Numbers never lie. But they can be misinterpreted

I wrote how winning and losing streaks are a thing in World of Warships. In short: the outcome of a battle should be not correlated to the battle before. Ergo your chance to lose twice is L*L, win twice is W*W, lose once and win once is L*W*2. In reality, both double (and triple, and quadruple) wins and losses are more common, proving correlation between them.

I wrote some reasons why it can happen:

  1. me being tired, annoyed, distracted or other way unfit to play competitively
  2. if a game ends, many players queue again, so the next battle likely contain many of the people from the old game. If I manged to make them mad with my unique playstyle, they start the game mad when they see me on their team again.
  3. win chances greatly depend on ship composition, a 4-4 destroyer game is completely different from a 4x battleship game. Since most players play the same ships again and again, ship compositions are likely the same in the following games.

Then I “wisely” made the rule to don’t push “Battle On” after a defeat but do something else for 20-30 minutes. My results indeed increased, reaching rank 3 on Saturday. Then on Sunday I managed to get back to rank 5, losing 12 out of 14 games. I kept the letter of the rule.

I was sure that if I do statistics, I will find solutions and it clearly didn’t work and it upset me to no end (sure that helped with playing). But as the title says, the numbers don’t lie, but can be misinterpreted. For example see the list of possible explanations. Out of them only #2 is removed by waiting half an hour. #1 can be somewhat mitigated, but not if you spend your “break” in a random battle because “+200% XP weekend”.

So I went back to the same numbers and this time looked for longer trends:
prevscore

“Previous score” means the outcome of the previous N games, win being 1 and lose being 0. The first line is my total winrate during that period.

The first section, looking just the directly previous game is what I’ve found earlier: I have much higher chance to win a game after a won game than after a lost.

The second section looked for 2 previous games: the winrate after 2 losses is abysmal, it’s great after 1 win 1 loss (in any order) and average after 2 wins.

Looking at 3 games at a row was the most interesting: winrate after 3 losses or “2 loss 1 win” is bad. It’s great after “2 win 1 loss”. Surprisingly it’s bad again after 3 wins in a row.

I don’t know why win-streaks predict worse results than “good winrate with some losses”. It’s possible that I get overconfident and pull stupid stunts. It’s possible that the matchmaker has some anti-streak method. But the new rule is: I “Battle On” even if I lose my first game in the session and keep “Battle On” until

  • I lose both of my first 2 games
  • My last 3 games have 2 losses
  • All my last 3 games are won

After these I end my session and do something else for at least 2 hours. If I do randoms for XP, the 2 hours starts from the end of closing the client.

I am pretty confident that I’ll rank out soon with this. Long pauses help regenerate if the problem was my lack of ability and help the players replace if the problem was unfavorable ship composition.

.

Update: I wrote this post on early Monday, since then I’ve done some sessions:

  1. 2x Loss
  2. 3x Win
  3. 2x Loss
  4. LWL
  5. WWLWL
  6. 3x Win
  7. 3x Win
  8. WWLL
  9. WLWWW

This works like a charm. As you can see 4 out of 9 sessions contain 3x Win blocks, despite the chance is about 1/8. To the victor go the spoils:
rank2

Author: Gevlon

My blog: https://greedygoblinblog.wordpress.com/

14 thoughts on “Numbers never lie. But they can be misinterpreted”

  1. How about you program a RNG to give you 54% heads and then analyze your results the same way? see what will come up.

    In case of your wins and losses streaks, it’s the weekend. While in Randoms weekend means, in general, a drop in players quality, as the weekend warriors jin the fun, in Ranked it is exactly the opposite.

    Some players have a lot of time and play every day. If they were really good they’d have already ranked out. Therefore, the ones left in the R5 bracket are the good but not great ones.

    Some players have little time and mostly play weekend afternoons and evenings. If they were bad or mediocre they’d still be in R10. If they were great, they didn’t have the time to rank out and are now catching up.

    You were playing against different people over the weekend. I had worse results myself. Yesterday I got a 5 win streak easily and the Shimakazes were back to feed me. I expect to rank out before the end of the week.

