Thoughts on this stat?

[Deleted]

The following are excerpts from a paper I wrote proposing another way to measure hitting efficiency and I am seeking feedback from the VT community.

"The purpose of this paper is to propose a new statistic that more accurately reflects an individual’s contribution to the overall success of the team: kill-to-error ratio plus hitting percentage (k/e+hp). The proposed statistic adds a variable to hitting percentage that more directly reflects team success- points scored versus points lost."

"Generally, the outside hitter will have the largest amount of attempts due to the nature of the position. Almost all “out-of-system” sets are directed to the outside hitter and it is tough to terminate these balls with regularity. However, a middle hitter is almost always set when the pass is perfect and everything is “in-system”. It is easier to terminate the ball “in-system” as opposed to “out-of-system,” setting up the middle hitter to have the potential for a much higher efficiency than an outside hitter receiving less desirable attempts. Considering this, both the outside hitter and middle hitter in this example equally contributed to the point total since they had the same amount of kills and errors yet the hitting percentage stat largely favors the middle hitter who had less attempts. In a sense the outside hitter was punished for not terminating unfavorable sets and keeping them in play. This is even more inauspicious since the outside hitter had fewer errors per attempt than the middle hitter."

Below are the 2013 Sweet Sixteen participants and their individual kill leaders. The numbers following indicate hitting % (rank) and k/e+hp (rank)

• American         .289 (5)/3.648 (6)         Lindovska   .285 (8)/3.613 (9)          
• BYU                 .262 (11)/3.394 (8)       Gray           .305 (7)/3.946 (7)    
• Florida State    .266 (9)/3.146 (10)        Walch        .270 (11)/3.099 (13)
• Illinois             .210 (16)/2.641 (16)      Birks          .191 (16)/2.716 (16)
• Kansas            .254 (12)/3.122 (11)      Jarmoc       .320 (5)/3.503 (10) 
• Michigan State .245 (13)/2.808 (14)      Wicinski      .253 (13t)/2.977 (14)
• Minnesota        .288 (6)/3.869 (3)         Dixon         .399 (3)/5.261 (3)
• Nebraska         .270 (8)/3.154 (9)         Robinson    .318 (6)/3.948 (6)
• Penn State       .306 (2)/3.781 (5)         McClendon .279 (10)/3.500 (11)
• Purdue             .241 (14)/2.725 (15)     Nichol        .241 (15)/2.825 (15)
• San Diego        .264 (10)/3.035 (12)     Ferrari        .444 (1)/5.879 (2)
• Stanford          .308 (1)/4.223 (1)         Wopat        .429 (2)/6.156 (1)
• Texas              .296 (3)/3.841 (4)         Eckerman   .280 (9)/3.666 (8)
• USC                .290 (4)/3.914 (2)         Bricio          .253 (13t)/3.499 (12)
• Washington     .278 (7)/3.617 (7)         Vansant       .323 (4)/4.355 (4)
• Wisconsin        .239 (15)/2.925 (13)     Chapman    .265 (12)/3.949 (5)

"Chapman was ranked lower in hitting percentage yet significantly higher in k/e+hp. Contrarily, Jarmoc was ranked higher in hitting percentage and significantly lower in k/e+hp. Both of these accounts can be explained by analyzing the k-e-a.
 Chapman had 490 kills, 133 errors, and 1,348 total attempts. This translates to a .265 hitting percentage and 3.949 k/e+hp. Jarmoc had 382 kills and 120 errors on 820 attempts, translating to a .320 hitting percentage and 3.503 k/e+hp. The difference in attempts (528) is the primary factor for the large spread in hitting percentage between the two players. The k/e+hp statistic is higher for Chapman because, again, k/e+hp is primarily focused on a hitter’s ability to score points (kills) versus give points away (errors). Ultimately Chapman was responsible for scoring more total points than Jarmoc as demonstrated by the higher k/e+hp number, but not by hitting percentage. Chapman had a greater contribution to her team’s outcome than Jarmoc despite having a hitting percentage 55 points lower."

"Now examine Bricio (422-130-1154; .253) and Wicinski (523-192-1310; .253). Their k-e-a numbers have some variance, but they have the same hitting percentage, tying for 13th on the list. However, upon calculation of k/e+hp Bricio (3.499) moves up one spot to 12 and Wicinski (2.977) drops one spot to 14... Further investigation discovers
 that Bricio has an error-per-attempt ratio of .113 while Wicinski’s error-per-attempt ratio is .147. This factor is not considered in the k/e+hp statistic, however if both players had the same amount of attempts, Bricio would always (based on the error-per-attempt ratio) have fewer errors than Wicinski, resulting in more chances for her team to win the rally."

