# Receive or Pull? Part 3 — Take the wind! (usually)

Upwind / Downwind Games — Even Teams

This is Part 3 in a six part series.

Part 1 | Part 2 | Part 3 | Part 4 | Part 5 | Part 6 | Appendix

Team Decision: It is common that ultimate games are played in windy conditions. Some windy conditions do not impact an offense’s probability of scoring in either end zone. But some games have a distinct upwind end zone and a downwind end zone. In these games if you win the flip, should you take the wind or start on offense?

Takeaway: With a strong enough wind, you should select to start downwind. The chart below gives a rule of thumb about the threshold of when you should select offense to start the game or attack the downwind end zone to start the game. This chart assumes even teams, so each team has the same expected downwind and upwind offensive probability per point.

Simulation Data

The tables below show the probability of a team winning a game against an equivalent opponent with different probabilities for the offensive team to score based on the direction they are attacking.

Probability of Winning a Game to 15 — Results

The first table provides data that show the probability of winning if a team receives the disc going upwind to start the game. This table should be used to think about the question, “so we won the flip, do we take the wind or start on offense?”

As one would expect, there is a threshold in upwind offensive probability that a team should choose the wind over receiving the disc. This threshold is highlighted by the black border in the table. Using the simulation results, a team should select the wind to start the game where the win probability is shown in red.

The second table shows the probability of winning if a team is receiving downwind to start the game. The results are not surprising. I would be hard-pressed to find anyone that would not want to receive downwind if given the chance.

How to read the tables?

• Columns — Each column corresponds to both teams’ probability to score an offensive point that they start going downwind. For example, the “0.90” column simulates games where both teams have a 90% probability of scoring every downwind offensive point.
• Rows — Each row corresponds to both teams’ probability to score each upwind offensive point. For example, the “0.60” row simulates games where both teams have a 60% probability of scoring every upwind offensive point.
• Values — The data in each cell of the table show percentage of games that the team receiving to start the game wins based on both teams’ probability to score each downwind offensive point and upwind offensive point. Each scenario was simulated 250,000 times.

Notes

• The reason for the cone shaped tables is that both teams’ upwind offensive probability per point should not be more than (1 — downwind offensive probability). For example, if both teams score with 80% probability on their downwind offensive points that means that they score 20% of their upwind defensive points. It doesn’t make sense to simulate games where their upwind offensive point probability is less than their upwind defensive point probability.
• For games to 15, 13, and 11, I show simulations for teams receiving downwind to start the game as well as receiving upwind to start the game. The latter includes much more interesting results.
• All results are comparing teams that have the same offensive probabilities to score both upwind and downwind. Think of this in that you are playing a game of two identical teams.
• The values in the tables are estimates of what the true probability is for each scenario. For each scenario, 250,000 games were simulated and therefore the values in the tables have a 95% confidence interval of +/- 0.2% when the win probability is 50%.

Reading the Tables — Examples

• Look at a game where both teams have a probability to score 80% of their downwind offensive points, and both teams have a probability to score 70% of their upwind offensive points. This would be a game with a mild upwind/downwind component due to the difference in downwind versus upwind offensive probabilities. The simulations show that team starting the game on offense receiving going upwind wins these games 50.3% of the time. The team winning the flip in this type of game should choose to start the game on offense.
• Take for example another game that has a much heavier upwind/downwind component. Both teams have a probability to score 90% of their downwind offensive points, and both teams have a probability to score 50% of their upwind offensive points. The simulations show that the team starting on offensive going upwind wins these games only 47.7% of the time. Therefore, the team winning the flip in this type of game should choose to start the game attacking downwind.

Analysis

From these results, a few things came to mind.

• In most games with a downwind/upwind component, the data show that starting the game attacking downwind is preferable to starting the game on offense. For example, if both teams have the probability of scoring 80% (or 4 out of 5) offensive points, it only makes sense to start on offense if you think both teams have a 70% or higher probability of scoring each upwind offensive point.
• For games with a significant upwind/downwind component, the impact of winning the flip is huge. Take a game with very strong wind. Assume that both teams score only 1 out of 10 points upwind regardless if they start on offense or defense. This corresponds to “0.90” downwind offensive probability and a “0.10” upwind offensive probability. Winning the flip increases a team’s probability of winning to 53.5% and losing the flip decreases a team’s probability of winning to 46.5%. That’s a 7% swing in win probability. This impact is even bigger for games capped or played to 13.

Impact of winning the flip — Increase in team’s probability of winning the game

So if your team wins the flip and you correctly choose to start on offense or attack downwind to start the game, how big of an impact is this on your team’s probability of winning the game?

The table below shows the difference between the team’s win probability that won the flip and the team’s win probability that lost the flip.