Here are two questions that persist in ultimate.
(1) Your team won the flip. Should you take offense, defense, or the wind?
(2) Your team won the flip. How valuable is this outcome on your chances of winning a game?
For the first question, barring any unusual circumstances, a team should select offense or choose to go downwind. And for the second, well it depends.
This 6-part series will highlight which choice to make and how valuable this choice is depending on various assumptions. Instead of just thinking through the issue, I will try to put some numbers behind the decision and its impact.
How to read this series?
I admit that I am writing a lot about the topic in this series (6 parts — am I crazy??). My goal for each part in this series is to (a) suggest a decision that coaches or captains should make to start a game and (b) provide statistical evidence for the impact of that decision. If numbers and stats bore you and you want to skip ahead, go straight to the conclusion (Part 6) for a high-level summary of my findings.
There are a lot of numbers and tables provided throughout. The reason is that this allows you to test different assumptions and see what the data show. You DO NOT need to read all the numbers to get the main takeaways from this series. They are provided for curious readers to dig deeper and test the results with different assumptions.
Lastly, I am not a trained data scientist, but I do have a base level of statistical knowledge from graduate school coursework. I wrote this series to share my curiosity on the topic, and I would really value feedback and ideas on other areas to explore further.
The “Receive vs. Pull” question has persisted in ultimate at all levels. As a captain for both college and club teams, I can tell you that there has been disagreement on each team I’ve played for. From my experience most recently in the club open division, I observed that most teams will choose to “receive” if they win the flip. But, there are top teams that consistently still choose to “pull” if they win the flip.
There are various claims that you can find in ultimate circles that will stipulate on why pulling or receiving is the best choice. Here are a few of the most common as well as a few that are more ridiculous.
- “Always start on O. If each team has the same number of breaks, you win.” This is true, but only if the team that starts on O takes half. If the team that starts on D takes half, that team will win the game if both teams have the same number of breaks.
- “Pick defense. You can get an extra break if you take half.” Yes if you start on D and take half 8–7, then your opponent must get two additional breaks to beat you. But, wouldn’t you rather start on O and take half 8–6 (your team is +1 on breaks just like the previous example)? I would.
- “Start on D. Stay on D.” This one appears more about team attitude and motivating players than it is about addressing the question with any rigor. If your team can pull off eight consecutive breaks to start a game, you probably are good enough to win regardless of your decision to pull or receive.
- “Pick offense. If the o-line doesn’t get broken all game, then we can’t lose.” Can’t argue with the logic, but how many games have zero breaks?
Let’s take more of a statistical approach. Do both teams have a 50% chance of winning regardless of the decision? How valuable is winning the flip in a heavy upwind/downwind game? Can we estimate the value of winning the flip?
Simulations — Methodology
The data in succeeding parts were created from a model to simulate ultimate games based on a certain probability for each team to score an offensive point.
- Every point is simulated to determine if Team A scores depending on the following inputs.
- “Receive” — Team A is receiving or pulling this point
- “O Prob” — Team A’s probability to score an offensive point. Note this is not the probability to score a possession, but instead the probability to score a point.
- “D Prob” — Team A probability to score a defensive point if they are pulling.
- “Downwind” — Adjusts Team A’s offensive or defensive probability to score a point based on if Team A is attacking downwind or upwind.
- The model leaves out certain inputs to each point. The model assumes that a team’s probability to score an offensive point is the same regardless of what the score is in the game, the outcome of the previous point, or how early or late in the game it is.
- The model can simulate the results of a game that has an upwind/downwind component meaning that a team’s offensive probability to score is improved when going downwind and decreased when going upwind.
- The model is used to simulate a large enough sample of games to determine what the probability is for a team to win a game to a specific score based on the offensive probability for each team.
- The results of the simulation are not absolutely precise for each scenario. There is a confidence interval around each result. Despite, this we can still make conclusions with statistical certainty and evaluate the trends in the data.
The takeaways from the simulations are dependent on accepting the assumptions to the model. There are rational arguments on why these assumptions are invalid. Factors such as momentum, team depth, team identity, and many others could affect how the flip decision is made for each team. Regardless, I believe this is a valuable tool to use when making your decision to start a game.
Comparison to Other Sports
Ultimate is not unique in the decision facing teams after a flip. We can look to other sports and how the analytics community has measured the value of making this decision.
- Football (NFL) — The NFL has an interesting overtime rule set. A coin flip determines who starts with the ball. A touchdown on the first drive ends the game, a field goal provides the opponent a drive to prolong the game, and if there is no score on the first drive then the next score wins. Based on ESPN’s win probability model, winning the flip in overtime increases a team’s chances of winning from 50% to 53.8%. A 538 piece from Dec. 2015 measured that since the new OT rules were adopted in 2012, the team that won the OT coin flip won 51.5% of games. For the coin flip to start an NFL game, most teams now choose to receive. This article points out that 53% of teams winning the opening flip and deferring end up winning the game.
- Football (NCAA) — The NCAA has different overtime rules. Teams alternate possessions from the opponent’s 25 yard line in each overtime. Here, the coin flip can be very consequential. The following paper does a deep dive into the topic. I quibble with the author’s methodology of using the outcome of the first offensive possession in overtime in his model. But empirically, he shows that teams that start on defense first in overtime, win at an expected rate of 55%.
- Tennis — In tennis matches, there is a coin flip to determine who serves first in the first set. The rule of thumb is to always serve first if you win the flip. IBM’s Big Data Hub posted an extensive report on the value of this decision. The conclusion was that there is no statistical advantage to winning this pre-match flip.
Still with me? Let’s dig into the data for limited wind games in Part 2.