Introduction

Dropouts are the bane of Diplomacy. Rare, but not unheard of, in tournament games, they are more common in social games ("Most of the face-to-face games I was in before I took up play-by-mail had dropouts!" --Eric Brosius, 8th August 1994) and they have been a "feature" of postal Diplomacy since the earliest days. Dropouts surely disrupt the flow of a game since the replacement player is under no obligation to follow the policies of his or her predecessor, but do they affect the game result? Is the dropout rate uniform across the hobby or are there "quality zines" with "quality players" running "quality games"?

Before examining the effect of a low (or high) number of dropouts, we need to identify the base figures. We use three "indicator functions":

• the percentage of games finishing in a win (the WIN number),
• the length of an average game (the LENGTH number), and
• the number of dropouts in the average game (the DROPOUT number).

In order to answer these questions, datasets containing these games and the games listed in Everything #85 (May 1992) through Everything #88 (September 1993) were set up. Games which were orphaned or had a change in GM whilst remaining in the same 'zine were discarded from the datasets because these processes often cause dropouts. After this process, the datasets contained 112 postal games and 28 games played over the CompuServe network. In the following analysis the postal and CompuServe games are treated as distinct groups; at no point are they combined.

The CompuServe sample is small and the analysis of games played on CompuServe should be treated carefully. How about the postal size? At a latter day we intend to examine the historical variation of the three indicator functions. Are there more dropouts today than twenty years ago? Is it easier to win a game today than ten years ago? Has the slowing down of the postal hobby -- a decrease in average 'zine frequency -- resulted in a change in the average length of a game? Bearing in mind that there roughly 120 game starts a year throughout the 1980's we believe that a dataset of 112 games is a reasonable one.

What is Meant by "Dropout"?

A feature of American 'zines is this use of standby players. Yet few 'zines will use a standby player for every position; a small power may (will) be placed into civil disorder if its leader drops out. In this study we assume that the placement of a power into civil disorder, rather than using a standby player, has negligible effect on the values that the indicator functions take. The standby policies of CompuServe GM's vary from GM to GM, but the standard policy is to call a standby if the vacant position either has more than two centres or if it is part of a stalemate line. We assume that the practice of putting one- or two-center positions into CD has negligible effect on our indicator functions.

In comparing figures based on North American postal games to games played over CompuServe we assume that Diplomacy games are homogeneous and that there were no important differences in the way that they were run, between CompuServe and the postal hobby. We make a similar assumption when comparing figures based on games played in particular 'zines.

Survey of Games Reported in Everything #85 through Everything #88

Of the 112 postal games, 55 (49%) finished in wins. Table 1, below, shows the distribution of games with "n" dropouts and how the percentage of games finishing in a win varies with "n".

In order to make the data in this last row more clear, this data is presented as a rolling average in Table 2, below.

From the data in Tables 1 and 2, we see that the typical postal game has 3 dropouts, but the standard deviation is large, and just under three in every five games played have three, four or five dropouts. There is also a correlation between the number of dropouts and the result of the game. Games with few dropouts (0-2, 1-3) are less likely to end in a win than the hobby average, and games with a middling number of dropouts (2-4, 3-5, 4-6) are more likely to finish in a win than the hobby average. Games with a large turnover in original players (5-7) finish in a win in accordance with the hobby average.

Of the 28 games played over CompuServe, 13 (46%) ended in wins. Since the sample size is small I shall regard this figure as being the same as the postal figure (51%). For instance, if the next three reported CompuServe games in Everything end in wins, the CompuServe average will be 52% (16/31). If we view the percentage of games that end in a win as a crude measure of the standard of play, assuming that as the standard of play decreases the percentage of games finishing in wins increases, then we conclude that the standards of play in the North American Hobby and over CompuServe are identical.

Table 3 shows the distribution of games with "n" dropouts and how the percentage of games finishing in a win varies with "n". This data is then presented as rolling averages in Table 4.

From the data in Tables 3 and 4 we see that the the average number of dropouts per CompuServe game is 2.07 +/- 1.36. That is, the typical CompuServe game has 2 dropouts and the standard deviation for the number of dropouts in a CompuServe game is smaller than that for postal games. Just over seven in every ten (71%) CompuServe games have no, one, or two dropouts. The sample size is not large enough to see if there is a correlation between the number of dropouts and the game result.

We have already seen that the average game played over CompuServe is as likely to finish in a win as the average postal game. Further, there are far fewer dropouts in CompuServe games, suggesting that CompuServe games are more stable (and hence more enjoyable?).

We have examined the effect of the number of dropouts on the result of the game and calculated the average number of dropouts per game. There is one more "fundamental" quantity: the length of the game. Do postal games finish "prematurely"? Postal players might not want to play to the bitter conclusion because the four or five game-years that are required for the game to reach its "logical conclusion" may easily take a year of real time. Four or five game-years on CompuServe might only take a couple of months. Is the average length of a game dependent on the mode of playing the game?

Tables 5 and 6 show the distribution of game finishes for postal and CompuServe games.

From Tables 5 and 6 we see that there is very little distinction in average game length between CompuServe and the North American postal Diplomacy hobby. The average game-year of finish for a postal game is 1910.00 +/- 3.45, while the average game-year of finish for a CompuServe game is 1909.75 +/- 3.44. From this we can conclude that postal games do not seem to end "prematurely."

