### Post by probaddie on May 22, 2012 18:57:09 GMT -5

So it seems that there's been some latent interest for some time in having an objective way to compare the recoil statistics for CoD's weapons. I remember it starting when the original stats chart came out for MW3, in which the author included his own -- and with all respect, very unscientific -- gun ranking charts, and very recently someone attempted to pound out a "balance formula" for the weapons; ultimately, the inability to compare recoil stats was the coup de grace for that idea.

In the hopes that this interest still lingers, I've developed a method for creating a statistic that does just what the title says: grades recoil plots. More than simple, unguided arithmetic, this method uses probability distributions representing the weapons' behavior to calculate the amount of "spread" and "deviation" from the original point of aim to form a statistic, which can be compared between guns to rank their efficacy.

The basic idea is that I create a pdf (probability density function) to represent the likelihood of the point of aim landing in a given spot (on each axis) after the first shot. I then use these functions to calculate the "origin-centered" variance on each axis, and use those in turn to create an overall statistic that represents the "spread" and "deviation" of the recoil plots we have. This statistic is not perfect; in fact, it is considered impossible to represent the variance of a bivariate distribution with a single number (see en.wikipedia.org/wiki/Covariance_matrix for more on that). But I was generally impressed with the results and I think most of them agree with my own intuition about where the guns should rank compared with each other.

~~Here is a link to my Mathematica code (8.0.1) which I wrote to develop the statistic.~~

Here are the latest results for MW3:

Unbiased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dEhubGRTUXpBNmtHVmFLSGVFdWdLd0E#gid=0

Biased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dDVNNTdDWUUxT0NzRUVrT3FCdXcxdnc&pli=1#gid=0

Here are results for BO using the same statistics:

Unbiased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dGNZNkNtWTdMWFJfRi1LVWdEXzZIcFE#gid=0

Biased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dHN2T01Pb25zdm5naEM3YWY2RTdUZFE#gid=0

Results for CoD4:

Unbiased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dE9QcEdBanZZUC1wSDJ5bnlIZzJaTEE#gid=0

Biased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dFdJdnFkV3pRN1hwMTJuaERCbnJvMXc#gid=0

And for MW2:

Unbiased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dHMzYi1KdVpNeWtTa3c2X19DSjIzUGc#gid=0

Biased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dElMNDltNVFHMWNBNm9jNV9KS0I3dnc#gid=0

And finally W@W:

Unbiased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dFRWdm85MWRvcGRnWWdwaUFpNUl0bVE#gid=0

Biased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dHpuczl3SV9PX0hLWmt4cmt4SFpLaWc#gid=0

~~And psijaka's recoil plots to compare with:~~

I look forward to your feedback and to answering any questions you may have.

Update: I've compiled a spreadsheet of inaccuracy scores for

Edit: Added link to psijaka's recoil plots.

Edit: Removed the Mathematica code, replacing it with a link to the Google Docs version of the same.

Edit: Removed first draft-specific questions.

Edit: Removed link to product metric (obsolete), replaced it with link to most recent draft.

Edit: Added link to Black Ops results.

Edit: Updated latest results to contain, well, the latest results.

Edit: Fixed broken link

Edit: Removed link to psijaka's recoil plots due to an inconsistency between his simulation method and my calculation methods which make the two works incomparable

Edit: Added links to CoD4 results

Edit: Added link to MW2 results

Edit: Added link to W@W results, as requested by Marvel4

Edit: Added recoil scores for Advanced Warfare

In the hopes that this interest still lingers, I've developed a method for creating a statistic that does just what the title says: grades recoil plots. More than simple, unguided arithmetic, this method uses probability distributions representing the weapons' behavior to calculate the amount of "spread" and "deviation" from the original point of aim to form a statistic, which can be compared between guns to rank their efficacy.

The basic idea is that I create a pdf (probability density function) to represent the likelihood of the point of aim landing in a given spot (on each axis) after the first shot. I then use these functions to calculate the "origin-centered" variance on each axis, and use those in turn to create an overall statistic that represents the "spread" and "deviation" of the recoil plots we have. This statistic is not perfect; in fact, it is considered impossible to represent the variance of a bivariate distribution with a single number (see en.wikipedia.org/wiki/Covariance_matrix for more on that). But I was generally impressed with the results and I think most of them agree with my own intuition about where the guns should rank compared with each other.

Here are the latest results for MW3:

Unbiased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dEhubGRTUXpBNmtHVmFLSGVFdWdLd0E#gid=0

Biased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dDVNNTdDWUUxT0NzRUVrT3FCdXcxdnc&pli=1#gid=0

Here are results for BO using the same statistics:

Unbiased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dGNZNkNtWTdMWFJfRi1LVWdEXzZIcFE#gid=0

Biased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dHN2T01Pb25zdm5naEM3YWY2RTdUZFE#gid=0

Results for CoD4:

Unbiased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dE9QcEdBanZZUC1wSDJ5bnlIZzJaTEE#gid=0

Biased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dFdJdnFkV3pRN1hwMTJuaERCbnJvMXc#gid=0

And for MW2:

Unbiased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dHMzYi1KdVpNeWtTa3c2X19DSjIzUGc#gid=0

Biased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dElMNDltNVFHMWNBNm9jNV9KS0I3dnc#gid=0

And finally W@W:

Unbiased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dFRWdm85MWRvcGRnWWdwaUFpNUl0bVE#gid=0

Biased: docs.google.com/spreadsheet/ccc?key=0AnFeORnwotj_dHpuczl3SV9PX0hLWmt4cmt4SFpLaWc#gid=0

I look forward to your feedback and to answering any questions you may have.

*You are by bro, bro.*Update: I've compiled a spreadsheet of inaccuracy scores for

*Advanced Warfare*. Note that these are not at all comparable to the statistics I used in my older work. I guess this is the tenth draft...?Edit: Added link to psijaka's recoil plots.

Edit: Removed the Mathematica code, replacing it with a link to the Google Docs version of the same.

Edit: Removed first draft-specific questions.

Edit: Removed link to product metric (obsolete), replaced it with link to most recent draft.

Edit: Added link to Black Ops results.

Edit: Updated latest results to contain, well, the latest results.

Edit: Fixed broken link

Edit: Removed link to psijaka's recoil plots due to an inconsistency between his simulation method and my calculation methods which make the two works incomparable

Edit: Added links to CoD4 results

Edit: Added link to MW2 results

Edit: Added link to W@W results, as requested by Marvel4

Edit: Added recoil scores for Advanced Warfare