It's one of the most frustrating things about pinball. You've recently put up a really solid high score, let's say 200M on the TPA version of FunHouse. Then for the next five games you don't break 50M. So you take a break, come back two days later, play five more games and still don't break 50M. Then you play five more games off-and-on and on your fourth one you hit 100M. But still you wonder: if I can hit 200M, shouldn't 100M be relatively easy? Shouldn't I get at least half my high score at least half the time?
Not at all. If you are, it's a sign your high score probably should be much higher.
Pinball scores are not evenly distributed. Not even close. They actually roughly follow something called the gamma distribution, which means something to those who are skilled in statistics and nothing to the rest of us. But the basic gist is that the median score - the most likely score - is significantly below the mean score or arithmetic average. You will score low more often than you score high. There is a limit - your score cannot drop below 0, most tables have a certain minimum achievable score unless you tilt (TZ's is 4.8M, for example), and even in your worst games you usually exhibit some flicker of skill and score a little above the minimum. So really bad games mercifully still have a relatively low probability.
On the brighter side, your 5 best scores - presumably the ones stored in your TPA tables - are the most extreme outliers, your 1-in-1000 games. These are not anywhere near your "normal" performance. Even games that look merely above-average will be relatively uncommon. Most of your games by comparison will suck. But if you're playing in a league or match-play tournament, you don't need to have a 1-in-1000 game, you just need to beat your current opponents. And most of their games will suck compared to their high scores as well.
Let's examine three rounds of qualifying from the recent PAPA 15 tournament: A Division on AC/DC, B Division on Twilight Zone, and C Division on Whirlwind. PAPA 15 is not a match-play format (that's Pinburgh, PAPA's other tournament), but examining qualifying scores gives us a large number of games played on the same machine under identical conditions. Even though these games were played by many different players, we can hypothesize their averaged performance as being roughly equivalent to a single "average" A-Division player, same with B and C Divisions.
The first thing you'll note is that must have been one hell of a Whirlwind. After that, you'll notice that roughly one-eighth of the high score was enough to beat 50% of the competitors, about a quarter of the high score beat 80% of the field, a little less than half of the high score takes out 95%, and two-thirds of the high score would win 99 of every 100 head-to-head matchups. Note that this result is relatively independent of game played (there are exceptions - Bride of Pinbot's billion shot throws the whole show off) and relatively independent of player division (as long as scores are compared within the same division - mixing A and C division scores together would skew the results).
Now obviously when you first start a new TPA table, you will exceed your personal best easily and often, so the above does not apply yet. But once you've played enough games (about 50) to establish a high score that you find very hard to make further progress against, then you can apply the rules.
So what can you do with this information? Well, first of all, when you score one-quarter of your high score, be happy instead of beating yourself up! You've just had an above-average game. Just got half your high score? Rejoice! You've just had a 1-in-20 performance.
You'll also see that even the 99% column - the once in 100 games performances - aren't above the high scores. It turns out that if your high score is well-established and is a true representation of your skill, beating it is literally a thousands-to-one proposition. For example, beating that 821M TZ score, assuming you have the skill of the average B Division player, is expected to happen only once in 1700 games. So you can reevaluate your expectations, and realize that a well-established high score might take a while to best.
Well, that sounds depressing. But there are some rays of hope. First, your skills may continue to improve even after you hit an apparent plateau - you may master the drop catch, or discover a certain way of nudging is highly effective at saving from the right outlane, or you may just become more patient and make fewer risky shots. Or you may discover that you've been playing on a really hard physical table - perhaps it was just used in a tournament - and this particular machine you're playing now is much more friendly.
Which brings us to pitfalls. To use these statistics effectively, you must make sure to compare apples to apples. Two physical machines may be set up differently. Tournament conditions obviously won't score as well (usually - my AFM high score was under league conditions) as arcade play. And for most people, your physical scores will be one-eighth to one-tenth of your corresponding TPA score. And - the big clincher to accurately tracking your play - if you restart games, then you will be artificially keeping only the higher-scoring games and your actual performance will be worse than indicated.
You can also use the 1/8-1/4-1/2-2/3 rule to estimate what score you need to take down an opponent in a head-to-head match (or whether you even can). These are very rough estimates indeed - basing any probability estimate off a sample of one (and that sample being the most extreme observed value!) is dicey business. But if you know your opponent has a high score of 300M on a particular machine, then you know you need at least 75M to have about an 80% chance of beating him, and you can use your own high score on that machine to estimate your chances of getting that 75M. You will find that even with intimidating-looking differences in high score, you will very likely still have a fighting chance at winning. Again, this is because in comparison to his high score, most of your opponent's games suck.
So go forth and play more pinball, and hopefully you feel a little more reassured while doing so.
