UPDATE (6:30 p.m. March 18): We’ve updated this post to add information about the excitement index.
Welcome to FiveThirtyEight’s forecasts of the men’s and women’s NCAA basketball tournaments. We’ve been issuing probabilistic March Madness forecasts in some form since 2011, when FiveThirtyEight was just a couple of us writing for The New York Times. While the basics of the system remain the same, we unveil a couple of new wrinkles each year.
Last season, we issued forecasts of the women’s tournament for the first time. Our big change for this year is that we won’t just be updating our forecasts at the end of each game — but also in real time. If a No. 2 seed is losing to a No. 15 seed, you’ll be able to see how that could affect the rest of the bracket, even before the game is over.
Live win probabilities
Our interactive graphic will include a dashboard that shows the score and time remaining in every game as it’s played, as well as the chance that each team will win that game. These probabilities are derived using logistic regression analysis, which lets us plug the current state of a game into a model to produce the probability that either team wins the game. Specifically, we used play-by-play data from the past five seasons of Division I NCAA basketball to fit a model that incorporates:
- Time remaining in the game
- Score difference
- Pre-game win probabilities
- Which team has possession, with a special adjustment if the team is shooting free throws.
These in-game win probabilities won’t account for everything. If a key player has fouled out of a game, for example, his or her team’s win probability is probably a bit lower than we’ve listed. There are also a few places where the model experiences momentary uncertainty: In the handful of seconds between the moment when a player is fouled and the free throws that follow, we use the team’s average free-throw percentage. Still, these probabilities ought to do a reasonably good job of showing which games are competitive and which are in the bag.
We built a separate in-game probability model for the women’s tournament that works in exactly the same way but uses historical women’s data. Thus, we’ll be updating our forecasts live for both the men’s and women’s tournament.
Excitement index
Our March Madness “excitement index” (loosely based on Brian Burke’s NFL work) is a measure of how much each team’s chances of winning changed over the course of the game and is a good reference for picking the best games to flip to.
The calculation is simple: It’s the average change in win probability per basket scored, weighted by the amount of time remaining in the game. This means that a late-game basket has more influence on a game’s rating than a basket near the beginning of the game. We give additional weight to changes in win probability in overtime. Ratings range from 0 to 10, except in extreme cases where they can exceed 10.
The index isn’t perfect — this year’s play-in game between Holy Cross and Southern was good, but perhaps not deserving of its 9.4 rating. But even if it doesn’t quite capture the difference between a closely contested slog and a Dunk City run to the Sweet 16, it does a nice job of quantifying how tight a game was and how many big shots were hit.
Elo ratings
Otherwise, the methodology for our men’s forecasts is also largely the same as last year. But we’ve developed our own computer rating system — Elo — which we include along with the five computer rankings and two human rankings we used previously.
If you’ve followed FiveThirtyEight, you’ll know that we’re big fans of Elo ratings, which we’ve introduced for the NBA, the NFL and other sports. We’ve now applied them for men’s college basketball teams dating back to the 1950s, using game data from ESPN, Sports-Reference.com and other sources.
Our methodology for calculating these Elo ratings is highly similar to the one we use for NBA. They rely on relatively simple information — specifically, the final score, home-court advantage, and the location of each game. (College basketball teams perform significantly worse when they travel a long distance to play a game.) They also account for a team’s conference — at the beginning of each season, a team’s Elo rating is regressed toward the mean of other schools in its conference — and whether the game was an NCAA Tournament game. We’ve found that historically, there are actually fewer upsets in the NCAA Tournament than you’d expect from the difference in teams’ Elo ratings, perhaps because the games are played under better and fairer conditions in the tournament than in the regular season. Our Elo ratings account for this and also weight tournament games slightly higher than regular season ones.
