The greatest comebacks in post-2000 Boston sports history, ranked by a combination of estimated statistical improbability & game importance (postseason only).

**1. Red Sox 2004 Series vs. NY Yankees: Win Probability, 0.0175 (1 in 60). **

This win probabilities accounts for Mariano Rivera as the Yankees closer (0.14 chance of the Sox winning Game 4), and uses an equal chance of each team winning the final 3 games (1 in 8 for the Sox winning all 3). I thought this graph was pretty unique, as it looks at the series probabilities across all seven games. The opponent and situation (ALCS) increase the importance of this comeback, helping to make it the greatest in recent Boston sports history.

**2. Bruins 2013 Rd 1 Game 7 vs. Toronto: Win Probability: 0.02 (down by 3, 10 minutes left) and 0.007 (down by 2, 1.4 minute left). **

I don’t think I realized how unlikely this comeback was until I computed the win probabilities. The more (relative to their previous deficit) unlikely comeback by the Bruins was to win after trailing by two goals with 1.4 minutes remaining. Let’s start with this graph, from advancednflstats.com (yes, they do more than the NFL).

Down 2 goals with 1.4 minutes remaining, it’s clear the Bruins win probability was less than 1%. To get a sense of how much less than 1% their chances were, start by calculating the probability of the Bruins scoring 2 goals and the Leafs scoring exactly 0 goals in 1.4 minutes, and multiplying that whole probability by 0.50, because we’d assuming the overtime win probabilities were equal. In normal situations, the probability of a team scoring a goal is 0.0465 each minute. This equates to 0.0651 as a rate in 1.4 minutes. Of course, with their goalie pulled, the Bruins probability of scoring (and the Leafs) was substantially higher. Estimates I’ve seen allow for the opposing team to score roughly three times as often as the team which pulled the goaltender. So, even allowing for the Bruins to be four times as likely to score with an empty net as they’d be in normal situations (rate, 0.25), which would then increase the Leafs chances as well (rate, 0.75), we have the following:

Pr(Bruins score 2) = 0.024

Pr(Leafs score 0) = 0.607

Pr(Bruins win in OT) = 0.50

Piecing those together, we have 0.024*0.607*0.50 = 0.007 (1 in 140). This is probably an overestimate, since I’m probably being generous with regarding the likelihood of the Bruins scoring two goals in this time. This article at JQAS would’ve saved me a little bit of time. It used roughly the same idea to estimate that a team’s chances with exactly 1 minute remaining (Bruins had 1.4) and down two goals was 0.002. My best guess is that the true Bruins chances of a comeback were about 1 in 200 (0.005). Add in the fact that this was a Game 7, and this comeback nearly tops the list.

**3. Celtics 2008 NBA Finals Game 4 vs. LA Lakers: Win Probability, 0.04 (1 in 25). **

The Celtics were down 21 points at the end of the first quarter, and came back to win and take a 3-1 series lead. It’s the largest end-of-first-quarter comeback in NBA playoff history. Tenacious *defense* like this from Sasha Vujacic helped things for the Celtics. The opponent, game importance, and location also make this comeback more impressive.

**4. Red Sox 2008 Rd. 2 Game 5 vs. ALCS: Win Probability, 0.01 (1 in 100).**

Former Sox manager Terry Francona called the 2008 Red Sox the best team he ever managed. In Game 5, the Sox erased a 7-run deficit in the final three innings before escaping with an 8-7 win. The graph at the bottom of this page does a pretty good job of putting the comeback in perspective, as at all points in the game between the 3rd and the 7th innings, the Rays had at least a 90% chance of winning. Had the Sox actually completed the series comeback, this game might be higher on the list.

**5. Celtics 2002 Rd. 3 Game 3 vs. NJ Nets: Win Probability: 0.0025 (1 in 400).**

Down 21 in 4th quarter, the Celtics posted the then-largest 4th Q comeback in league history. In the 1614 best-of-7 NBA playoff games from 1947 through 2001, when a team trailed by 19 or more points after three quarters, its game record was 0-171 (.000). This comeback seems worse because the Celtics eventually lost the series, 4-2. It also lacks historical perspective because no one was beating the Lakers that year (4-0 winners over the Nets). Win probability calculated using comments from this website.

**6. Red Sox 2004 Rd. 1 Game 4 vs. NY Yankees: Win Probability, 0.40 or 0.14 (accounting for a standard MLB closer of accounting for Mariano Rivera as the closer).**

Like the Snow Bowl game listed below, Game 4 looks fancier and more impressive in retrospect. If the Sox had gone on to lose the series in five, this game might not even make the list. The game-specific probabilities are higher than you might think, in part because of how potent the Sox lineup was in 2004; The ’04 Sox had nine players with an OBP above 0.360…the ’12 Sox, as a reference group, had just one. Lastly, if you recalled Paul Quantrill and Curtis Leskanic as being the losing and winning pitchers in this game, you are making that up.

**7. Patriots 2001 Rd. 2 vs. Oakland: Win Probability, 0.05 (1 in 20).**

This comeback looks substantially better in retrospect because it started a dynasty. At the time, the Patriots were still heavy underdogs in their next two games and this specific comeback wasn’t completely improbable. The numbers give the Patriots a 1 in 20 chance of this comeback…but unfortunately, there’s no way of accounting for the conditions that made this game so ridiculous. Win probability calculated using this.

Great stuff!

Reblogged this on Stats in the Wild and commented:

I meant to send this out earlier in the week, but I’m just getting to it now. Great stuff from StatsByLopez. Make sure to check out the FanGraphs graph of the 2004 ALCS series. Really neat display of that data.