A Game’s Hirsch Index
by Chuck Berry as of June 21, 2018
Gamers have a Hirsch Index (“HI”) for games they’ve played. For example, if you’ve played at least 34 Games at least 34 times each, your HI = 34.
But the Games themselves have an HI based on Gamers who have played them. If at least 34 Gamers have played a Game at least 34 times, that Game’s HI is 34. Let’s call this the “Game’s Hirsch Index,” or “GHI.”
This GHI statistic may be an interesting way to evaluate the popularity of games. But first, a little background about the Hirsch Index in general. (Feel free to skip this next section if you’re not interested or already know about the HI.)
Hirsch Index and Applications
The Hirsch Index was suggested in 2005 by Jorge E. Hirsch (a physicist at the University of California San Diego) as a tool for evaluating success in academic publications. One physicist might have many papers but they have been cited only a few times each. Another might have just a few papers but they have been widely cited. The HI measures both dimensions, so that a third physicist with several papers cited several times each might have a higher HI than the other two.
You can use the HI in many other situations. Some of them you can figure out accurately. If you’ve lived in 4 different houses for at least 4 years each, your HI is 4. Perhaps you can list 6 movies you’ve watched at least 6 times. Unless you have recorded a lot of trivial data during your lifetime, some HIs can only be roughly estimated. Have you eaten at least 15 times each at 15 or more local restaurants? Do you have 34 shirts you’ve worn at least 34 times?
You can easily determine your HI for games you’ve played, at least since you began logging them on Board Game Geek. Simply look at My Geek / Played / by Game and count down from the top of the list until your number of plays equals how far down you’ve counted.
But what about an HI for the games themselves? It would be interesting to calculate the academic-style “Real HI” for games based on the number of citations in all publications of all types, but this is impossible with today’s technology. Might someone be able to tabulate the times in BGG discussions that each game is mentioned in connection with other games? Probably not, especially if comments in videos were included.
Investigating the GHI
But a Game’s Hirsch Index (GHI) based on its number of plays by different players is straight-forward to calculate (though time-consuming to do for a large number of games). In June of 2018 I compiled the GHI for about 200 games including the top 20 most highly ranked on Board Game Geek, every 10th game up to #200, every 50th up to #1,000, every 100th up to #2,000, plus several other games I’ve played several times and was interested in.
The results of this sample are in a separate file: ghi_data_version_1_180621.xls
You might enjoy sorting and graphing these data in various ways. Here are some observations:
(1) The highly-ranked games on BGG do not necessarily have the highest GHIs. The GHIs for the Top 10 range from 23 to 80. Even the Top 20 only rise to Agricola with a GHI = 109. At least ten other lower-ranked games have GHIs > 100, including Can’t Stop which ranks #633.
(2) Shorter games tend to have higher GHIs. Many people play several games of Can’t Stop, Dominion, Race for the Galaxy, and Splendor in a single session. In contrast, several of the highly ranked games take 120 minutes or more to complete (and that’s just what the ad on the box says!).
(3) Newer games tend not to have high GHIs; there simply hasn’t been time yet for people to play them a large number of times.
(4) Older games also have a disadvantage; most of their plays probably happened before BGG was launched, and before many of us began logging our plays on BGG.
After all, in The Good Ol’ Days there were not many games so we had to play them a lot of times, right? So if the truth could be known, several would have very high GHIs. In fact, some of the data logged on BGG appear to be gamers’ (perhaps-conservative) estimates of the number of times in the past that they played Monopoly or Risk or Axis & Allies. Nobody actually played one of those 50 times on a single day and never at any other time.
It is interesting to see that a few classic games (say, older than Catan in 1995, GHI=100) are still being played: Go, Backgammon, Poker, Scrabble, etc. Though technically an ancient game, Liar’s Dice probably got a boost by being republished and featured in a movie.
(5) Games with the highest number of total plays of course tend to have high GHIs. Most GHIs for these are close to or over 100. But Pandemic Legacy Season 1 is an exception, with a GHI of only 44. Evidently not many gamers have played through multiple years of this hit game (now ranked #2 on BGG).
(6) Naturally, games with a large number of different players also have a better chance of earning a high GHI. But Power Grid is an exception; among games in my sample it ranks #10 in different player count but has a GHI of only 60. In contrast, Race for the Galaxy has slightly fewer unique players but a GHI of 221. PG has an average of only 4.6 plays per player, while RftG’s average is 18.7. This may well be due to their different lengths, 120 versus 45 minutes.
