## Math Beyond the Madness: Bing Predicts on AreWeIn.net

Three weeks ago, we launched the site Are We In?, which gives you the latest status for whether your favorite college basketball team will or won’t make the tournament. Early feedback has been positive, and some users had questions around the insight for how probabilities match with our projections. In this blog we’ll describe in more detail the numbers and use visualizations from the newly-released Power BI “Publish to Web” feature to provide you with greater insight about the data presented on AreWeIn.net.

### Building the 68-Team Field

To start, the college basketball tournament is a 68 team event which includes a guaranteed invitation for each of 32 conferences, 31 of which rely on the end-of-season conference tournament to determine this automatic entry. The Ivy League is the lone exception as those schools use the regular-season champion to determine a representative.

Because most conferences wait for this tournament, even the top-ranked teams won’t hit 100% probability of qualifying since guaranteed entries require winning the conference tournament. On the other hand, for the Ivy League, once one team clinches the regular season conference title, that team will hit 100% and the others will drop to 0% because it’s not expected for that conference to receive an at-large bid.

These at-large bids are provided to the 36 best teams that do not receive a guaranteed invitation. Teams from stronger conferences can qualify either by winning their conference tournament, or being “good enough” to qualify for these at-large positions. Thus, the probability of making the tournament is the sum of “chance to win conference tournament” plus the “chance of getting an at-large bid assuming not winning the conference tournament.”

### Single Bid Conference

Since the Ivy League is extremely unlikely to get an at-large bid, let’s first illustrate the probabilities there so we can focus on predicting the chances of a team winning its conference. A frequently asked question is “how can you say my team is in but their chance of making the tournament is <50%?” Consider an 8-team conference like the Ivy League which has three top contenders, each having a reasonable chance of winning, and five others with a small chance. While the best team can receive the largest probability, it’s unlikely to exceed 50% early in the season.

### Multiple-Bid Conference

Many of the stronger conferences receive multiple bids. In fact, Bing Predicts currently projects the following distribution across conferences.

Looking more closely at the teams on the borderline of making the tournament, the bar chart shows the probabilities for teams expected to make the tournament, and, in order of strength, the first few expected to miss. The probabilities are not strictly decreasing, which may prompt some of us to wonder why that’s so.

One frequent question was: “How can a team with a low probability be in, when a team with a higher probability is out?” The reason is there are two ways to get into the tournament, and this creates the asymmetries in the chances of some teams making the tournament.

Projecting which 68 teams out of 351 in Division I will be in is a hard decision. In essence, less than one in five teams make the tournament, so if all teams were equal, everyone would have a 20% chance of qualifying and 68 teams predicted in could have a probability as low as 20 percent! However, not all teams are even, so we have a few teams in the high 90s that are virtually guaranteed to make the tournament, and then we have teams ranging down to about 30% that might still be projected to qualify.

To illustrate, let’s isolate the discussion to the probabilities for the Big 12 and West Coast Conferences, with all 20 teams listed in one bar chart. In the Big 12 conference, one team will qualify as the conference champion while we currently predict that five others will qualify. On the other hand, the West Coast Conference is expected to have one automatic qualifier and just one other at-large bid.

The key observation is that Kansas State and Texas Tech are predicted to be out despite a 40% chance of qualifying, while Gonzaga is in at 37%. Kansas State and Texas Tech are unlikely to win the conference tournament, so those teams have approximately a 40% chance of qualifying as at-large teams. But there happen to be other at-large teams with higher chances of getting in.

In the West Coast Conference, one team is guaranteed a bid, and the conference is dominated by the top three teams, so much so that each has about a 30% chance of winning the conference and another few percent to qualify as an at-large should that team not be the conference champion. The sum is still less than 40% for all three teams, but at least one is guaranteed to be in the tournament.

We hope you find the information useful as you track the odds of your team making the tournament. Please also visit us once the 68-team field is announced and we’ll provide projections for the full tournament as we did last year.

– Walter Sun, Bing Predicts Team Lead