"This paper was written to propose the k/e+hp statistic as a better evaluator of the impact a hitter makes on the outcome of the game. The primary difference between the two is that k/e+hp is not weighted on how many attempts a player has, but ultimately how many points were scored versus how many points were lost (offensively) directly as a result of that player’s actions. Without much weight on attempts, hitters tend to receive a higher k/e+hp as long as they keep the ball in play, presenting their team a chance to win the point."

Thoughts?

[beachdude]

If you are trying to say that outside hitters have the most impact on a game, I agree. Oh's and OPP determine the outcome of a match 90% of the time.

[johnbar]

If you make one attempt and get the kill, your k/e = 1/0, which is undefined.

That's an edge case, but I also find it strange you are adding together two numbers, one which runs from 0 to "infinity", and the other is bounded by zero and one. It seems like it is going to be dominated by the former. Why add the HP at all?

[mikegarrison]

Sept 16, 2014 12:14:40 GMT -5 johnbar said:

If you make one attempt and get the kill, your k/e = 1/0, which is undefined.

That's an edge case, but I also find it strange you are adding together two numbers, one which runs from 0 to "infinity", and the other is bounded by zero and one. It seems like it is going to be dominated by the former. Why add the HP at all?

HP is bounded from -1 to +1, actually. But good point about the kill/error ratio. It's always infinite when there are no hitting errors, and that happens more often than one might think, especially for players who have few attempts.

[Wolfgang]

I'm sure you've already done this but there are numerous metrics for basketball that are incredibly interesting. Some examples:

Player Efficiency Rating - looks at a player's full stat line to measure his per-minute performance.
True Shooting % - calculates what a player's shooting % would be if free throws and 3-pointers are taken into account
Effective FG% - calculates a modified FG% by counting made 3-pt FGs as 1.5, thus making it a more fair assessment of a player's shooting ability
Estimated Wins Added - calculates a player's contribution to his team's wins by comparing it to some baseline value

These may give you some insights on how to create a metric for volleyball.

Personally, I never understood the error stat. The dynamics of an attack are very complex: (a) the blocker may have made an excellent block, (b) the player may have attempted to hit high hands which resulted in the ball landing out of bounds, hence an error, (c) the player may have attempted to hit high hands which resulted in a touch and hence, a kill, (d) the ball hits the blocker's hands and bounces to the floor in the hitter's side of the court, hence an error, (e) the ball hits the blocker's hands and bounces to the blocker's side of the court, hence a kill. It seems to me that, quite often, the means by which the ball lands in/out seems somewhat random/lucky to me.

In basketball, a blocked shot is merely counted as a missed shot for the shooter. Also, I don't think basketball counts shooting errors (e.g., airballs). In fact, if we analogized basketball to volleyball (to the extent that such an analogy can be made), a missed shot in basketball should count as an error. Since there are way more missed shots than made shots, the FG% line would be negative for 99% of the players.

Someone more versed in volleyball stats can discuss this better.

[johnbar]

Mikegarrison: thanks for the correction. I should have caught that. "Hitting negative" is also not that uncommon, especially for players with a small number of attempts.

[Wolfgang]

Sept 16, 2014 12:14:40 GMT -5 johnbar said:

If you make one attempt and get the kill, your k/e = 1/0, which is undefined.

That's an edge case, but I also find it strange you are adding together two numbers, one which runs from 0 to "infinity", and the other is bounded by zero and one. It seems like it is going to be dominated by the former. Why add the HP at all?

In instrumentation design, boundary values are not counted; that is, the output of a measuring device is only valid from a predefined range of values. For example, your bathroom weight scale may only give you valid numbers if your weight was anywhere between 30-250 lbs. If you are less than 30 lbs or above 250 lbs, your bathroom weight scale cannot give accurate results. Also, you should go see a doctor about your troubling weight.

It's possible that the OP's "formula" is only valid for certain limited number of kill attempts. Below this number, the formula isn't valid. It should just be labeled as DNQ (did not qualify). For example, you could say that a stat that shows basketball player A who is 50 of 100 attempts (50%) is more accurate than a stat that shows basketball player B who is 1 of 2 (50%). Also, the type of shot should be taken into consideration. In volleyball, a middle hitter's attacks may be considered more "easy" than an outside hitter's attacks, hence the disparity in hitting% of MHs to OHs. In basketball, a layup/dunk is "easier" than a medium- to 3 pt-range jumpshot -- although you've got to have the moves to drive to the hoops to layup/dunk the ball. I suppose any cement-footed guy can make a jumpshot. This brings up another point: the contested shot vs. an open shot. In volleyball, the hitter who goes up against 1 blocker/no blocker vs. a hitter who goes up against 2+ blockers.

[mikegarrison]

Sept 16, 2014 13:15:35 GMT -5 Wolfgang said:

Sept 16, 2014 12:14:40 GMT -5 johnbar said:

If you make one attempt and get the kill, your k/e = 1/0, which is undefined.

That's an edge case, but I also find it strange you are adding together two numbers, one which runs from 0 to "infinity", and the other is bounded by zero and one. It seems like it is going to be dominated by the former. Why add the HP at all?

In instrumentation design, boundary values are not counted; that is, the output of a measuring device is only valid from a predefined range of values. For example, your bathroom weight scale may only give you valid numbers if your weight was anywhere between 30-250 lbs. If you are less than 30 lbs or above 250 lbs, your bathroom weight scale cannot give accurate results. Also, you should go see a doctor about your troubling weight.

It's possible that the OP's "formula" is only valid for certain limited number of kill attempts. Below this number, the formula isn't valid. It should just be labeled as DNQ (did not qualify).

That kind of thinking makes sense for a physical device, like a scale, that has to deal with limitations on spring strength, the flexing of the supports, friction, etc.

But for something like this, that sort of reasoning screams "I am a kludge metric that only seems to work because of coincidental correlations." It's like the Bill James Pythagorean formula for baseball wins v. runs scored and runs allowed. It's a decent fit when runs scored and runs allowed fall into normal baseball ranges, but the fact that it doesn't work very well for teams on the extremes shows that it's not really correct.

[Wolfgang]

Not really. I added to my post. A stat that shows 50/100 (50%) is more accurate than a stat that shows 1/2 (50%). The more data, the more accuracy. This has nothing to do with boundary values and doesn't reveal that the formula is wrong.

Also, what the heck is a "kludge"?

I don't know who Bill James is.

And I meant what I said about going to see a doctor.

[Deleted]

Sept 16, 2014 12:14:40 GMT -5 johnbar said:

If you make one attempt and get the kill, your k/e = 1/0, which is undefined.

This was a noticeable dilemma when creating the stat. Below is my solution listed in the paper.

"*= Since dividing by zero equals zero... the author determined that the fairest way to calculate the formula for a player with zero errors is to add one to the kill total then add the hitting percentage. A player with one error receives credit for the exact number of kills attained per the k/e ratio, therefore committing no errors should be deemed better than committing one error."

[Deleted]

Sept 16, 2014 12:14:40 GMT -5 johnbar said:

That's an edge case, but I also find it strange you are adding together two numbers, one which runs from 0 to "infinity", and the other is bounded by zero and one. It seems like it is going to be dominated by the former. Why add the HP at all?

This is why:

"Although this paper has frequently discussed that the points won versus points lost ratio (k/e) should be the most important factor when determining a hitter’s effectiveness, it should be duly noted that a hitter with the ability to achieve better k/e numbers on fewer attempts should be deemed more successful than a hitter that achieves the same numbers on more attempts. This is the primary reason that hitting percentage is added to the k/e ratio. Without this addition, two hitters could have an equal k/e ratio achieved on twice as many swings and considered equally efficient. Assume two hitters each have 37 kills and eight errors (one achieved this on 50 swings, the other on 100 swings). The k/e by itself would be 4.625 for each hitter. But when hitting percentage is added (factoring efficiency), the k/e+hp for 50 swings is 5.205 and for 100 swings is 4.915. These numbers are very similar because each equally contributed to the scoring ratio; however since efficiency is important the hitter that accomplished this on fewer swings should be rewarded for it."

[mikegarrison]

Sept 16, 2014 13:28:11 GMT -5 Wolfgang said:

A stat that shows 50/100 (50%) is more accurate than a stat that shows 1/2 (50%). The more data, the more accuracy.

That's a completely different issue.

(And it's not correct, either. It's only correct if the extra data is part of the same sample. For instance, if you measure the temperature of a pot of water 10 times v. one time, you should get a better understanding of what the temperature of the water is. But if you put that same pot of water on a burner and then measure the temperature 10 times, the simple average of the measurements is not better than each individual measurement, because the water has heated up between each of the measurements. Instead, you need to measure both temperature and time and do a regression.)

[johnbar]

Sept 16, 2014 13:43:35 GMT -5 @wingoz34 said:

Since dividing by zero equals zero...

That is not correct. Dividing anything (including zero) by zero is mathematically undefined; it is not zero. Loosely speaking, people sometimes say it is "infinity", but that is not correct either. What a mathematician would say, for example, is that  the limit of 1/x as x approaches zero is unbounded.

[Deleted]

Y'all is smart

[dkh]

The big picture. Stats never seem to be accurate to begin with. Solve that problem and you're a genius. This may be a blanket statement, but it has been my experience that the stats at the end of a game don't match up to what actually took place.