# Paper: Miscellaneous Statistics Projects 2018

I decided to take another look at the hypothetical “serpentine valley” I investigated last year. Back then, I was more interested in if teams going into an event had an incentive to perform worse than their ability. I found that if there was a so-called serpentine valley, it was very small and centered around rank 10.

Here, I did a similar investigation using end of event rank instead of start of event Elo. A serpentine valley here might indicate that teams in matches near the end of the quals might be incentivized to get fewer RPs if they want to maximize their chances of winning the event. Here is a book with that data as well as a summary sheet: serpentine_valley_v2.xlsx (1.4 MB)

I pulled rankings and results from all events since 2008. Which gave me a sample size of about a thousand events. I found how many event wins and how many wildcards were achieved from each ranking position, and dividing those by the number of events where a team got this rank gives us a win and win/wildcard probability from each rank. Below are graphs summarizing that data:

These graphs actually look remarkably similar to the pre-event Elo graphs from my earlier work. The “serpentine valley”, if it exists at all, is centered around rank 8 or 9. For reference, the gap between rank 8 (bottom of the valley) and 10 (top of the valley) is 1.1%, jumping from 3.8% to 4.9%, or about 12 out of 1000 events. This is much smaller than I probably would have expected, and that is the lowest point compared against the highest point. Comparing rank 7 or rank 9 to rank 10 is nearly identical. The “valley” that we are seeing could feasibly be largely noise, as there are larger “valleys” at ranks 15 and 23, and I have no reasonable explanation for why there would be dips around those ranks.

My takeaway is that this methodology really doesn’t provide evidence that any reasonable number of teams are incentivized to throw matches. That doesn’t mean those incentives don’t exist, just that you’d really have to dive much deeper into the data to prove that they actually do. Maybe someday when I add alliance selections into my event simulator I’ll revisit.