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  2. you guys and listening to chewie yesterday make me really want to play this now… Dam it gevlon I followed you into eve. Can you recommend and/or write a how to start wows post? Im still battering neverwinter trying to get to CR, but I think I can learn this too.

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  3. Gev dont complain then when I drive a battleship straight at a Cv. I got it downloaded. Im googling your join a guild thingy cos I recall that gives extra leveling points. You got a ref link might give advantage to you or (prefer)me?

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  4. The result of any one match is not truly independent from the preceding game. You highlighted some carry-over factors but there are many more that will are consistent across matches in the same session such as overall physical/mental health (although this will deteriorate over a longer series of games), tactics used, quality of internet connection and your matchmaking recent W/L record.

    Also, because you imposed “battle on until” conditions the possibility of getting a triple win in any one session would be 25% for independent coin-flip events. (3 end conditions – LL (0.5), LWL (0.25), WWW (0.25) )

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  5. @nightgerbil: if you are on the EU server, I can invite you.

    @Dobablo: the end conditions doesn’t force triple-wins. If you flip coins, most of your sessions would end with the LWL condition.

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  6. Have you ever done a guide on how someone can pull useful data like you do for games. If you know of high quality resources to do such work I know I would appreciate the info.

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  7. Exactly, where there are four equally likely end conditions your chance of ending HHH is 0.25, not 1/8.

    By the way, there are notfour equally likely end conditions in your scenario.
    A quarter of your sessions will end played 2 lost 2. The remaining 3/4 of sequences can end in the following three combinations which are all equally likely.
    P(LWL), P(WLL), P(WWW) are all equally likely, therefore the likeihood of ending with three wins is 1/3 *x 3/4 = 1/4

    I have linked a probability tree (https://docs.google.com/spreadsheets/d/1kWl_o7ezR8w9lZ_d_4A7xxIB5KWXTnJ2cCWTuUbC84w/edit?usp=sharing). 25% of the time you end after the second game with two losses but after that, each generation has a 1/6 chance of ending WWW, 1/6 of ending WLL, 1/6 of ending LWL and 3/6 of going to another round.

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  8. What are you talking about?

    Win*Win*Win = 1/2^3 = 1/8
    WWW, WWL, WLW, LWW, WLL, LWL, LLW, LLL
    8 possible outcomes.

    If he stops after 2 losses then we get
    WWW, WWL, WLW, LWW, WLL, LWL, LL
    It doesn’t change anything because it just collapses the chances of LLW and LLL into double the chance of LL. WWW is still 1/8.

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  9. I finally did it! After having played WoWs in open Beta and after launch, I was interested in rejoining the naval battles again, especially now that a huge carrier rework is being done. So, I started the US and IJN battleship line to get into carriers…
    Playing battleship is somewhat difficult as they are rather sluggish and slow and their RoF is not great either. I struggled to get kills or even do a lot of damage, but I made some progress and I can say that it takes a lot of planning and improvisation to survive and support one’s team. I am very close to unlocking my first carrier.
    While I enjoyed destroyers a lot when I started WoWs, I currently lack the experience to successfully do a good job in random battles…
    Do you have any data, whether playing in a division with clanmates raises your overall performance?

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  10. @Stawek:

    He is referring to the fact that LWW, WLW, WWL are not end conditions – leaving only WWW, WLL, LWL, and LL as the possible end conditions for the last 3 games played (or 2 played in the event he loses both initial games).

    The LWW case has a 50% chance of ending in WWW, with a 50% chance of becoming a WWL scenario. Both of the WLW and WWL scenarios in turn have 50% chances to result in 2 losses within the past 3 games (one way or another) – but alternatively have a 50% chance to transform into LWW and WLW scenarios respectively.

    Because these simply shift through the same 3 scenarios with the same 50% chance of ending the streak (1/3 in WWW, 2/3 in LWL or WLL) and a 50% chance of shifting to the next scenario – the odds of a WWW rise to an infinitely small fraction below 1/4 overall…assuming Gevlon always keeps playing until he hits one of his end cases rather than quitting early due to time constraints/other factors.

    Theoretically there also exists the edge case where he would simply loop “WWLWWLWWLWWLWWL” repeating forever as well – but realistically it won’t ever happen.

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