Rosenberg: Introducing the Comeback Index

When I was a (younger) boy, my father and I devised a statistic to quantify comeback victories in playoff baseball: The Comeback Index. Stick with me while I explain it.

The Index produces a numerical value based on the formula: R x O x I. “R” is the number of runs by which the trailing team is behind when the comeback begins. “O” is 27 minus the number of outs that remain in the game for the trailing team at that point. And “I” is a measure for calculating the importance of a game.

Here is a sample calculation, excluding “I,” which I will treat in a moment: the Red Sox trailed the Yankees in Game 4 of the 2004 ALCS. The Sox were one run down when they came to bat in the ninth inning. As they came back to win the game, the Comeback Index would be [1 x (27 – 3)] = 24.

Intuitively, we can see why we need a measure “I” for importance. A team coming from one run behind with no outs in the ninth inning in the first game of a seven-game series would also score a Comeback Index of 24. But we know that the Red Sox’ comeback, with the team down 3–0 and facing elimination, was much more important than that.

“I” is calculated in two different ways. If the comeback team is not ahead in the series, “I” is equal to 1 / [(1+GR)^2 + GB], where GR equals the number of games remaining in the series and GB equals the number of games behind the leading team (if any). The denominator of the fraction is a measure of how much time the trailing team has before elimination and how close the teams are in the series. The smaller the denominator, the greater the importance of the comeback. In a Game 7 situation, “I” is always equal to one.

When the team making a comeback is leading in a series, “I” is equal to 1 / [(1+GR)^2 + GA/2], where GR is as above and GA equals the number of games ahead in the series. GA is halved because a comeback victory is more impressive when you are trailing in the series.

Let’s return to the 2004 ALCS. We determined a Comeback Index of 24 without using “I.” Now let’s put it in. At the time of the Red Sox’ comeback in the ALCS Game 4, they were losing 3–0 in a best-of-seven series. Thus, “I” equals 1 / [(1+3)^2 + 3)] = 1/17. The adjusted Comeback Index of the game is 24/17 = 1.41. Consider the same comeback (three outs remaining, one run down) if it had happened in Game 1 of the ALCS. “I” would be 1 / [(1+6)^2  + 0] = 0.0204. All comebacks of the same extent, even in the same series, are not equal.

The Comeback Index can be extended beyond baseball, too.

We all saw the San Francisco 49ers overcome a 17–0 deficit in the NFC Championship Game. This was the largest comeback ever (in terms of points) in an NFC Championship game. But how does this really compare to other similar comebacks? Let’s find out.

For football, the Comeback Index is P x T x I, where “P” is the number of points by which the trailing team was behind, “M” is 60 minus the number of minutes remaining when the comeback began, and “I,” again, is a measure of importance of the game, calculated in the same way as in baseball.

Importance is easier to measure for the NFL because each playoff game is an elimination game. Therefore, for each playoff game, “I” equals one.

The 49ers scored their first points with 8:08 remaining in the second quarter, trailing the Falcons 17–0. Their Comeback Index would be: 17 x (60 – 38.13) x 1 = 371.79.

Let’s compare the 49ers’ Comeback Index to the largest comeback ever in an AFC Championship game, when the Indianapolis Colts overcame an 18-point deficit beginning with just 8:21 remaining in the third quarter. The Colts’ Comeback Index would be: 18 x (60 – 23.35) x 1 = 659.7.

Even though the 49ers’ comeback was by just one fewer point, the Colts’ comeback six years ago was almost twice as impressive.

In a similar way, the Comeback Index will work for basketball, too. The formula is again P x T x I, where “P” is as above, “T” is 48 (or 40, for college basketball) minus the number of minutes remaining when the comeback begins, and “I” would revert to the baseball model, where playoffs include series.

Let’s use as an example the Yale Bulldogs’ legendary comeback versus Columbia last year in New York. The Elis trailed the Lions 51–30 with 11:30 left to play. This was the eighth game of the 14–game Ivy season. Yale was 5–2 in Ivy play before the game and trailed Harvard by two games in the league standings. Thus, the Comeback Index would be: 21 x (40 – 11.5) x { 1 / [(1+6)^2 + 2] } = 11.74.

It’s not clear whether having a high average Comeback Index is a good or bad thing. On the one hand, a high average Comeback Index means that a team is resilient. On the other hand, it means they fall behind, often by large margins.

I plan on calculating the average Comeback Index for the Ivy League basketball and baseball teams this spring. By calculating all eight teams’ Comeback Indices, we can try to see whether there is a correlation (either positive or negative) between eventual league place and average Comeback Index. Although one season’s results may not prove conclusive, perhaps we’ll be able to see the start of a trend.

Let’s hope that our Bulldogs finish first in basketball and baseball, with a (high? low?) calculable Comeback Index.

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