Elo ratings for the 68 teams to qualify for the men’s tournament follow below.
| RATINGS | PROBABILITY OF… | |||||
|---|---|---|---|---|---|---|
| TEAM | REGION | SEED | ELO | COMPOSITE | FINAL 4 | CHAMPS |
| Kansas | South | 1 | 2097 | 94.5 | 45.1% | 19.1% |
| North Carolina | East | 1 | 2075 | 93.9 | 43.6 | 15.0 |
| Virginia | Midwest | 1 | 2052 | 92.5 | 30.4 | 9.8 |
| Michigan State | Midwest | 2 | 2078 | 91.8 | 33.9 | 8.9 |
| Oklahoma | West | 2 | 1972 | 90.0 | 32.0 | 6.8 |
| Villanova | South | 2 | 2045 | 91.3 | 22.4 | 6.4 |
| Kentucky | East | 4 | 2014 | 90.7 | 15.9 | 4.4 |
| West Virginia | East | 3 | 1956 | 89.3 | 16.2 | 3.4 |
| Purdue | Midwest | 5 | 1938 | 88.7 | 13.0 | 2.7 |
| Oregon | West | 1 | 2033 | 88.0 | 22.6 | 2.6 |
| Texas A&M | West | 3 | 1915 | 86.8 | 12.4 | 2.4 |
| Xavier | East | 2 | 1973 | 87.7 | 9.9 | 1.8 |
| Arizona | South | 6 | 1953 | 89.0 | 6.0 | 1.8 |
| Duke | West | 4 | 1910 | 87.3 | 12.1 | 1.7 |
| Maryland | South | 5 | 1876 | 87.4 | 6.3 | 1.3 |
| Indiana | East | 5 | 1938 | 87.4 | 5.8 | 1.1 |
| Miami (FL) | South | 3 | 1933 | 87.1 | 4.9 | 1.0 |
| Iowa State | Midwest | 4 | 1867 | 86.5 | 6.4 | 1.0 |
| Baylor | West | 5 | 1837 | 85.5 | 6.0 | 1.0 |
| Texas | West | 6 | 1788 | 84.7 | 5.9 | 0.9 |
| Utah | Midwest | 3 | 1887 | 86.6 | 5.3 | 0.8 |
| Wichita State | South | 11 | 1893 | 86.6 | 2.7 | 0.7 |
| California | South | 4 | 1871 | 86.5 | 4.0 | 0.7 |
| Iowa | South | 7 | 1904 | 85.9 | 3.2 | 0.6 |
| Vanderbilt | South | 11 | 1846 | 85.6 | 2.4 | 0.5 |
| Gonzaga | Midwest | 11 | 1916 | 86.0 | 3.2 | 0.5 |
| Wisconsin | East | 7 | 1896 | 84.8 | 2.9 | 0.4 |
| Notre Dame | East | 6 | 1832 | 84.4 | 2.6 | 0.3 |
| Connecticut | South | 9 | 1872 | 85.3 | 2.1 | 0.3 |
| Cincinnati | West | 9 | 1794 | 83.7 | 3.2 | 0.3 |
| Butler | Midwest | 9 | 1815 | 84.2 | 2.5 | 0.3 |
| Seton Hall | Midwest | 6 | 1914 | 84.5 | 1.8 | 0.2 |
| Virginia Commonwealth | West | 10 | 1798 | 83.1 | 2.2 | 0.2 |
| Dayton | Midwest | 7 | 1788 | 82.4 | 1.6 | 0.1 |
| Syracuse | Midwest | 10 | 1772 | 82.7 | 1.3 | 0.1 |
| Pittsburgh | East | 10 | 1787 | 82.3 | 1.2 | 0.1 |
| Saint Joseph’s | West | 8 | 1814 | 81.6 | 1.1 | 0.1 |
| Providence | East | 9 | 1824 | 82.5 | 0.8 | 0.1 |
| Northern Iowa | West | 11 | 1751 | 80.2 | 0.8 | <0.1 |
| Stephen F. Austin | East | 14 | 1824 | 81.0 | 0.4 | <0.1 |
| Colorado | South | 8 | 1756 | 81.5 | 0.4 | <0.1 |
| Yale | West | 12 | 1792 | 80.2 | 1.0 | <0.1 |
| Texas Tech | Midwest | 8 | 1777 | 81.3 | 0.4 | <0.1 |
| Tulsa | East | 11 | 1690 | 79.9 | 0.2 | <0.1 |
| Michigan | East | 11 | 1768 | 79.6 | 0.3 | <0.1 |
| Southern California | East | 8 | 1733 | 81.4 | 0.2 | <0.1 |
| Arkansas-Little Rock | Midwest | 12 | 1734 | 78.9 | 0.2 | <0.1 |
