Good IMPS Average

[corners1]

Still getting use to the idea of International Matchpoints scoring. Right now I'm gaining about 0.6 IMPS a hand. Is that good or bad? What would be a good average?

[semeai]

It depends who you're playing. Anything positive means you've done better than your opponents (at least compared to the field of other BBOers playing the hands).

 

I have the sense somehow that 1 imp/board (in the very long run) corresponds roughly to being one "skill level" (int/adv/exp) above your opponents.

[HighLow21]

This website has a rating based on hands you've played. It seems like it needs some work overall but is a pretty good indicator:

 

http://bboskill.com/

 

Just type in your username and it will give you a rating.

 

Roughly speaking, it assigns the following ratings:

Below -1.4 IMPs average: NOVICE

-1.4 to -0.6 IMPs average: BEGINNER

-0.6 to 0 IMPs average: INTERMEDIATE

0 to 0.6 IMPs average: ADVANCED

0.6 to 1.4 IMPs average: EXPERT

Above 1.4 IMPs average: WORLD CLASS

 

I'd actually change it a bit if I were building the model, roughly as follows:

Intermediate covers -0.6 to +0.6

Advanced is 0.6 to 1 or so

Expert about 1-1.5

World Class 1.5+.

 

This is because Intermediate is designed to handle the great majority of players who aren't superstars at the game but know what they are doing on most decisions in the game.

 

Those IMP estimates in my version are just approximate based on experience.

 

But you have to keep in mind that they are assigning these ratings strictly based upon one dimension of your performance -- your average IMP score (or MPs converted to IMPs). Given that that is the only information available, it's not a bad system, just one indicator. There are many other factors that go in to determining how you stack up.

 

In my experience a +0.6 average is way better than average. To consistently take 60 IMPs from the opponents on average every 100 hands, day in day out, is a strong effort. It doesn't sound like a big number, but consider it this way: 100 hands takes about 8 hours to play online assuming no interruptions. That's about a work day, and if you're "earning" 60 IMPs every day you're doing very well at your job.

 

The flip side of it is, there are a lot of very poor players on BBO, so if you're only playing against randoms all the time -- if you're leaving when the competition is decent and racking up big IMPs against beginners, flubbers and fools -- then it's not a big deal at all. If you're playing, on average, against average opponents, I'd be happy to partner you.

[Fluffy]

What would be a good average?

 

+0.01

[TylerE]

BBOSkill is the dumbest thing ever. It does not properly account for strength of competition. It rewards bunny bashing. That is all.

[awm]

Perhaps a better question is this one:

 

Suppose I play n boards against the same opponents. If we are equally matched, what range should my IMPs/board fall into?

 

While IMPs/board are not the best way to determine skill level, it might let me determine if I am better or worse than these particular opponents.

[Fluffy]

another question I sometimes wonder, regular pairs at MBC usually sit NS, should this biase the results NS vs EW slightly?, I mean, it should be easier to score good comparin against non regular pairs, than regular pairs on average.

[HighLow21]

Perhaps a better question is this one:

 

Suppose I play n boards against the same opponents. If we are equally matched, what range should my IMPs/board fall into?

 

While IMPs/board are not the best way to determine skill level, it might let me determine if I am better or worse than these particular opponents.

 

In that case, 0+. If you are equally matched then a score over zero is good and under zero, not good.

 

The standard deviation of IMPs is, in my experience, around 5. This means you should get 10+ IMP swings (in either direction) around 5% of the time and 5-10 IMP swings around a quarter of the time.

[helene_t]

humans against three robots usually sit south so ns is generally weaker

[HighLow21]

BBOSkill is the dumbest thing ever. It does not properly account for strength of competition. It rewards bunny bashing. That is all.

 

It does not properly account for them yet; as more names get added to the database, its ability to account for the skill level of the opponents will continue to improve.

 

Hence all my caveats about its use. But all that said -- it beats the pants off of not knowing anything, and it also beats the pants off of the "self-rating" that people give.

 

But to say that "it rewards bunny bashing," and nothing else, is demonstrably false.

[awm]

My question is basically about the distribution of IMP scores. My intuition is that over 8 boards, I would not be surprised to win or lose against an equal team by 16 IMPs or so (2/board) whereas over 32 boards I'd expect to be within 32 IMPs (1/board) but this has no statistical backing.

[PhilKing]

BBOSkill is the dumbest thing ever. It does not properly account for strength of competition. It rewards bunny bashing. That is all.

 

FWIW, this assertion is misleading, though it may depend how you define "properly".