(7) Average plays per player are interesting. How can Unlock! Squeek & Sausage have an average of only 1.1 plays per player? It has only been around since 2017, but it startled me that nobody has yet played it more than 4 times.
At the other extreme, Bridge has an average of 23.2. I assume that this is because not many BGGers are still active Bridge players, but several evidently estimated an aggregate number of past plays and logged them. Those who played only a few times in the past likely did not log any old estimates. By the way, what is “one game” of Bridge ... one hand, one rubber, or maybe a whole duplicate session?
(8) Are YOU supporting the GHI for any games? If your logged plays are at least equal to a game’s GHI, you might be part of the reason for some of the numbers I came up with. Thank you for that contribution. And if you’re close got some favorite game, you might play a few more games and boost the GHI a notch.
(9) The GHI WINNERS are (in case you haven’t played with the worksheet):
244 Dominion
221 Race for the Galaxy
112 Ascension: Deckbuilding Game
111 Ticket to Ride
110 Lost Cities
109 Agricola
106 7 Wonders
105 Codenames
104 Hanabi
103 Can't Stop
Does this appear to you to be a reasonable basis for picking Great Games?
Many of these (Agricola being an exception) are fast to set up as well as quick to play, so the GHI could be used as a Filler Finder.
My friend Olaf Slomp suggests other calculations that might be made with these data. What about multiplying average playing time by number of plays to gauge total time spent? There are some problems with the time ranges listed for some games, but this approach might still help offset the advantage enjoyed by shorter games.
You can probably think of other interesting calculations to make with the data in the worksheet.
More Data?Of course, with only about 200 games in my sample (out of over 15,000 ranked on Board Game Geek), the list of “Winners” above is far from complete. But figuring out the GHI game by game takes a great amount to time. And what’s worse, these numbers are already out of date. So . . .
Can someone with access to BGG data calculate GHIs mechanically? Would that be worth doing, and perhaps adding to the statistics for each game?
Also, have I perhaps “invented” something that others already came up with? I’d appreciate links to other references to this idea.
* * * * *
If you have comments, I would love to hear from you! Thank you!
Chuck Berry <[email protected]>
BGG User = BetsyChuck
by Chuck Berry as of June 21, 2018
Gamers have a Hirsch Index (“HI”) for games they’ve played. For example, if you’ve played at least 34 Games at least 34 times each, your HI = 34.
But the Games themselves have an HI based on Gamers who have played them. If at least 34 Gamers have played a Game at least 34 times, that Game’s HI is 34. Let’s call this the “Game’s Hirsch Index,” or “GHI.”
This GHI statistic may be an interesting way to evaluate the popularity of games. But first, a little background about the Hirsch Index in general. (Feel free to skip this next section if you’re not interested or already know about the HI.)
Hirsch Index and Applications
The Hirsch Index was suggested in 2005 by Jorge E. Hirsch (a physicist at the University of California San Diego) as a tool for evaluating success in academic publications. One physicist might have many papers but they have been cited only a few times each. Another might have just a few papers but they have been widely cited. The HI measures both dimensions, so that a third physicist with several papers cited several times each might have a higher HI than the other two.
You can use the HI in many other situations. Some of them you can figure out accurately. If you’ve lived in 4 different houses for at least 4 years each, your HI is 4. Perhaps you can list 6 movies you’ve watched at least 6 times. Unless you have recorded a lot of trivial data during your lifetime, some HIs can only be roughly estimated. Have you eaten at least 15 times each at 15 or more local restaurants? Do you have 34 shirts you’ve worn at least 34 times?
You can easily determine your HI for games you’ve played, at least since you began logging them on Board Game Geek. Simply look at My Geek / Played / by Game and count down from the top of the list until your number of plays equals how far down you’ve counted.
But what about an HI for the games themselves? It would be interesting to calculate the academic-style “Real HI” for games based on the number of citations in all publications of all types, but this is impossible with today’s technology. Might someone be able to tabulate the times in BGG discussions that each game is mentioned in connection with other games? Probably not, especially if comments in videos were included.
Investigating the GHI
But a Game’s Hirsch Index (GHI) based on its number of plays by different players is straight-forward to calculate (though time-consuming to do for a large number of games). In June of 2018 I compiled the GHI for about 200 games including the top 20 most highly ranked on Board Game Geek, every 10th game up to #200, every 50th up to #1,000, every 100th up to #2,000, plus several other games I’ve played several times and was interested in.
