 change!), Ryoma and Spoonboy (reaching the 1900 points milestone) have reached personal bests. Last but not least, Chulk has returned to the competition, and to the current ranking -- welcome back!

Below is the updated evolution chart:

[Duplode]

A small but useful update to the Folyami graph: the legend is now sorted according to the current ranking. That helps with something @alanrotoi asked for a long time ago: a convenient way to check past rankings. Now you can hover the mouse over (or touch) any chosen race (to make that easier, use the handles under the chart to zoom into a smaller range), and the legend below will, in effect, display the ranking: