# BPI, PPI, BPASI, PPASI and OPI

#### 2/5MR2

##### amateur
For those interested in the analytical aspect of 14.1:

I have been scoring matches of the Amsterdam Billiards 14.1 league for a while now, so much that I have enough data now to compare various 14.1 metrics. For some players (mostly open/pro-level players) I have multiple matches. I have also scored the final and semi-finals of last year's American 14.1 championship as I was watching them so I also have some data for the very top players.

Here is what I think the data shows:

BPI, PPI: The values doesn't appears correlated with anything we could care about. The same player sometimes have 2.00 for one match and 14.00 for the other match. Over multiple matches, the weighted average (by innings) fails to rank the players in the order you would put them if you are familiar with their skill level.

BPASI, PPASI: Doing much better than than BPI and PPI but again, values vary wildly in size for the same player (6.00 to 21.57), (7.35 to 24.00). The weighted average (by offensive innings) roughly ranks the player in the order you would put them.

OPI: This is the metric I am proposing to measure a player -offensive- performance during a match. Just like BPASI, PPASI it measures only the offensive aspect of the game. The major difference is that the averaging is over offensive shots (instead of over offensive innings). I find the result from this very small set of data to be very encouraging. For the same player, values are very consistent, the weighted average over all matches (weighted by the number of offensive shots) does rank the players in the correct order. Also, since the values are so consistent, the OPI value for just 1 match does say something about the absolute skill level of the player. Some time ago I came up with these rough categories after scoring the first few matches with OPI calculated. I have way more data now but these categories have held up:

0.000 to 0.200: Beginner
0.200 to 0.500: Amateur
0.500 to 0.750: Good amateur
0.750 to 0.900: Pro
0.900 to 1.000: Top pro

Even for amateurs players: players in the 'Gold' division score in the 'Good amateur' category almost always, and people in the 'Silver' division in the Amateur category (very little data in this case but still).

If you want to know more about how OPI is calculated, I have started to work on a webpage with the details:

http://www.metaobjects.ca/foe/opi.html

Would love to hear what people interested in that kind of analytical stuff think. All 3 or you.

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#### zencues.com

##### AzB Silver Member
Silver Member
You should explain the acronyms. Most people have no idea what they mean.

#### 2/5MR2

##### amateur
BPI = Balls per innings
PPI = Points per innings
BPASI = Balls per attempted scoring innings
PPASI = Points per attempted scoring innings
OPI = Offensive play index

The first 4 have existed for a while. You can find BPI and PPASI in a few scoring apps already. To calculated BPI/PPI, you calculated the average number of balls/points scored in and inning. For BPASI/PPASI it is the average number of balls/points in -attempted scoring- innings, meaning only innings where the player is trying to pocket balls. OPI is a new measure I an proposing it is a little more work to calculate it.

#### sjm

##### Older and Wiser
Silver Member
I admire what you are trying to do here, but will always contend that offense cannot be separated from defense.

The all-time greats such as Sigel and Mosconi tended to have BPI in the 13-15 range, but Irving Crane's was only in the 7-8.5 range. That's because he played more defense than them. His BPASI in his prime would have been nearly as high as theirs, but even that is misleading, because if you compared his defense to his contemporaries, the offensive chances he created were, on average, just a little easier than theirs, so his offensive execution may have been a little below theirs if all ball pocketing attempts are considered, but his scoring comparable. He also tended not to take flyers, so stylistically, the nature his offensive innings were not always comparable to those of guys like Mosconi, Sigel and, even more so, Jimmy Caras.

If one pockets the one loose ball on the table, plays shape for a safety, and then plays safe, is that an offensive inning or not?

OPI looks like an ambitious step in the statistical separation of offense, but it still comes with quite a few issues that can make it misleading. As defined, one cannot say that the player with the higher OPI is the better player offensively.

Still, some nice work here. Take a deep bow, for every small step forward is worthy of recognition and respect.

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#### 2/5MR2

##### amateur
Hi Sjm,

First to answer your question:

"If one pockets the one loose ball on the table, plays shape for a safety, and then plays safe, is that an offensive inning or not? "

Yes it is considered an offensive inning in the calculation of OPI and also in the calculation of BPASI/PPASI (offensive inning = attempted scoring inning), and yes it is a problem. But it is a -small- problem for OPI and a -big- problem for BPASI/PPASI. Consider the following example:

Imagine that a player, in a race to 150, runs 40 and then 110 and out after the initial safety battle. The PPASI will be 75.00. Now let's say that during the initial safety battle, on two occasions, the player pockets 1 stray ball and returns to the safety battle. He then runs 38 and 110. The PPASI is now only 37.50 (half !) even tough it is almost the exact same match !!!

The numbers for OPI would be 0.978 and 0.940. The 2 small unimportant 1 ball innings make only a 0.038 difference.

This quick example shows that OPI is much more resistant to the problem you pointed out (I call this the 'planned short offensive innings'). It also shows that, to measure offensive performance, averaging should be over -shots- not -innings- because all innings are not equally important.

As for BPI, I find it very hard to assign any meaning to it. The data I gave above clearly shows that it can be anything for anyone. Same player can have 2, 10, 14, 17. What is it supposed to measure? Good offensive play drives the value up and good defensive play drives the value down.

If I tell you somebody won a match 150-95 with a BPI of 4.2, it can be a total be total beginner or it can be the champion of the world. Because if you get into 1 or 2 long safety battles, your BPI will be minuscule even if you run 100 balls after.

If I tell you somebody won a match 150-95 with an OPI of 0.940, he is a top pro, or maybe an average pro who had a really good night, no doubt. If the OPI is 0.195, the guy is a beginner, no way around it.

Thanks for those compliments. I appreciate. If you find other issues you think makes OPI misleading please share, it is still early and I would be willing to change the formula if I can make OPI better ...

#### sjm

##### Older and Wiser
Silver Member
Hi Sjm,

First to answer your question:

"If one pockets the one loose ball on the table, plays shape for a safety, and then plays safe, is that an offensive inning or not? "

Yes it is considered an offensive inning in the calculation of OPI and also in the calculation of BPASI/PPASI (offensive inning = attempted scoring inning), and yes it is a problem. But it is a -small- problem for OPI and a -big- problem for BPASI/PPASI. Consider the following example:

Imagine that a player, in a race to 150, runs 40 and then 110 and out after the initial safety battle. The PPASI will be 75.00. Now let's say that during the initial safety battle, on two occasions, the player pockets 1 stray ball and returns to the safety battle. He then runs 38 and 110. The PPASI is now only 37.50 (half !) even tough it is almost the exact same match !!!

The numbers for OPI would be 0.978 and 0.940. The 2 small unimportant 1 ball innings make only a 0.038 difference.

This quick example shows that OPI is much more resistant to the problem you pointed out (I call this the 'planned short offensive innings'). It also shows that, to measure offensive performance, averaging should be over -shots- not -innings- because all innings are not equally important.

As for BPI, I find it very hard to assign any meaning to it. The data I gave above clearly shows that it can be anything for anyone. Same player can have 2, 10, 14, 17. What is it supposed to measure? Good offensive play drives the value up and good defensive play drives the value down.

If I tell you somebody won a match 150-95 with a BPI of 4.2, it can be a total be total beginner or it can be the champion of the world. Because if you get into 1 or 2 long safety battles, your BPI will be minuscule even if you run 100 balls after.

If I tell you somebody won a match 150-95 with an OPI of 0.940, he is a top pro, or maybe an average pro who had a really good night, no doubt. If the OPI is 0.195, the guy is a beginner, no way around it.

Thanks for those compliments. I appreciate. If you find other issues you think makes OPI misleading please share, it is still early and I would be willing to change the formula if I can make OPI better ...

Thanks for the reply. I'm still thinking about all this, but gave you my snap judgements.

#### justnum

##### Principal Investigator of Magic Trick Shots
Silver Member
Interesting post analysis that helps identify strong player metrics.

I like statistics as well, it helps generalize and validate various assumptions.

Using statistics to help players and make good decisions is where my interest are at.

The break shot resulting in a freeze to the rack is an example.

Some break shots have much higher percentages of leaving the cue ball frozen to the rack.

The direction I am going is using statistics to track ball layout patterns that result in unfavorable conditions.

However keeping statistics on ball layouts is more focused on establishing a library situations to avoid.

Statistics on player performance during a match may have more useful data in categorizing the data as qualitative measures as oppose to specific finite values.

Everyone knows what a strong run looks like. Even more dangerous is watching a pro push the 3 foul rule and have it result in them winning the rack.

Qualitative statistics are something to look at is all I am saying.

Characteristics of a pro in a 14.1 match, they usually have a break shot, most times it results in a clean break, sometimes it doesn't.

#### stevekur1

##### The "COMMISH"
Silver Member
First off, very good work Pascal !!!

I am both for and against BPI.

I like to see someones OPI to see their true scoring game.

but BPI is something to be counted as well. Some players play a lot of safeties as a strategy, this can be correlated against there W/L to help to determine if their strategy works. but BPI should be left in tact as a measure.

A Lot of ball runners lack in the safety game, and the game is not purely about running balls. Nothing wrong with a smaller run then playing a good safety leading to another successful inning.

Hope this makes sense.
Steve

#### sjm

##### Older and Wiser
Silver Member
Interesting post analysis that helps identify strong player metrics.

I like statistics as well, it helps generalize and validate various assumptions.

Using statistics to help players and make good decisions is where my interest are at.

The break shot resulting in a freeze to the rack is an example.

Some break shots have much higher percentages of leaving the cue ball frozen to the rack.

The direction I am going is using statistics to track ball layout patterns that result in unfavorable conditions.

However keeping statistics on ball layouts is more focused on establishing a library situations to avoid.

Statistics on player performance during a match may have more useful data in categorizing the data as qualitative measures as oppose to specific finite values.

Everyone knows what a strong run looks like. Even more dangerous is watching a pro push the 3 foul rule and have it result in them winning the rack.

Qualitative statistics are something to look at is all I am saying.

Characteristics of a pro in a 14.1 match, they usually have a break shot, most times it results in a clean break, sometimes it doesn't.

Some good out-of-the-box thinking here.

You make some really god points, but I don't agree with the point about differentiating some break shots form others due to more chance of getting stuck. I'm of the opinion that it's almost always the shooter's fault when they get stuck. The qualitative variable that I believe to be more important is what kind of opportunity you had when you came to the table. Did you win control of the table by taking a flyer, perhaps a combo or a shot out of the rack? Did you try a difficult shot to get started because you reached the point where playing safe was similarly difficult? These methods of winning control cannot be compared to gaining control of the table through safety play or after opponent's miss. Also, are we to water down a player's statistics because they came to the table at 148 and ran 2 and out?

So, in short, I'm on board with your idea to introduce qualitative variables here, but it's very tricky business how to go about it.

#### justnum

##### Principal Investigator of Magic Trick Shots
Silver Member
Some good out-of-the-box thinking here.

You make some really god points, but I don't agree with the point about differentiating some break shots form others due to more chance of getting stuck. I'm of the opinion that it's almost always the shooter's fault when they get stuck. The qualitative variable that I believe to be more important is what kind of opportunity you had when you came to the table. Did you win control of the table by taking a flyer, perhaps a combo or a shot out of the rack? Did you try a difficult shot to get started because you reached the point where playing safe was similarly difficult? These methods of winning control cannot be compared to gaining control of the table through safety play or after opponent's miss. Also, are we to water down a player's statistics because they came to the table at 148 and ran 2 and out?

So, in short, I'm on board with your idea to introduce qualitative variables here, but it's very tricky business how to go about it.

The pro matches I think about are when top pros:

Play a safe but leave a hidden dead combo from the rack.
Play to pocket a shot from a bad position and end up in worse position.
Play a break shot to result in no available shot to continue rack.
Play a shot and just miss

The type of qualitative variable I think about is how likely would another top pro have selected that same shot.

I see 14.1 as having stats more closely to quarterback attempt/completions.
How many break shots were attempted and how many were successful. At the higher levels most pros can run well above 60 balls easily. The main variation I think is in break shot data.

As for the 148 and 2 run, we are talking about the smallest differences in the top 1% of pro players. A small modification in their approach can have huge impact on their performance at tournaments.

#### sjm

##### Older and Wiser
Silver Member
More good stuff here.

The pro matches I think about are when top pros:

Play a safe but leave a hidden dead combo from the rack.

With rare exception, I consider this to be an error, not a bad roll, and don't see it any different from any other defensive error.

Play to pocket a shot from a bad position and end up in worse position.

Yes, good example of something you'd have to account for somehow,

Play a break shot to result in no available shot to continue rack.

This is really quite rare in today's game. It was a big issue 40 years ago before Simonis cloth was in use in 14.1. There is a little bit of luck involved, of course, but I feel that most times, failure to get a shot is the shooter's fault, and is to due with either a poor attack angle or stroke.

Play a shot and just miss

Yes, the difficulty of the shot is a key consideration. A miss on a flyer or chancy combo is a little different form a routine, open table miss. A qualitative variable could help out here.

The type of qualitative variable I think about is how likely would another top pro have selected that same shot.

Yes, excellent point.

I see 14.1 as having stats more closely to quarterback attempt/completions.
How many break shots were attempted and how many were successful. At the higher levels most pros can run well above 60 balls easily. The main variation I think is in break shot data.

I think this may be an oversimplification, because it ignores that the better pattern players will, on average, get better shape onto the break shots. Not every missed break shot is the same.