You either made it through all the parts (and I commend you) or you skipped ahead to the conclusion. Either way, let me summarize some key points that I am taking away from this analysis.
- Part 2 — Winning the flip and receiving gives a team approximately a 1.4% advantage in win probability (50.7% vs. 49.3%) over their opponent. This assumes even teams, game to 15, and both teams’ expected offensive hold rate is 75%. This advantage varies based on the assumptions you select.
- Part 3 — Take the wind as opposed to offense in most upwind/downwind games. If you win the flip, you need to determine how large the advantage is scoring upwind vs. downwind. Based on this, you should either select offense or the wind.
- Part 4 — If your opponent takes the wind, start the game on offense. If it’s an upwind/downwind game, you are better off starting on offense going upwind as opposed to starting on defense going upwind.
- Part 5 — If you are trying to pull a big upset, still start on offense. Starting on defense does not produce higher win probabilities for an underdog.
Of course, these principles do not apply universally to all ultimate games. Individuals making decisions for their team need to consider a wide range of other factors and the impact on their team’s performance. I offer these conclusions as guidelines and a tool for making game decisions.
Should we change the rules of the flip?
One thing I was considering as I did this analysis is whether or not the existing rules for the start of the game are fair. In games that have a heavy upwind/downwind component, winning the flip can have a significant advantage.
Personal Example (… and yes I’m still bitter)
My freshman year playing for Ohio State, we lost in the Great Lakes Regional final to Michigan State 17–16. That day in Naperville, IL in 2006 was the worst ultimate conditions I’ve ever witnessed. Out of 33 points in the game, each team scored only once upwind. So only 6% of the points were scored upwind that game.
If we assume that each team had a 5% chance to score upwind points that means that winning the flip pushed Michigan State’s probability to win the game to 65.5%. And Ohio State’s win probability decreased to 34.5% by losing the flip! (See Part 3 for simulation data corresponding to these win probabilities). This is a huge swing in win probability from the flip! (Way to not throw your “Fire” Geoff)
Rule Change Proposal
What if we did the following? In place of the flip, team captains have an auction to start the game. Assume both teams want to start the game going downwind. The auction works by granting the team starting upwind a guaranteed number of points on offense to start the game. Both teams simultaneously submit their bid of the number of points that they need to start on offense in order to prefer starting the game going upwind.
- Example A — consider a heavy upwind/downwind game with 15+mph winds. If Team A bids 7 and Team B bids 9, then Team A would start the game going upwind. For the first 7 points of the game, regardless of the previous points’ outcome, Team A would start on offense. The attacking endzone would change as always each point. Team B would start the game going downwind.
- Example B — consider a game with a moderate upwind/downwind component (5–10mph winds). Team A would prefer to start downwind but is not willing to start multiple points on defense. Team A therefore bids 1. Team B does not believe the wind will affect them and is willing to start on offense either direction. Team B therefore bids 0. The outcome is that Team B starts on offense going upwind. No succeeding points are affected as far as which team pulls.
- Example C — consider a modest game with relatively no wind. Since both teams would like to start on offense, they both bid 0. With a tied bid, a flip ensues as normal under current rules.
This bidding process would help nullify the huge advantage of the flip in these heavy upwind/downwind games. In addition, I think it would be absolutely fascinating to see how teams approach the auction. I don’t expect USAU to ever adopt this rule due to the confusion it will cause, but I think it is an interesting approach to experiment with.
So where do we go from here? As more empirical data is collected, it will be great to estimate offensive hold rates for different divisions of play to determine the exact advantage of winning the flip. In addition, I am really interested in coordinating wind measurements with point-by-point game data in various tournaments.
The more data the better. If you have collected any point-by-point data and would be willing to share, please reach out to me.
Also, if you’re still interested in reading further, check out the Appendix section with empirical data from a few different data sets (WUGC 2016 & AUDL 2014–2016).