[HighLow21]

My question is basically about the distribution of IMP scores. My intuition is that over 8 boards, I would not be surprised to win or lose against an equal team by 16 IMPs or so (2/board) whereas over 32 boards I'd expect to be within 32 IMPs (1/board) but this has no statistical backing.

 

Assuming that the swings are random and independently distributed, then you can mutliply the st deviation of a single board by the square root of the number of boards played to get your error measurement.

 

I stated in a previous reply that the standard deviation of IMP swings is, in my experience, about 5. 5 times the square root of 8 yields about 14.

 

In other words, the standard deviation of the score for the 8-board match would be about +/-14, which means, roughly speaking, about 2/3 of the time it'd be smaller than that and about 1/3 of the time, larger (in other words, -15 or lower, or +15 or higher).

 

In 32 boards, the same math applies: 5 times the square root of 32 yields about 28. So about 2/3 of the time, the winner will net 28 IMPs or fewer, while 1/3 of the time, the winner will net 29 IMPs or more.

 

And actually, my personal, if overly precise, standard deviation of IMPs estimate is closer to 5.3. Using this instead of 5 above, I would get standard errors of 15 and 30 rather than 14 and 28.

 

In this case, intuition and math lead to very similar answers. :-)

[awm]

So to return to the original post, it seems that if he can maintain a +0.6 average over 100 boards or more, it is a decent bet that his partnership is better than the opposition.

 

Whether this is "good" or not will depend on the opposition of course.

[HighLow21]

So to return to the original post, it seems that if he can maintain a +0.6 average over 100 boards or more, it is a decent bet that his partnership is better than the opposition.

 

Whether this is "good" or not will depend on the opposition of course.

 

Right, we can only talk about "good" relative to the opposition -- not to the general bridge population as a whole.

 

Assuming a 5 for standard deviation, the typical variation over 100 boards will be 5 x sqrt(100) = 5 x 10 = 50. So +/-50 IMPs. A 0.6 average would imply 60 IMPs, which is not "statistically significant" but you typically need a ratio of around 2 or better for that --> your ratio is 60/50 = 1.2. This value is called the t-statistic, and the corresponding p-value is around 11%.

 

(To take out the math and jargon here: if you WERE, in fact, equal, then after 100 boards, you would only be up +0.6 IMPs about 11% of the time. Similarly, you would only be down -0.6 IMPs 11% of the time.)

 

So as a statistician, I would say that 100 boards is not enough to tell for reasonably certain. The magic "p-value" number for statisticians is typically around 5%. But it's not far off; at 500 hands, it would start to be pretty certain. (At 500 boards, the standard deviation of the accumulated IMPs total would be 5 x sqrt(500) = 112 IMPs, but you're up by +0.6 x 500 = 300 total; this is would happen by random chance well less than 1% of the time.)

 

As a bridge player, I would say that +0.6 means that you are very likely the better pair, though I'm not conclusively convinced yet. :-)

 

One thing I will tell you: I track many of my results in a spreadsheet and calculate the running IMPs total on the previous 200 hands at all times. (Yes, I am a math nerd.) It is very rare that, at any given time, the previous 200 hands have an average IMP score that is as much as 0.6 above (or below) my long term IMPs average.

 

Hope this helps.

[Trinidad]

I did a quick calculation based on the Cross-Imp competition at our club.

 

We play 26 boards per evening. At the end of the evening, we get the results: for each pair the number of IMPs/board. I calculated the standard deviation of the IMPs per board for 7 of these evenings. It was slightly above 1.1 IMPs/board. Assuming that the skill at BBO and in our club are normally distributed and that the standard deviation of the skill in my clubs is as large as the standard deviation in skill on BBO (quite bold assumptions, but you have to assume something) this would give the following percentile table for BBO:

 

-2        3

-1.8      5

-1.6      7

-1.4      10

-1.2      13

-1        18

-0.8      23

-0.6      29

-0.4      35

-0.2      43

0         50

0.2       57

0.4       65

0.6       71

0.8       77

1         82

1.2       87

1.4       90

1.6       93

1.8       95

2         97

 

The first column shows your IMPs/board score. The second shows what percentage of the pairs are worse than you.

 

I wouldn't call it the exact science, but it will give you an indication.

 

Rik

[eagles123]

Surely the IMPS average entirely depends on who you play with? For example, in the last month on bbo I have an IMPS average of 0.76 (168 boards) but that's just playing with the dumb idiots you tend to come across on the main bridge club, doesn't mean i'm an expert player or anything. If it was to play against experts players then i'm sure my average would be a big minus!

