What makes an exciting game, revisited

Bill James defined sabermetrics as “the search for objective knowledge about baseball.” Thus, sabermetrics attempts to answer objective questions about baseball, such as “which player on the Red Sox contributed the most to the team’s offense?” or “How many home runs will Ken Griffey hit next year?” It cannot deal with the subjective judgments which are also important to the game, such as “Who is your favorite player?” or “That was a great game.”
David Grabiner, The Sabermetric Manifesto

It’s winter.

Okay, technically winter begins on Dec. 21, but for us baseball nuts winter begins when the World Series ends. Baseball talk continues during the winter here at Hardball Times, but sooner or later you are going to miss actual ballgames.
You probably already have your emergency ballgame kit, something like:

{exp:list_maker}A few of the A&E DVD Box Sets of historical postseasons;
A bunch of old videocassettes of your favorite games;
MLB.com’s Baseball Best;
MLB Network’s historical great games aired in the offseason.{/exp:list_maker}
There is also the MLB.tv archive, a complete library of all the games played since 2006. But you surely don’t want to watch a May game between the Pirates and the Nationals, do you?

However, buried in the huge archive are several more or less meaningless games that are nevertheless really good games, especially if you are unaware of the final score (there might actually be a Pirates-National match-up among them). Let’s see if there’s a way to unearth those gems quickly.

First, we’ll never reach a consensus of what constitutes an exciting game; some people get chills out of a 1-0 pitching duel, while others prefer a 10-9 affair in which teams exchange punches back and forth. But there are some traits that separate games worth watching from… well… boring contests. Let’s try to list a few:

{exp:list_maker}equilibrium: if a team runs away with a big lead, it doesn’t make a fun game, unless it’s the other team which actually ends up winning;
rally: following from the exception above;
late game importance: if the deciding plays happen near the end of the game, the contest should be more enjoyable; obviously this is somewhat correlated to the previous two points. {/exp:list_maker}

Win Expectancy and Leverage Index present us with ways to measure (well, at least try to measure) the aforementioned three areas.

For example, the average distance, throughout the game, from a 50-50 Win Expectancy could be one way to measure equilibrium (lower equals greater equilibrium). Take the April 30, 1991 game between the Dodgers and the Expos.

Pitchers Mike Morgan and Dennis Martinez combined for six base hits allowed, and just a couple of baserunners went as far as third base, until Delino DeShields connected for the game winning homer in the bottom of the ninth. The highest Win Expectancy for both teams during the game was around 60 percent and the average difference from 50 percent was a mere four percent throughout the contest.

Image courtesy of FanGraphs.

Conversely, in this Indians-Yankees game of July 27, 1978, the Bronx Bombers erupted for seven runs in the second to get a 9-0 lead and, on average, the game was 48 percentage points away from the 50-50 equilibrium.

According to this stat, a big rally game would not be considered to have great balance, since for part of the contest one team (the one ending up on the losing side) would have a Win Expectancy way higher than 50 percent.

As an example, go to the May 10, 2005 game between Milwaukee and Chicago, in which the Brewers took an 8-3 lead in the top of the ninth and promptly retired the first two Cubs hitters: their Win Expectancy was 99.9 percent. Four walks, two errors and a homer later, the game was tied and the North Siders managed to get the win in the bottom of the 12th. The Win Expectancy throughout the game was, on average, 22 percent away from the 50-50 line. The average distance from 50-50 Win Expectancy is a good tool to outline 1-0 or 2-1 games, plus some high scoring games in which no team ever gets a lead higher than one or two runs.

The highest Win Expectancy reached during the game by the losing team can give an idea of the magnitude of the rally. As an example, refer again to that Brewers-Cubs game.

Image courtesy of FanGraphs.

A Hardball Times Update
Goodbye for now.

To get a sense of the importance of the last phases of a game, we can look at when the moment with the highest Leverage Index occurs. We can indicate the moment as a percentage of game played.

The Sept. 17, 1989 Reds-Astros match-up had its highest Leverage Index in the top of the ninth, when Cincinnati, trailing 1-0, had Eric Davis on first with nobody out; after Paul O’Neill grounded into a double play and Todd Benzinger was out on strikes, the game was over. The top Leverage occurred on the 61st play of the game, which ended after 63 plays. Thus the percentage of game played was 96.8.

Probably it would be advisable to give a value over 100 percent for games in which the most dramatic at-bats happen in extra innings.

On this July 31, 1988 game between Atlanta and San Francisco (the second of a doubleheader), the highest Leverage Index was measured on the last play of the game, in the bottom of the 10th inning. Instead of assigning a value of 100 percent, we can note that the regulation innings went 75 plays long, and the most important moment occurred at the 87th play; thus the assigned value can be 116 percent.

There are other combinations of Win Expectancy, Leverage Index and game progress that can be useful to assess whether a game is potentially exciting; probably they all revolve around the three areas previously outlined (equilibrium, rally, late game importance), giving some kind measure of one or more of those.

Running a correlation between the Leverage Index and the percentage of game played we can gauge the increasing tension of tight games, as opposed to the fading interest of lopsided contest.

Look at the pitching duel between Dan Petry and Bryan Clark on May 13, 1981 (Mariners @ Tigers). The Leverage Index chart steadily increases until the final at-bat, a walk-off single by Rick Peters off Dick Drago.


Conversely, nothing was exciting, especially for the home crowd, on April 27, 1980, when the Cardinals scored in the first, second, third, fifth and seventh innings en route to a 10-1 victory: the fading Leverage Index chart reflects the game becoming less and less interesting.