Not at all. If you are, it's a sign your high score probably should be much higher.
Pinball scores are not evenly distributed. Not even close. They actually roughly follow something called the gamma distribution, which means something to those who are skilled in statistics and nothing to the rest of us. But the basic gist is that the median score - the most likely score - is significantly below the mean score or arithmetic average. You will score low more often than you score high. There is a limit - your score cannot drop below 0, most tables have a certain minimum achievable score unless you tilt (TZ's is 4.8M, for example), and even in your worst games you usually exhibit some flicker of skill and score a little above the minimum. So really bad games mercifully still have a relatively low probability.
On the brighter side, your 5 best scores - presumably the ones stored in your TPA tables - are the most extreme outliers, your 1-in-1000 games. These are not anywhere near your "normal" performance. Even games that look merely above-average will be relatively uncommon. Most of your games by comparison will suck. But if you're playing in a league or match-play tournament, you don't need to have a 1-in-1000 game, you just need to beat your current opponents. And most of their games will suck compared to their high scores as well.
Let's examine three rounds of qualifying from the recent PAPA 15 tournament: A Division on AC/DC, B Division on Twilight Zone, and C Division on Whirlwind. PAPA 15 is not a match-play format (that's Pinburgh, PAPA's other tournament), but examining qualifying scores gives us a large number of games played on the same machine under identical conditions. Even though these games were played by many different players, we can hypothesize their averaged performance as being roughly equivalent to a single "average" A-Division player, same with B and C Divisions.
| High Score | 20% Score | 50% Score | 80% Score | 95% Score | 99% Score | |
| A Division - AC/DC | 248,317,600 | 11.3M | 29.4M | 61.9M | 108M | 161M |
| B Division - Twilight Zone | 821,289,510 | 45.3M | 109M | 217M | 368M | 537M |
| C Division - Whirlwind | 12,834,410 | 0.99M | 1.95M | 3.41M | 5.34M | 7.41M |
The first thing you'll note is that must have been one hell of a Whirlwind. After that, you'll notice that roughly one-eighth of the high score was enough to beat 50% of the competitors, about a quarter of the high score beat 80% of the field, a little less than half of the high score takes out 95%, and two-thirds of the high score would win 99 of every 100 head-to-head matchups. Note that this result is relatively independent of game played (there are exceptions - Bride of Pinbot's billion shot throws the whole show off) and relatively independent of player division (as long as scores are compared within the same division - mixing A and C division scores together would skew the results).
Now obviously when you first start a new TPA table, you will exceed your personal best easily and often, so the above does not apply yet. But once you've played enough games (about 50) to establish a high score that you find very hard to make further progress against, then you can apply the rules.
So what can you do with this information? Well, first of all, when you score one-quarter of your high score, be happy instead of beating yourself up! You've just had an above-average game. Just got half your high score? Rejoice! You've just had a 1-in-20 performance.
You'll also see that even the 99% column - the once in 100 games performances - aren't above the high scores. It turns out that if your high score is well-established and is a true representation of your skill, beating it is literally a thousands-to-one proposition. For example, beating that 821M TZ score, assuming you have the skill of the average B Division player, is expected to happen only once in 1700 games. So you can reevaluate your expectations, and realize that a well-established high score might take a while to best.
Well, that sounds depressing. But there are some rays of hope. First, your skills may continue to improve even after you hit an apparent plateau - you may master the drop catch, or discover a certain way of nudging is highly effective at saving from the right outlane, or you may just become more patient and make fewer risky shots. Or you may discover that you've been playing on a really hard physical table - perhaps it was just used in a tournament - and this particular machine you're playing now is much more friendly.
Which brings us to pitfalls. To use these statistics effectively, you must make sure to compare apples to apples. Two physical machines may be set up differently. Tournament conditions obviously won't score as well (usually - my AFM high score was under league conditions) as arcade play. And for most people, your physical scores will be one-eighth to one-tenth of your corresponding TPA score. And - the big clincher to accurately tracking your play - if you restart games, then you will be artificially keeping only the higher-scoring games and your actual performance will be worse than indicated.
You can also use the 1/8-1/4-1/2-2/3 rule to estimate what score you need to take down an opponent in a head-to-head match (or whether you even can). These are very rough estimates indeed - basing any probability estimate off a sample of one (and that sample being the most extreme observed value!) is dicey business. But if you know your opponent has a high score of 300M on a particular machine, then you know you need at least 75M to have about an 80% chance of beating him, and you can use your own high score on that machine to estimate your chances of getting that 75M. You will find that even with intimidating-looking differences in high score, you will very likely still have a fighting chance at winning. Again, this is because in comparison to his high score, most of your opponent's games suck.
So go forth and play more pinball, and hopefully you feel a little more reassured while doing so.
