Let's suppose a map is destined to get rated 65%, if everyone voted. We can call this the map's "true" rating. Now, we don't expect a map's current rating to be exactly the same as it's true rating. There's variation, sometimes it's a little higher and sometimes it's a little lower, but over time the current rating should get closer to the true rating.
For example, if we toss a fair coin 10 times and get 3 heads and 7 tails, that's not unusual. But if we toss it 100 times and get 30 heads and 70 tails, we know that something's wrong--the coin must be biased. We expect something much closer to a 50-50 split. (The math: With 10 tosses there's a 34% chance we'll see 3 or fewer heads or 3 or fewer tails. But with 100 tosses, there's only a 0.0079% chance that we'll see 30 or fewer heads, or 30 or fewer tails.)
So, what're the statistics for transformice maps?
Here are the rules as I understand them: the map gets 50 votes and starting with the 51st vote, if it ever falls below 60% it gets deleted. The math is relatively simple for calculating the probability that a map's alive after 51 votes. For a map with a true rating of 50%, there's an 8.0% chance it'll be alive with 51 votes--that is, that 31 or more of the 51 people voted yes. For a map with a true rating of 65%, there's a 21.7% chance that it'll be dead with 51 votes.
The math is more complicated if we want to calculate the probability that the map will ever be deleted, at 51 votes or at some point beyond that. So I ran a simulation. I did a million runs with 10,000 votes each, and saw how many times the map died. Here are the stats, with the true rating on the left. For example, with a true rating of 50%, all one million of the maps died. There's basically no chance that such a map can stay above 60% for 10,000 votes, although there's a small chance it'll be above that threshold with 51 votes. With a true rating of 65%, the map died in 424,444 of the 1,000,000 simulations, or a 42.4% chance. (The error's around 0.1% using a million simulations.)
**Edit: My earlier numbers were actually only for 1,000 votes, not 10,000. Below I've calculated the probabilities (using one million simulations) that the map will die after 51, 100, etc. votes. For example, for a map with a true rating of 65%, there's a 42.4% chance it will die after 10,000 votes. (For 68% and onward I stopped after 500 votes, since it was taking a long time and the numbers weren't changing.)
TRUE 51 100 200 500 1000 10000 votes
50% 91.9 99.2 100 100 100 100
51% 89.6 98.7 99.9 100 100 100
52% 86.9 97.9 99.8 100 100 100
53% 83.6 96.9 99.5 100 100 100
54% 79.7 95.3 99 100 100 100
55% 75.5 93.3 98.2 99.9 100 100
56% 70.7 90.5 96.7 99.6 100 100
57% 65.6 87 94.5 98.7 99.8 100
58% 60.1 82.7 91.2 97 99 100
59% 54.3 77.6 86.8 93.7 96.7 100
60% 48.6 71.8 81.2 88.4 91.9 97.4
61% 42.6 65.3 74.3 81 83.9 87.1
62% 37 58.4 66.5 71.9 73.8 74.7
63% 31.5 51.2 58.1 61.9 62.8 63
64% 26.3 44 49.4 51.8 52.1 52.2
65% 21.7 36.9 41 42.3 42.4 42.4
66% 17.4 30.3 33.2 33.9 33.9 33.9
67% 13.8 24.3 26.2 26.5 26.5 26.5
68% 10.6 18.9 20.1 20.3
69% 8 14.3 15 15.1
70% 5.9 10.6 11 11
71% 4.2 7.6 7.8 7.8
72% 2.9 5.3 5.4 5.4
73% 2 3.6 3.6 3.6
74% 1.3 2.3 2.3 2.3
75% 0.8 1.5 1.5 1.5
76% 0.5 0.9 0.9 0.9
77% 0.3 0.5 0.5 0.5
78% 0.2 0.3 0.3 0.3
79% 0.1 0.2 0.2 0.2
80% 0 0.1 0.1 0.1
81%+ 0 0 0 0
What does this all mean? I haven't seen any maps rated in the 70's lately. And below that, there's a decent-to-good chance that the map will be deleted. So maybe we should submit maps multiple times, to try to limit the chance of getting caught in these statistics? I've submitted some maps twice, but never three times.
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