# Receive or Pull? Part 2 — Take the Disc!

Limited Wind Games — Even Teams

This is Part 2 in a six part series.

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

Team Decision: So you are playing against a team of equal caliber and you win the flip. It’s not windy. Should you choose to pull or receive?

Takeaway: Assuming no wind, you should receive. And if you assume even teams and each team has an expected probability to score 75% of their offensive points, the impact of this decision swings your team’s chances of winning by 1.4%.

The plot below shows the probability of winning a game to 15 against an equal opponent for various assumptions of the probability each team scores its offensive points. These data in the graph and more are included in the subsequent sections below.

Simulation Data

The tables below show the probability of one team (Team A) winning a game to 15 depending on if they choose to receive or pull to start the game.

Probability of Winning a Game to 15 — Results

The results from these simulations show that there is a small advantage to winning the flip and deciding to start on offense. If we assume teams are the same and that teams have a probability of scoring 75% of offensive points, then starting on offensive increases a team’s chance of winning the game by 0.7% and consequently choosing to start on defense decreases a team’s chance of winning the game by 0.7%. Here is further breakdown.

• The team that starts on offense now has a 50.7% of chance winning the game.
• The team that starts on defense now has a 49.3% chance of winning the game.

• Columns — Each column corresponds to Team A’s probability to score each point that they start on offense. For example, the “0.55” column simulates games where Team A has a 55% probability of scoring every offensive point.
• Rows — Each row corresponds to the difference in Team A’s probability to score each offensive point relative to their opponent, Team B. For example, the “Same” row simulates games where Team A and Team B are equal teams since they have the same probability of scoring each offensive point. The “-0.02” row simulates games where Team B has a probability of scoring offensive points 2% more often than Team A does.
• Values — The data in each cell of the table show percentage of games that Team A wins based on Team A’s probability to score each offensive point and Team B’s probability to score each offensive point relative to Team A. Each scenario was simulated 250,000 times.

Notes

• If a team has a 75% probability of scoring an offensive point, this is equivalent to flipping two coins every point. If both coins come up heads, the team is broken. All other flip outcomes result in the team scoring their offensive point. The simulations repeat this process for every point, for every game to determine the win probability for a game scenario. The 75% probability does not mean that the team scores exactly 75% of its offensive points every game in the simulations. With an expected probability of 75% for offensive points, the simulations will result in games some times where a team scores only 60% of its offensive points or 90% of its offensive points.
• 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%.
• I find the row titled “Same” to be most interesting. If you assume two teams are equal, this shows the value in selecting to receive to start the game. You can assume different probabilities that each team scores each offensive point.

• For the first table, If you look at the “Same” row and “0.75” column, this shows that Team A has a 50.7% of winning a game to 15 if they choose to receive to start the game. Both Team A and Team B have a 75% chance of scoring each offensive point.
• For the first table, if you look at the “+0.02” row and the “0.75” column, Team A is estimated to have a 55.8% chance of winning a game to 15 if they choose to receive to start the game. Team A has a 75% chance of scoring each of their offensive points and Team B has a 73% chance of scoring each of their offensive points.

Analysis

From these results, a few things came to mind.

• A small increase in your team’s probability of scoring offensive points (or decrease in your opponent’s offensive probability) has a sizeable increase in your team’s probability of winning the game. If your probability of scoring offensive points is just 3% higher than your opponent, you can increase your odds of winning by 6–10% (depending on your offensive probability assumption).
• If you are pulling to start the game, should you move a starter from the o-line to the d-line to reduce both teams’ offensive probabilities to score each point? I would think that these changes may not reduce both teams’ offensive probabilities per point the same amount. You should be assembling your lines to maximize offensive and defensive efficiency to win games regardless if you pull or receive to start a game.

Probability of Winning a Game to 13 — Results

Often ultimate games are only played to a winning score of 13. The tables below show the probability of one team (Team A) winning a game to 13 depending on if they choose to receive or pull to start the game. As expected, the trends are the same as games played to 15 but have a slightly larger advantage to starting on offense.

Selection Bias — Taking Half + Winning

Something to consider when trying to match these results to your intuition is selection bias. When teams start on defense and take half, they are more likely to win compared to a team starting on offense and taking half. This is obvious but I think this may push some to believe that starting on defense is better than starting on offense. It may be due to their selective recollection of winning games when they took half starting on defense. Here’s a breakdown to think about this further.

For the 250,000 simulations in the first tables (game to 15 or 13 — Team A receiving), the following are the probabilities of each team taking half, winning if the team takes half, and winning all games.

A team starting on defense and taking half wins games about 6% more frequently than teams starting on offense and taking half. This 6% advantage may push some to believe starting on defense is advantageous. Don’t be fooled by this.

But what if it’s windy?? Check out Part 3 in the series.