The Perks of Losing the Second Game: Order, Independence, and Representativeness

In recent years, the Milwaukee Bucks have frequently lost the first game of playoff series. Last year, they lost the first games against the Suns, Hawks, and Nets, nearly lost the first game against the Heat, and added another loss against the Suns and Nets for good measure. The year before that, they dropped the first game against the Magic (!) as well as the Heat (and three of the next four to boot). And the year before that, they dropped the first game against our current foe.

This year, however, the Bucks have thrown caution to the wind and dared to win the first game of both series, only to revert to their early-series woes in Game 2. Game 2 against the Bulls featured Khris’ slip, with the loss adding insult to injury. Game 2 against the Celtics only came with a bruised ego, but still left a sour taste in our mouths - a taste that lingered during the years that have passed before today’s Game 3. Thanks a lot, Godsmack (which I initially misread, assuming it was the knock-off line of candies that Charlie Bucket created in an alternate universe where he stole Wonka’s everlasting gobstobbers. Anyone else? No? Okay.)

As such, during the aforementioned years between Game 2 and Game 3, I wondered about the difference between WL and LW. What follows are my thoughts on order, independence, and representativeness; in other words, why the perks of losing the second game.

At first glance, the difference between WL and LW is meaningless. In both cases, the series is tied at 1-1, effectively becoming a best-of-five series with the home-court advantage reversed. So I’m sure that Bucks Twitter would respond to each outcome equally.

Ha. Winning the first game but losing the second has inspired considerable doom and gloom in both series. Losing the second game thrusts the series into parity and deflates any momentum gained from the Game 1 win. It creates a sense that the other team has “solved” the Bucks. Boston clamped down on Giannis’ assists to behind-the-arc teammates, and Chicago... well, Khris was injured.

In contrast, losing Game 1 is not a cause for celebration, but it can be hand-waved away due to Bud needing time to make the right adjustments. At any rate, the hand-wringing evaporates after Game 2, at which point it is the Bucks who have solved their opponents. Indeed, clearer formulas for success emerged after one (or two) losses during last year’s championship run.

To bring in some numbers, Basketball Reference provides relatively useful charts that enable comparisons of series outcomes. Let’s focus on the middle column, starting with teams being tied 1-1. When the away team wins the first game and loses the second, it has a record of 32-52 (.381). When the away team loses the first game and wins the second, it has a record of 24-49 (.329). At least historically, there seems to be a marginal advantage of WL over LW.

Why might that be the case? One idea is that a loss reveals more information from a win. After a Game 1 win, most teams likely try to stay the course. However, after a loss in Game 2, coaching staffs have a clear sense of how the other team can win and are able to plan for Game 3 accordingly. In contrast, after a Game 1 loss, coaching staffs would have to put together a blueprint to course-correct for Game 2. After a Game 2 win, they have effectively shown their hands.

This theory would hold weight if teams are more likely to win Game 3 after a Game 2 loss. Are they? Using the left column (Team is Up 2-1) and right column (Team is Down 2-1) on Basketball Reference, I contrasted the number of series that are WLW and WLL and the number of series that are LWW and LWL to determine whether WL or LW is more predictive of Game 3 success. When the away team wins the first game and loses the second, it has a record of 44-40 in Game 3 (.524). When the away team loses the first game and wins the second, it has a record of 35-38 in Game 3 (.479).

This provides some support for my theory that teams are more likely to follow a Game 2 loss with a Game 3 win. But it still strikes me as unsatisfactory. Coaching staffs are paid a pretty penny to design effective gameplans. Can they really wring less information from a win than a loss? They should be able to find plenty to improve upon, even in wins: Bud angrily calling timeouts due to sloppy turnovers when we are obliterating the Magic comes to mind. Does it come down to whether teams are marginally more aggrieved following losses? Can that really explain an additional five percentage points in the win column?

Fundamentally, I am interested in whether playoff games can be treated as independent or interdependent. If two good teams are playing each other, and both coaching staffs are preparing their hearts out for each game, I might posit that game outcomes are largely independent from one another (with the exception of home court advantage - more on that later). However, we tend to put a lot of weight on sequences. The sequences hold the narrative of the series: the difference between WL and LW is the way that fans, talking heads, and even players perceive the trajectory of the series. Although that perception may be invalid, it appears as though it may have a tangible (though weak) impact.

The idea of independence brings me to my final bone to chew on: representativeness. Representativeness emerges from the work of Daniel Kahneman and Amos Tversky, recently made notable by Kahneman’s book Thinking Fast and Slow as well as Michael Lewis’ billionth novel The Undoing Project. Representativeness holds that we evaluate the likelihood of events based on how representative they are of the universe of circumstances that may create those events.

The canonical example involves flipping a coin. What is more likely: flipping a coin seven times and yielding HTHHTTH or HHHHHHH? The impulse is to designate the former as more likely because it is more representative of most outcomes, which typically contain a variety of heads and tails. However, they are actually equally likely: flipping heads or tails is a 50/50 proposition, and it is thus similarly probable that we would happen to flip seven heads in a row as that exact sequence of heads and tails.

As alluded to, the main difference between flipping a coin and a playoff series is home-court advantage; even if we alternated between heads- and tails-partisan crowds, it is still a coin toss. (Another key difference is that coin flips do not stop after a given number of heads or tails, whereas playoff series can be won.)

But besides that, does the assumption of independence hold? Technically, a LWWLLWW series and a LLLWWWW series - which, using the away team as the reference point, both involve two away wins and one home loss - are equally likely. But the representativeness heuristic is powerful; LLLWWWW series seem less representative. Perhaps this is because the narrative is simply too much to surmount.

I returned to the middle column (Teams are Tied 3-3) in oder to see if patterns emerge that shed light on these ideas, again focusing on the away team’s perspective. The first impression is the importance of home-court advantage. Of the 88 series that have gone the distance, 19 have followed home-court advantage exactly over the first six games, and 15 of those series were won by the home team (the Bucks beating the Nets as one of only four exceptions).

The second impression is that three series have never occurred: WWWLLL, but also WWLWLL and LWLWWL. If we expect the home team to win, both of these series feature four deviations from that prediction, which reduces their likelihood (although, interestingly, there have been a few series with five or six deviations, especially in recent years). On the flip side of unrepresentative series, LLLWWW has only occurred twice. Is that less likely that chance?

Doing the math (sorry for the trivia flashback!), there are 64 (2^6) possible combinations of W’s and L’s in a six-game sequence. However, there are only 20 (6C3) that involve three W’s and L’s (and thus would require a seventh game). WWWLLL and LLLWWW comprise 2/20 or 10% of those possibilities. We would thus expect 88 * 10% = 8.8 series to have began with a 3-0 hole and become level at 3-3. That is a far cry above 2!

In conclusion, in the context of playoff series, the representative heuristic is valid, because playoff games are not independent, because order matters, because we humans - players too! - buy into narratives about sequences. The statistically equivalency of WWWLLL and WLWLWL is meaningless to the psychological weight of staring down the barrel of three elimination games. Bucks fans can find some upside in the fact that losing Game 2 tends to fuel Game 3 victories, but they can also find some solace in the fact that, until the season is on the line, sequence differences seem to be all in our heads.