| South Dakota State | South | 12 | 1735 | 78.6 | 0.2 | <0.1 |
| Temple | South | 10 | 1730 | 78.5 | 0.2 | <0.1 |
| North Carolina-Wilmington | West | 13 | 1722 | 77.7 | 0.2 | <0.1 |
| Oregon State | West | 7 | 1740 | 77.6 | 0.2 | <0.1 |
| Iona | Midwest | 13 | 1759 | 78.2 | 0.1 | <0.1 |
| Green Bay | West | 14 | 1667 | 76.2 | 0.1 | <0.1 |
| Stony Brook | East | 13 | 1663 | 77.1 | 0.1 | <0.1 |
| Chattanooga | East | 12 | 1610 | 76.6 | <0.1 | <0.1 |
| Hawaii | South | 13 | 1737 | 78.0 | <0.1 | <0.1 |
| Fresno State | Midwest | 14 | 1708 | 76.6 | <0.1 | <0.1 |
| Buffalo | South | 14 | 1613 | 75.7 | <0.1 | <0.1 |
| Cal State Bakersfield | West | 15 | 1635 | 75.0 | 0.1 | <0.1 |
| Middle Tennessee | Midwest | 15 | 1638 | 75.0 | <0.1 | <0.1 |
| North Carolina-Asheville | South | 15 | 1553 | 74.2 | <0.1 | <0.1 |
| Weber State | East | 15 | 1623 | 73.3 | <0.1 | <0.1 |
| Florida Gulf Coast | East | 16 | 1544 | 71.4 | <0.1 | <0.1 |
| Southern | West | 16 | 1392 | 68.0 | <0.1 | <0.1 |
| Austin Peay | South | 16 | 1477 | 68.8 | <0.1 | <0.1 |
| Hampton | Midwest | 16 | 1488 | 68.6 | <0.1 | <0.1 |
| Holy Cross | West | 16 | 1420 | 66.9 | <0.1 | <0.1 |
| Fairleigh Dickinson | East | 16 | 1417 | 66.7 | <0.1 | <0.1 |
Note, however, that Elo is still just one of six computer rankings that we use for the men’s tournament. The other five are ESPN’s BPI, Jeff Sagarin’s “predictor” ratings, Ken Pomeroy’s ratings, Joel Sokol’s LRMC ratings, and Sonny Moore’s computer power ratings. In addition, we use two human-generated rating systems: the selection committee’s 68-team “S-Curve”, and a composite of preseason ratings from coaches and media polls. The eight systems — six computer-generated and two human-generated — are weighted equally in coming up with a team’s overall rating.
We’ve calculated Elo ratings for men’s teams only. For women’s ratings, we rely on the same composite of ratings systems that we used last year. You can find more about the methodology for our women’s forecasts here.
As has been the case previously, our ratings are also adjusted for travel distance and (for men’s teams only) player injuries. Our injury adjustment has been slightly improved to account for the higher or lower caliber of replacement players on different teams: Stony Brook, for example, won’t be able to replace a star player as easily as Kentucky can.
As a final reminder, these forecasts are probabilistic — something especially important to consider in the men’s tournament this year when there’s about as much parity among teams as we’ve ever seen. In some sense, every team but the UConn women should be thought of as underdogs to win the tournament this year.
Check out FiveThirtyEight’s 2016 March Madness Predictions.