 

Eagles

[Trinidad]

Surely the IMPS average entirely depends on who you play with?

Of course, it does.

 

For example, in the last month on bbo I have an IMPS average of 0.76 (168 boards) but that's just playing with the dumb idiots you tend to come across on the main bridge club, doesn't mean i'm an expert player or anything.

 

So, the table suggest that about 75% of those dumb idiots are playing worse than you and about 25% of these dumb idiots are playing better than you. So, it indicates that -for a dumb idiot- you are relatively smart. ;)

 

Rik

[mycroft]

Also: my belief is quite strongly that I and my practised partnerships are *at least* 1 IMP/board better than me and equally-strong-as-my-partner random, or partner and as-strong-as-me-random.

[helene_t]

So, the table suggest that about 75% of those dumb idiots are playing worse than you and about 25% of these dumb idiots are playing better than you.

No. Your stats were for a single session. Most of the variance is random. That 77% score less than 0.8 IMPs over a long session (Eagles' 168 boards) would only be true if the variance in your table was attributable to skill difference alone.

 

Even in a highly heterogenous field you wouldn't expect 23% to be able to maintain an average of 0.8 IMPs over 168 boards.

 

Maybe 98% of the dump idiots are dumper than Eagles :)

[Trinidad]

No. Your stats were for a single session. Most of the variance is random. That 77% score less than 0.8 IMPs over a long session (Eagles' 168 boards) would only be true if the variance in your table was attributable to skill difference alone.

 

Even in a highly heterogenous field you wouldn't expect 23% to be able to maintain an average of 0.8 IMPs over 168 boards.

 

Maybe 98% of the dump idiots are dumper than Eagles :)

That is correct.

 

Probably the best way to get a feeling for your result is to convert the IMPs to victory points. This is corrected for the number of boards played.

 

Rik

[HighLow21]

I did a quick calculation based on the Cross-Imp competition at our club.

 

We play 26 boards per evening. At the end of the evening, we get the results: for each pair the number of IMPs/board. I calculated the standard deviation of the IMPs per board for 7 of these evenings. It was slightly above 1.1 IMPs/board. Assuming that the skill at BBO and in our club are normally distributed and that the standard deviation of the skill in my clubs is as large as the standard deviation in skill on BBO (quite bold assumptions, but you have to assume something) this would give the following percentile table for BBO:

 

-2        3

-1.8      5

-1.6      7

-1.4      10

-1.2      13

-1        18

-0.8      23

-0.6      29

-0.4      35

-0.2      43

0         50

0.2       57

0.4       65

0.6       71

0.8       77

1         82

1.2       87

1.4       90

1.6       93

1.8       95

2         97

 

The first column shows your IMPs/board score. The second shows what percentage of the pairs are worse than you.

 

I wouldn't call it the exact science, but it will give you an indication.

 

Rik

 

Rik just to be clear:

- To me what this looks like is 1.1 is the standard error of the average of the IMPs, which would make sense if you were playing 20-40 boards. (As you said, 26 boards.)

- And if I multiply this by the square root of 26 I get 5.6, which would be the standard deviation of the IMPs score on any individual board. This is very consistent with my math.

- Just to be clear -- 1.1 is the standard deviation of the 7 nightly IMPs averages? Can you type in the data so I can see it? :)

[HighLow21]

Of course, it does.

 

 

 

So, the table suggest that about 75% of those dumb idiots are playing worse than you and about 25% of these dumb idiots are playing better than you. So, it indicates that -for a dumb idiot- you are relatively smart. ;)

 

Rik

No, the percentiles given only indicate what percent of the time you are likely to receive that score GIVEN THAT you are all equally matched. In other words, if you are evenly matched, 75% of the time you will score +0.76 IMPs average or lower. 25% of the time it would be higher than that.

 

It says nothing about what percent of pairs are better/worse than you.

[HighLow21]

No. Your stats were for a single session. Most of the variance is random. That 77% score less than 0.8 IMPs over a long session (Eagles' 168 boards) would only be true if the variance in your table was attributable to skill difference alone.

 

Even in a highly heterogenous field you wouldn't expect 23% to be able to maintain an average of 0.8 IMPs over 168 boards.

 

Maybe 98% of the dump idiots are dumper than Eagles :)

To go from 26 boards to 168 boards you would have to divide everything in the left-hand column by the square root of 7, which is the square root of the ratio of hands played. The variation decreases as a function of the square root of the number of observations.

 

Assuming Trinidad's data is correct, I've included a table here. Each row represents the number of boards, and each column represents the percent of the time you would achieve that score or lower, assuming your expected score is zero. (If your expected score is different, simply add your expected score to ALL of the entries in this table.)