It has been noted that standby players interrupt a game on a strategic and tactical level, and there is something intrinsically unsatisfying in playing a game which has a rapid turnover in players. One way to quantify which 'zines offer "good" games of Diplomacy is to examine their dropout rate. 'Zines with low dropout rates are more likely to contain enthusiastic players. You may be less likely to win if you play in these zines (is this true?!) but you are more likely to enjoy the game (unless, of course, winning is the sole criteria for judging your enjoyment of the game!).

If the average length of a game in two 'zines differs, then comparing the average number of dropouts would be meaningless because the longer a game lasts the more dropouts you expect. Hence 'zines which have longer games, which would also seem to be a good indication of quality of play, might have a higher dropout rate than zines with shorter games. Instead of quantifying 'zines by their average drop-out rate, a more useful quantity is the average dropout rate per game-year played (Q). This is defined as the ratio of average game-length to average dropout rate, and has non-SI units of years per drop-out (!). For the North American Hobby we have

These figures reflect our earlier finding that CompuServe games suffer from fewer interruptions than postal games.

Table 8 contains a breakdown of 'zines in our sample. In the survey that follows, we have arbitarily decided that the minimum number of games required to have run to completion in a 'zine in order to calculate Q for that zine is five.

Games played in the following pairs of 'zines were not discarded from the dataset: The Boob Report/ The Abyssinian Prince, Cathy's Ramblings/Rambling By Moonlight, Vertigo/Meet George Jetson and Don Del Grande's various 'zines.

Table 9 contains the calculation of Q for the six 'zines which ran five or more games. Three of these 'zines have lower values for Q than the hobby average: Maniac's Paradise, Rebel, and The Home Office. It should not be surprising that Rebel has a lower Q value than the hobby average because Rebel has always attracted a large number of novices and it is well known that novice players drop-out at a higher rate than non-novice players. Since the dataset for the other 'zines is small, one or two rogue games exert considerable influence; for example, two of the six games to have been finished in Maniac's Paradise finished in 1903 and 1905.

Discussion

In this survey we compared "basic Diplomacy indicators," the percentage of games finishing in a win, the average number of original players who drop from a game, and the average game-length, for CompuServe and postal games. We then examined the dependence of the WIN number on the DROPOUT number.

Conrad Minshall has suggested that variations due to dropouts might be more pronounced in the number of powers eliminated from a game, rather than the win percentage. If this true -- and the datasets are not (yet!) setup to investigate this possibility -- then we might see a difference in the type of draw agreed to in high-dropout games; are 2-way and 3-way draws more pronounced in high dropout games than in low dropout games? We suspect that 2-way and 3-way draws are more common amongst orphaned games (as it isn't uncommon for the players that don't drop after orphaning to agree a draw amongst themselves), and that the variation in draw type with dropout number in non-orphaned games is slight -- having discarded details of orphaned games we now find that they need to be examined after all!

We presented the variation of the WIN number as a rolling average of the number of dropouts. The resulting data suggests that if you are an original player then your chances of winning the game increase as more original players drop. However it could be the case that players dropout when they consider a win to be unstoppable, so the nearer to a win you are the more likely it is that players will drop. We believe that the former is the correct interpretation (because we would like to believe that players don't drop because they think that another player is going to win the game).

There is one fundamental factor which may affect all of the indicator functions: DIAS or no-DIAS. Dick Martin has suggested that an analysis based on DIAS and no-DIAS lines is worthwhile. This task requires reading the houserules for the 'zines listed in Table 7. If someone reading this is in a position to carry out such a survey, let me know the results! (Graustark and Retaliation are the only 'zines I know of which run DIAS.)

Although 'zines which have a reputation as places to play good games of Diplomacy also have high Q-values, too much emphasis should not be placed on the ranking of 'zines by Q-value; the sample size is small and the standard deviation in the number of dropouts and gamelength is large. A GameMaster who has a solid core of players that play in a couple of games with a torpid turnaround could show up very highly in this survey; this would not necessarily be a place to play.

Let us merely note that Boast and Graustark appear to the "best" 'zines to play in, followed by Carolina Command & Commentary and Cheesecake.

At the core of this survey is the assumption that the number of dropouts is an important parameter in determining how "good" a game of Diplomacy is. Perhaps a better parameter would be the number of NMRs in a game; that is, what is the effect if a player who NMR's every other turn but is not replaced? Unfortunately, a survey based on NMR's can not undertaken based on information presented in Everything.

Conclusions

1. Provided that "too many" of the original players don't drop out, the percentage of games finishing in a win increases with the number of original players that drop out
2. The average strength of players is the same in the postal and CompuServe hobbies but CompuServe games have a higher Q-value
3. The 'zines with the highest Q-values are Boast, Graustark, Carolina Command & Commentary and Cheesecake.

Acknowledgements

I would also like to thank Eric Brosius (72060.1540@compuserve.com), Conrad Minshall (conrad@apple.com), and Andrew York (wandrew@aol.com) for reviewing a draft version of this article. I would also like to thank Doug Kent (73567.1414@compuserve.com) for advice on GM'ing practices on CompuServe.

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