Measuring excitement: Introducing Win Path Length

What was the most exciting baseball game of last season?

Excitement is an inherently subjective quality, and as such, this question has any number of possible answers. The most common choices would likely be postseason contests, since they come with additional stakes; Game 3 of the World Series, a back-and-forth affair in which the winning run scored in the ninth on an obstruction call, would be a popular selection, as would the first game of the NLCS (which lasted 13 innings), the second game of the NLCS (a 1-0 pitcher’s duel between Kershaw and Wacha), and the second game of the ALCS (a Red Sox comeback on a David Ortiz grand slam).

If you expand the scope of the question to include the regular season, however, the question quickly becomes unmanageable. There are hundreds of extra-inning games to choose from, and dozens of walkoff hits, and any number of astounding defensive plays or surprising rallies or great individual performances that could qualify a game for a particular list. So how does one go about sorting through all 2430 regular season games and picking the best?

With the caveat that any objective measurement of a subjective quality is inherently flawed before it even begins, I have an idea for an objective measurement of the subjective quality of excitement.

The most important of the many factors that can make a baseball game exciting is the path it takes in identifying the winner. The best games will have their outcomes remain in doubt for as long as possible, preferably with both teams threatening to take over at some point. And since we already have Win Expectancy and its close relative, Win Probability Added, available to describe any game for which the play-by-play is recorded, we can simply add up the changes in WPA throughout any such contest and use it as a proxy for the overall excitement generated.

This is not a unique idea; it has been used in other places, although I did come by it independently. There are two things I have that are unique, as far as I know. First is the name I use for the measurement, which is Win Path Length (or WPL for short). Second, and more important, is my collection of large spreadsheets containing WPL data for a significant number of baseball games, including every postseason and All-Star game ever played (plus the end-of-season playoffs in every year in which WPA has been calculated), and all of the regular season games from 2011-13 and 1977. Simply having that information available enables me to take a particular game and place it on the invigoration spectrum.

Here is that spectrum for all 2430 games of the 2013 regular season:

Percentile (Rank)	WPL
0 (2430)	0.57
1 (2405)	0.86
5 (2308)	1.12
10 (2187)	1.34
20 (1944)	1.67
30 (1701)	1.96
40 (1458)	2.23
50 (1215)	2.50
60 (972)	2.82
70 (728)	3.13
80 (486)	3.57
90 (243)	4.17
95 (121)	4.81
98 (48)	5.69
99 (24)	6.73
99.5 (12)	7.54
99.96 (1)	9.55

It should be noted that the absolute minimum WPL for a non-rain-shortened game is 0.50, so the year’s worst game (a 10-0 Cincinnati win over the Cardinals on August 28, in which the Reds scored six in the first and three more in the second, immediately excising any semblance of drama) is about as uninteresting as possible. Meanwhile, of course, there is no theoretical maximum; a game could go on infinitely and have an enormous number of rallies and lead changes and continue to increase its WPL score without bound.

The postseason games mentioned in the introductory paragraph are evaluated as follows:

NLCS Game 2 (Kershaw vs. Wacha): WPL of 2.31 (42^nd percentile)

ALCS Game 2 (Ortiz’s grand slam): 2.62 (53^rd percentile)

World Series Game 3 (Obstruction call): 3.92 (86^th percentile)

NLCS Game 1 (13 innings): 5.22 (97^th percentile)

These games allow a bit of additional examination of things that WPL likes and doesn’t like. In particular, the system is not a big fan of high-quality pitcher’s duels; they typically involve very few scoring opportunities and therefore don’t rack up many large changes in win expectancy. (I enjoy a good pitcher’s duel myself, but it’s more an aesthetic pleasure than an edge-of-your-seat experience, which is what WPL looks for.)

The other popular type of game that WPL frowns on is the big comeback. Consider the fifth and final game of the 2012 NLDS between the Nationals and Cardinals. The ninth inning, in which the Cards scored four times to complete the transformation of a 6-0 deficit into a 9-7 win, was riveting (and for me, horrifying) baseball. But the eight innings leading up to it, which saw Washington jump ahead by six early and the Cards slowly chip away without mounting a major threat thereafter (the tying run never reached scoring position until the ninth), were rather lacking in high drama. On balance, the game still graded out favorably (with a WPL of 3.41), but a score in that range suggests "game that was very pleasant for a neutral fan to attend" more than it does "instant classic."

By comparison, WPL adores games that stay close throughout and have a significant number of lead changes. The aforementioned third game of the World Series swung from 2-0 to 2-2 to 4-2 to 4-4 before the Cardinals pushed across the game winner in the ninth. Unlike in the case of a large comeback, this game involved multiple swings in the fortunes of the teams and was constantly competitive.

There is only one thing that WPL likes better than a see-saw contest: extra innings, especially if there are several of them. Extra-inning games have two major advantages. First, they involve extra baseball; a longer game will have more chances for exciting things to happen. Second, they are guaranteed to be close, since games only go to extras when tied at the end of regulation.

WPL’s adoration extra innings borders on alarming. The system ranks 2013’s best nine-inning game as the #50 game of the season overall, meaning that it was listed behind 49 extra-inning affairs. Only one extra-inning game out of the 241 played during the year scored below the 65^th percentile in the rankings, and the median extra-inning contest (#121, coming in at 4.65) graded out behind less than 1% of the 9-inning games played in 2013. This seems a little extreme to me, but I can at least understand why the results are what they are.

The top 10 games of 2013 by WPL (links are to Baseball-Reference boxscores and play-by-play descriptions):

10. A's 3, Yankees 2 (18). Played June 13; WPL of 7.65.

9. Red Sox 5, Mariners 4 (15). July 31; 7.81.

8. Marlins 4, Mets 3 (15). April 29; 7.86.

7. Rockies 7, Cardinals 6 (15). September 19; 8.06.

6. Diamondbacks 10, Cardinals 9 (16). April 3; 8.34.

5. Diamondbacks 5, Mets 4 (15). July 4; 8.42.

4. White Sox 7, Mariners 5 (16). June 5; 8.59.

3. Marlins 2, Mets 1 (20). June 8; 8.62.

2. A’s 10, Angels 8 (19). April 29; 9.43.

1. Blue Jays 4, Rangers 3 (18). June 8; 9.55.

Two pairs of these games occurred on the same day. In both cases, the second-best game of the pair was between the Mets and Marlins, which is a rather remarkable bit of happenstance. All ten of the games lasted at least 15 innings. Many of them featured comebacks in extra innings, which WPL absolutely adores. The #5 game on the list featured not one, but two game-tying extra-inning rallies before the road team finally put it away; the #4 game included the first game-tying extra-inning grand slam in MLB history. It is, in short, a selection of 10 extremely exciting baseball games, which is primarily what the method is intended to identify.

There are a number of potential ways to use a measure of this type, and I’ll probably explore some of them in the near future. But the best thing to do with WPL is to put it to its intended use – picking out exciting baseball games. For the last two baseball seasons, I’ve compiled WPL for the games of the preceding day and written up a summary of the best one (with the summaries being posted in the daily Dugout thread at www.baseballthinkfactory.org), and I’m going to continue doing that here, starting with yesterday’s excellent slate of Opening Day games.