 

As an example -- if your expect score is zero (competition is TOTALLY EVEN), you play 52 boards, and you score a +0.81 IMP average, you've done better than you would have done 85% of the time.

 

If your expected score is 0.5 IMPs per board, you play 8 boards, and get a score of +2.04 IMPs, you have done better than you would have done normally about 75% of the time. (1.04 IMPs plus your expected boost of 1 IMP per board.)

 

Alternatively -- if you have an expected score of 0.8 IMPs and play 128 boards, you will win almost 95% of the time. (This is because the 5% observation for 128 boards is -0.82, and you expect to add +0.8 on average to that total.)

 

I've also attached how it looks in Excel.

http://2.bp.blogspot.com/-RPGassbceU8/UnwBdTRU7vI/AAAAAAAAAHY/qP_Wsdd34oE/s640/IMPS.png

 

NUMBER OF IMPs/BOARD AVERAGE: NUMBER OF HANDS PLAYED (FIRST COLUMN) VERSUS PERCENTILE ACHIEVEMENT (TOP ROW). 50% = NORMAL/EXPECTED RESULT.

H/P 1% 2% 5% 10% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 98% 99%

1 -13.1 -11.5 -9.23 -7.19 -4.72 -3.78 -2.94 -2.16 -1.42 -0.7 0 0.7 1.42 2.16 2.94 3.78 4.72 5.81 7.19 9.23 11.5 13.1

5 -5.84 -5.15 -4.13 -3.21 -2.11 -1.69 -1.32 -0.97 -0.64 -0.32 0 0.32 0.64 0.97 1.32 1.69 2.11 2.6 3.21 4.13 5.15 5.84

8 -4.61 -4.07 -3.26 -2.54 -1.67 -1.34 -1.04 -0.76 -0.5 -0.25 0 0.25 0.5 0.76 1.04 1.34 1.67 2.06 2.54 3.26 4.07 4.61

13 -3.62 -3.19 -2.56 -1.99 -1.31 -1.05 -0.82 -0.6 -0.39 -0.2 0 0.2 0.39 0.6 0.82 1.05 1.31 1.61 1.99 2.56 3.19 3.62

16 -3.26 -2.88 -2.31 -1.8 -1.18 -0.95 -0.74 -0.54 -0.36 -0.18 0 0.18 0.36 0.54 0.74 0.95 1.18 1.45 1.8 2.31 2.88 3.26

26 -2.56 -2.26 -1.81 -1.41 -0.93 -0.74 -0.58 -0.42 -0.28 -0.14 0 0.14 0.28 0.42 0.58 0.74 0.93 1.14 1.41 1.81 2.26 2.56

32 -2.31 -2.04 -1.63 -1.27 -0.83 -0.67 -0.52 -0.38 -0.25 -0.12 0 0.12 0.25 0.38 0.52 0.67 0.83 1.03 1.27 1.63 2.04 2.31

52 -1.81 -1.6 -1.28 -1 -0.65 -0.52 -0.41 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.41 0.52 0.65 0.81 1 1.28 1.6 1.81

64 -1.63 -1.44 -1.15 -0.9 -0.59 -0.47 -0.37 -0.27 -0.18 -0.09 0 0.09 0.18 0.27 0.37 0.47 0.59 0.73 0.9 1.15 1.44 1.63

96 -1.33 -1.18 -0.94 -0.73 -0.48 -0.39 -0.3 -0.22 -0.15 -0.07 0 0.07 0.15 0.22 0.3 0.39 0.48 0.59 0.73 0.94 1.18 1.33

128 -1.15 -1.02 -0.82 -0.64 -0.42 -0.33 -0.26 -0.19 -0.13 -0.06 0 0.06 0.13 0.19 0.26 0.33 0.42 0.51 0.64 0.82 1.02 1.15

168 -1.01 -0.89 -0.71 -0.55 -0.36 -0.29 -0.23 -0.17 -0.11 -0.05 0 0.05 0.11 0.17 0.23 0.29 0.36 0.45 0.55 0.71 0.89 1.01

[benlessard]

In chess it take 24 games vs players who have a rating to get a rating. IMO 24 boards approx equal a chess game in term of decision and possibility of mistakes however luck vs no luck mean that it should be divided by 2 at least . So ratings will only worth something when you have about 1200 hands vs opps that have ratings.

 

Since at the beginning nobody have valid ratings IMO around 1800 hands its going to make some sense (if the calculations are well done).