The correlation between Leverage Index and percentage of game played is 0.75 for the Mariners-Tigers game and -0.90 for the Cardinals-Phillies contest.

While the highest LI of the game shows how decisive was the single most important play of the contest, taking (for example) the 90th percentile of the Leverage Index gives an idea of the tension for a group of events, in this case the top 10 percent in importance. A comparison between the June 2, 1978, Orioles at Mariners game and the Aug. 22, 1980 Cubs-Astros 12-inning affair will serve as an example.

In the first case, the visiting Orioles went ahead 10-5 before Seattle made a comeback attempt in the last couple of innings, falling short by one and leaving the bases loaded. The final plays had Leverage Indexes of 5.79, 8.75 and 10.87 (the highest in the game, and one of the highest values you’ll ever see). But before those final moments of the game, since the O’s were well ahead, Leverage Index was low for the most part; the 90th percentile for the game is 1.58.

The second contest considered had a maximum Leverage Index of 5.85, but because it was a tight fight for 12 innings, the 90th percentile of the index wasn’t much lower at 4.11. Thus you have a match-up with one incredibly tense moment on one side, and another that doesn’t reach the same kind of tension but has a lot of very important moments throughout the game.

The highest change in Win Expectancy during the game measures the impact of the most important play. On April 26, 1985, Dan Gladden of the Giants homered with two out and two on in the bottom off the ninth to give San Francisco a 7-6 win over the Reds. The home team Win Expectancy went from 7.6 percent to 100 percent on that play, a net change of more than 92 percentage points.

On the other hand the mean change in Win Expectancy takes into account the swing produced by every single play The ultimate poster game for this indicator is the 2009 playoff game featuring the Tigers and the Twins: on average, every single play of that contest changed the Win Expectancy by more than seven percent.

This article is going to end with a list of good games, but not a ranking of the most exciting games since 1974 (FanGraphs has Win Expectancy and Leverage Index starting from the year Hank Aaron surpassed Babe Ruth).

Next time we’ll show how the variables presented here can be combined in a way that latent macro-variables such as equilibrium, rally and late game importance can emerge. We’ll also show how the combination of those variables does actually detect exciting games among the thousands of contests played in the past decades.

Finally, we’ll compile a (questionable, of course) ranking of the greatest games. The reason for the postponement is that I’m expecting readers to suggest other variables that can be used to measure the greatness of baseball games or criticize the ones I have used, and I plan to integrate the suggestions in the final analysis.

Just a note: the importance of the game itself in the season of each competing team is not considered at this moment.

While waiting for your suggestions, here’s a bunch of games from last season you may want to watch (each team is represented). They have been all detected by some ugly computer code, so if you do not agree they are good games, blame the code, not me.

April 9: Cardinals @ Brewers
April 28: Pirates @ Brewers
April 24: Orioles @ Red Sox
May 1: Royals @ Rays
May 9: Marlins @ Nationals
May 18: Mets @ Braves
May 22: Rangers @ Cubs
June 1: Rockies @ Giants
June 18: D-Backs @ Tigers
June 30: Phillies @ Reds
July 2: Blue Jays @ Yankees
July 21: White Sox @ Mariners
July 29: Dodgers @ Padres
Aug, 13: Athletics @ Twins
Aug. 18: Astros @ Mets
Sept. 8: Indians @ Angels

References & Resources
Play-by-play data, Win Expectancy and Leverage Index for every regular season game since 1974 from FanGraphs.

Dennis Boznango wrote a couple of articles here at THT, using similar approaches to uncover the best postseason games in baseball history. The title of this article pays a tribute to them. The links: part 1part 2.

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13 years ago

“Pitchers Mike Morgan and Dennis Martinez combined for six base hits allowed, and just a couple of baserunners went as far as third base, until Delino DeShields connected for the game winning homer in the bottom of the ninth. “

I imagine this game was still in the minds of the Dodgers front office when they decided to trade Pedro Martinez to get DeShields a couple of years later.

Anna McDonald
13 years ago

This was an exceptional article, perfect for those of us missing baseball.

This year, the Mets and Cardinals 20 inning game, on April 17th.  In a backwards way, the fact that nothing exciting happened for a marathon 6 ½ hours, made it one of the craziest, alluring, and exciting games of the year. It was almost as if the simple magnetic pull of indistinct play after indistinct play seemed to make the nothingness more exciting. As far as late game importance, there was plenty, and the Leverage Index was crazy. But then again, no one is going to want to watch that game again.

13 years ago

Giants vs Rockies – Zito pitched pretty well and got a hit to go with the nice pitching. Buster at first base was hitting. Pablo looked pretty bad at the plate everytime he was up.

Colorado did an amazing job to hang in there. They seemed done a couple of times, but pulled it out. Have to say it was a pretty exciting game, even on condensed replay.

Cuban X Senators
13 years ago

Ok, curmudgeon time:  the “highest win expectancy for both teams” is always 100% – unless it’s an All-Star Game and Bud’s looming.

You mean “highest win percentage for either team was 60%.”

I’m pledging to make no grammatical corrections on the interwebs except those around both/each/either/neither.

13 years ago

Not actually from this past season, but pretty close.  I find the graph for this game somewhat mind-boggling.


13 years ago

Actually come to think of it that graph makes me wonder if another useful metric could be the number of times the graph crosses the 50% line, or even crosses past 60-70% in one way or the other, as a way to try to find back-and-forth type games.