I decided to investigate how important breaks between matches were for team performance. If the effect of rest is large enough, I thought I might add it into my Elo model. I was originally going to use the match start times as the basis, but after finding serious problems with this data set, I switched to using scheduled start times.
Essentially, what I did was to give each team on each alliance an Elo penalty which was determined by how much “rest” they have had since their last match. I tried both linear and exponential fits, and found that exponential fits were far better suited to this effort. I also used the scheduled time data to build two different models. In the first, I looked at the difference in scheduled start times for each team between their last scheduled match and the current match. In the second, I sorted matches within each event by start time and gave each match an index corresponding to its placement on this list (e.g. Quals 1 has index 1, Quals 95 has index 95, quarterfinals 1-1 has index 96, quarterfinals 2-2 has index 101, etc…).
The best fits for each of these cases were the following:
Time difference: Elo penalty per team = -250exp((t_current_match_scheduled_time -
Match index difference: Elo penalty per team = -120exp((current_match_index -
Both of these models provide statistically significant improvements to my general Elo model. However, the match index method provides about 7X more of an improvement than the time difference method (Brier score improvement of 0.000173 vs 0.000024). This was surprising to me, since I would have expected the finer resolution of the times to provide better results. My guess as to why the indexing method is superior is due to time differences between quals and playoff matches. I used the same model for both of these cases, and perhaps the differences in start times is not nearly as important as the pressure of playing back-to-back matches in playoffs.
I have attached a table summarizing how large of an effect rest has on matches (using the match index model).
Playing back to back matches clearly has a strong negative impact on teams. This generally only occurs in playoff matches between levels. However, its effect is multiplied by 3 since all three alliance members experience the penalty. A 3-team alliance who just played receives a 80 Elo penalty relative to a 3-team alliance who played 2 matches ago, and a 108 Elo penalty relative to a 3-team alliance who played 3 matches ago. 108 Elo points corresponds to 30 points in 2017, and the alliance that receives this penalty would only be expected to win 35% of matches against an otherwise evenly matched opposing alliance.
The match index method ended up providing enough improvement that I am seriously considering adding it into future iterations of my Elo model. One thing holding me back from using it is because it relies on the relatively new data of scheduled times. At 4 years old, this data isn’t nearly as dubious as the actual time data (1.5 years old), but it still has noticeable issues (like scheduling multiple playoff replays at the same time).
You can see the rest penalties for every 2017 match in the “2017 rest penalties” document. The shown penalties are from the exponential fit of the match index model.