The results of this sample are in a separate file: ghi_data_version_1_180621.xls
You might enjoy sorting and graphing these data in various ways. Here are some observations:
(1) The highly-ranked games on BGG do not necessarily have the highest GHIs. The GHIs for the Top 10 range from 23 to 80. Even the Top 20 only rise to Agricola with a GHI = 109. At least ten other lower-ranked games have GHIs > 100, including Can’t Stop which ranks #633.
(2) Shorter games tend to have higher GHIs. Many people play several games of Can’t Stop, Dominion, Race for the Galaxy, and Splendor in a single session. In contrast, several of the highly ranked games take 120 minutes or more to complete (and that’s just what the ad on the box says!).
(3) Newer games tend not to have high GHIs; there simply hasn’t been time yet for people to play them a large number of times.
(4) Older games also have a disadvantage; most of their plays probably happened before BGG was launched, and before many of us began logging our plays on BGG.
After all, in The Good Ol’ Days there were not many games so we had to play them a lot of times, right? So if the truth could be known, several would have very high GHIs. In fact, some of the data logged on BGG appear to be gamers’ (perhaps-conservative) estimates of the number of times in the past that they played Monopoly or Risk or Axis & Allies. Nobody actually played one of those 50 times on a single day and never at any other time.
It is interesting to see that a few classic games (say, older than Catan in 1995, GHI=100) are still being played: Go, Backgammon, Poker, Scrabble, etc. Though technically an ancient game, Liar’s Dice probably got a boost by being republished and featured in a movie.
(5) Games with the highest number of total plays of course tend to have high GHIs. Most GHIs for these are close to or over 100. But Pandemic Legacy Season 1 is an exception, with a GHI of only 44. Evidently not many gamers have played through multiple years of this hit game (now ranked #2 on BGG).
(6) Naturally, games with a large number of different players also have a better chance of earning a high GHI. But Power Grid is an exception; among games in my sample it ranks #10 in different player count but has a GHI of only 60. In contrast, Race for the Galaxy has slightly fewer unique players but a GHI of 221. PG has an average of only 4.6 plays per player, while RftG’s average is 18.7. This may well be due to their different lengths, 120 versus 45 minutes.
(7) Average plays per player are interesting. How can Unlock! Squeek & Sausage have an average of only 1.1 plays per player? It has only been around since 2017, but it startled me that nobody has yet played it more than 4 times.
At the other extreme, Bridge has an average of 23.2. I assume that this is because not many BGGers are still active Bridge players, but several evidently estimated an aggregate number of past plays and logged them. Those who played only a few times in the past likely did not log any old estimates. By the way, what is “one game” of Bridge ... one hand, one rubber, or maybe a whole duplicate session?
(8) Are YOU supporting the GHI for any games? If your logged plays are at least equal to a game’s GHI, you might be part of the reason for some of the numbers I came up with. Thank you for that contribution. And if you’re close got some favorite game, you might play a few more games and boost the GHI a notch.
(9) The GHI WINNERS are (in case you haven’t played with the worksheet):
244 Dominion
221 Race for the Galaxy
112 Ascension: Deckbuilding Game
111 Ticket to Ride
110 Lost Cities
109 Agricola
106 7 Wonders
105 Codenames
104 Hanabi
103 Can't Stop
Does this appear to you to be a reasonable basis for picking Great Games?
Many of these (Agricola being an exception) are fast to set up as well as quick to play, so the GHI could be used as a Filler Finder.
My friend Olaf Slomp suggests other calculations that might be made with these data. What about multiplying average playing time by number of plays to gauge total time spent? There are some problems with the time ranges listed for some games, but this approach might still help offset the advantage enjoyed by shorter games.
You can probably think of other interesting calculations to make with the data in the worksheet.
More Data?Of course, with only about 200 games in my sample (out of over 15,000 ranked on Board Game Geek), the list of “Winners” above is far from complete. But figuring out the GHI game by game takes a great amount to time. And what’s worse, these numbers are already out of date. So . . .
Can someone with access to BGG data calculate GHIs mechanically? Would that be worth doing, and perhaps adding to the statistics for each game?
Also, have I perhaps “invented” something that others already came up with? I’d appreciate links to other references to this idea.
* * * * *
If you have comments, I would love to hear from you! Thank you!
Chuck Berry <[email protected]>
BGG User = BetsyChuck
Game H-Index Data version 1.xls | |
File Size: | 54 kb |
File Type: | xls |