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Asking the titular question is a bit like inquiring "which animal is best?" The answer will vary from person to person based on one's preferences. There is no wrong answer. For a box score, does one want a bare bones presentation, featuring traditional statistics? Or a more in-depth, sabery production, complete with the triple slasher for each player and WPA figures? What about colors and graphics?
I sampled box scores from seven well-trafficked websites in an attempt to find the "best". For purposes of this post, only content on the main page is counted as part of the box score. For instance, the Baseball-Reference page includes a detailed play-by-play of the entire game and is therefore part of the box score. The ESPN page includes a link to the play-by-play on a separate page and is not considered part of the box score. Here are images of each box score, complete with a brief review, in alphabetical order:
(click to embiggen -- Note: The BB-Ref box score is massive so the image above is an excerpt. The Retrosheet box score is also snipped. The other five box scores are presented in their entirety. A link to each box score is provided above the images.)
BB-Ref is bursting with information. Traditional stats, saber stats, detailed play-by-play (courtesy of Retrosheet), a WPA graph, weather, umpires -- it's all there. There's almost too much information, if the user is looking to the box score for a simple, numerical recap of the game. It's quite busy. I love information, so BB-Ref's box score rates as one of the best for this user.
A downside -- and correct me if I'm wrong on this -- is that it doesn't keep track of games as they happen. For that reason, this is my preferred source for historical box scores like the R.A. Dickey one-hitter against the Phillies seen in this post. It's a next day box score.
ESPN provides much of the same saber info as BB-Ref does -- AVG/OBP/SLG, pitch results -- while looking more presentable. It's not a gawdy production, as one might come to expect from ESPN. Additionally, it includes a "Game Notes" section which explains any out-of-the-ordinary game action. In the Dickey one-hitter game, Mike Hessman hit a home run, which was turned into a triple due to fan interference after umpire video review. This is clarified here, which most box scores don't do.
This is my preferred box score for purposes of writing a game recap, due to the detailed pitcher stats, number of pitches seen by batters and speed at which this information becomes available after the game. Good show, ESPN.
The FanGraphs box score isn't nice to look at but scores major points for details of individual player performance. Heavy saber is present, unsurprisingly, with WPA, LI and batted ball stats all appearing. Clicking to another page is required to view the inning-by-inning scoreboard. This is an area of improvement. Chances are, the user knows who won the game if he/she is viewing a FanGraphs box score, but a scoreboard at the top of the page would be an asset.
The info in the separate Play Log link is an excellent tool for writing game recaps. However, its contents aren't on the main page so it is ignored here.
This one of the more traditional packages, statistically. On-base percentage and slugging percentage aren't present, but batting average is. The LOB stat ("left on base") is generally useless. The team logos are a nice touch -- they seem to add a human element to the box score, for whatever reason. Maybe the sight of the logos conjures the image of players in uniform.
This is what box scores would look like if the Commodore 64 won the war. Retrosheet's role in the preservation of baseball history is commendable (if you can help complete the database, please do!). But the paucity of saber stats, combined with the robotic interface, makes Retrosheet inferior to BB-Ref as far as historical box scores go. However, it's worth noting that Retrosheet explains the Hessman homer-turned-triple in its play-by-play.
SBNation.com
SB Nation's box score is similar to MLB's in look and information presented. Maybe I should toe the company line, but honesty is my preference. There's nothing remarkable here.
SNY's inclusion of the triple slasher is noteworthy for a box score one would expect to be traditional. The logos at the top remind of MLB, and the bare minimum game info is similar in format to SB Nation. Not bad, not great, I am probably not a return customer.
Forced to choose just one, my pick is ESPN. Say what you will about the Worldwide Leader, and there's plenty to say, but it makes a mean box score. Baseball-Reference is a close second place.