Win Probability for Professional Matches

Introducing a new way to examine how likely a team is to win a Rocket League game, win probability. This information was collected and calculated by Squirrel Dude, which he supplied to Octane. You can find the win probability chart here.

I decided to do this while tracking how often teams won after scoring first over the past two seasons. Although that type of information can be mildly useful, it’s extremely limited. Win probability greatly expands on those statistics in terms of scope and precision.

Anyone familiar with professional sports will recognize that win probability is not a wholly new concept. It’s been a tool used by analysts covering every major sport for years. Although the rapid pace of Rocket League games prevents a win probability model from ever achieving the depth of NFL or MLB game models, it will still be a useful post-game analysis tool. Win probability says how likely it is for a team to win a game when given their lead and the time remaining in a game based on the results from thousands of games played before it. Win probability allows us to quantify exactly how incredible a comeback was, how brutal a collapse was, or see the twists and turns of a back and forth match.

I’ll explain the methodology and exactly how the win probability model was generated farther down. I suspect most of the people reading this are less interested in how it was made and more interested in how it works.

## Win Probability in Practice

The tool is fundamentally simple to use here. Input a lead, and input a time, the model will then provide the team’s odds to win the game at that moment. Leads of 4 goals and greater are all in one category.

I’ve selected two memorable games to help visualize what win probability says. FlipSid3 Tactics vs Supersonic Avengers during the Season 1 Qualifier 2 Regional Playoffs Semi Finals Game 7, and Cloud9 vs Method during the RLCS Season 4 LAN Lower Finals Game 5. The FlipSid3 vs Supersonic match is an example of what the model will show in a back and forth match. The Cloud9 vs Method is what it will show when a team blows a large lead late in the game. The graphs run from game start (5:00) to game end (0:00) along the X axis. Win probability is listed on the right, running from 0.0 to 1.0

FlipSid3 Tactics vs Supersonic Avengers

Cloud9 vs Method

Each jump in probability is when a team scores a goal. The impact varies by time and the change in lead. FlipSid3’s increase from a little after 4 minutes to 3 minutes is relatively flat, especially when compared to Supersonic’s increase after the 1-minute mark. This makes intuitive sense. We would expect a lead held in the last fifteen seconds to be more valuable than one held for fifteen seconds around half-time.

The model will usually value gaining a 1 goal lead more as valuable than a goal to extend a lead from 4-1 to 5-1. This is visible in the Cloud9 vs Method series, where the jump to a 1 goal and the jump to a 2-goal lead are larger than the jump a 3-goal lead. All leads provide a win probability of 1.0 with 0:00 on the clock. l If a game is tied at 0:00, then a team is recorded as having a lead until 0:01.

The model assumes that a team always have a 0.50 chance to win a game when it is tied, whether that tie is 0-0, 1-1, or 3-3 after a 3-goal comeback, regardless of region or relative team strength. In a tied game between a 2100 ELO rated European team and a 1200 ELO rated South American team, both will be given a 0.50 chance to win.

## Methodology

The games observed to create the model were sampled from competitive Rocket League games played by NA, EU, and OCE games during RLCS Season 1 and afterward. 2950 games were sampled in total. A full breakdown of where all the games came from is included at the bottom of this article. For each game, the following type of notations were recorded. When a lead was held, what size the lead was, and whether the team who held that lead won. Other pieces of tracking information were also recorded (Event, Season, whether a game was played on LAN or online, Game number, etc.). Effectively, the score at every second of every game was recorded.

14:154:09LossRegular Time5Cloud9 vs Method
24:084:04LossRegular Time5Cloud9 vs Method
34:031:57LossRegular Time5Cloud9 vs Method
21:561:42LossRegular Time5Cloud9 vs Method
11:411:23LossRegular Time5Cloud9 vs Method
10:070:00WinRegular Time5Cloud9 vs Method

The results of those games are shown on the graph below. It’s got quite a few peaks and valleys due to the limitations of the sample’s size. Those familiar with sports win probabilities will know that their samples usually include 8 to 10 thousand games at a minimum. There simply haven’t been that many games of competitive Rocket League both played and had either a VOD or replay saved and made available to the public. All situations where teams had a 4-goal lead or greater were combined into a single group. Overall, teams that failed to keep a lead, and let the game get to overtime won 49.8% of the time. To help smooth the graph and account for second to second discrepancies caused by relatively small sample size, any game that went to overtime was treated as a half of a win and half of a loss.

## Observed Win Probability

In the above graph you’ll see moments where the win percentage very early in a game is at 1.00. This is often due to a sample size of those moments of 1 to 3. These moments were removed from the sample, and then the using 4 OLS models, where the dependent variable is win probability and the explanatory variables are time (in seconds), time squared, and time cubed. The models were restricted so that they approached 1.0 at 300 seconds elapsed/0 seconds remaining.

Due to using OLS, some models would peak above 1.0 at certain times. FI changes the win probability for those times to be an arbitrary value close to 1.0 (.9999). The finished models that inform the Rocket League Win Probability tool are shown on the graph below.