Was Binom Dist the correct choice

[statnerds]

a few years ago, i compiled 5 years worth of data on the performance of Home teams relative to the Referee Crew. i wanted to avoid blind betting a game if a ref had numbers different from his peers. so i used Binom Dist. to establish the norm, possible bias and definite bias stats.

was that the right choice?

how much influence do referees have on outcomes of NFL games?

[20Four7]

The refs have huge outcomes, especially on the big penalties, the pass interference, the defensive holding etc. All I know is if I bet the game and that black ref is doing the game I win..... I think I got it down which side he bets.

[Busterflywheel]

The refs have huge outcomes, especially on the big penalties, the pass interference, the defensive holding etc. All I know is if I bet the game and that black ref is doing the game I win..... I think I got it down which side he bets.

lol....this is no doubt true..

[Wrecktangle]

Binomial dist: could be.

What folks don't seem to understand is that the "established" statistical distributions are all approximations. Binomial (and it's pal the Gaussian or "bell shaped curve") cover a lot of things, especially the Gaussian as this most easily fits a lot of things because (from the central limit theorem) the more distributions that are piled together, the more the aggregate tends towards being bell shaped. But in sports you have all sorts of quirky distributions that can happen that may or may not fit established stat dists.

Points in football is a good example of one that does not fall into any "known" category. If anything, it is up to 4 Poisson distributions dropped on top of each other: TS, FGs, extra points, and safeties, all with differing occurrences.

So what does this mean to you? Well, for one, you can throw all those statistical tests out the window as they are mostly based on the Gaussian dist.

Ain't nothing in this biz easy.

[Busterflywheel]

Binomial dist: could be.

What folks don't seem to understand is that the "established" statistical distributions are all approximations. Binomial (and it's pal the Gaussian or "bell shaped curve") cover a lot of things, especially the Gaussian as this most easily fits a lot of things because (from the central limit theorem) the more distributions that are piled together, the more the aggregate tends towards being bell shaped. But in sports you have all sorts of quirky distributions that can happen that may or may not fit established stat dists.

Points in football is a good example of one that does not fall into any "known" category. If anything, it is up to 4 Poisson distributions dropped on top of each other: TS, FGs, extra points, and safeties, all with differing occurrences.

So what does this mean to you? Well, for one, you can throw all those statistical tests out the window as they are mostly based on the Gaussian dist.

Ain't nothing in this biz easy.

You make a valid point

[statnerds]

So what does this mean to you? Well, for one, you can throw all those statistical tests out the window as they are mostly based on the Gaussian dist.

Ain't nothing in this biz easy.

thank you sir. and was most definitely not easy. it is almost as if the NFL doesn't want you to know refs exist. finding the stats on each one took hours, for each individual ref.

i was using it because the time period i researched had the home teams covering 49.8% or some number damn close to 50%. therefore i knew the system that the refs operate in, comprised of the compiled records of each ref. so i should assume that, given enough games, the number of home covers for each ref would trend toward being 50%. same thing with totals. games went Over the total slightly more than 50% of the time.

so then i needed to assign values to each ref to determine what constituted a potential or definite bias. i didn't even explore possible reasons for the bias, merely if one could possibly exist. again, given a large enough sample size for each ref i would expect the numbers to be near 50%. i used binomial dist so that i could use the total number of independent events (all records), the sample size (each ref), the number of successes (ATS win or Over). i wanted to assign a probability to each record for each ref.

so i ran all the numbers and most refs did not display abnormal results. Hoculi was actually the best as his numbers most closely mirrored the expected results.

in the end, i was unsure how to proceed anyway. i had no way to determine if a bias existed, was it intentional or merely random. if i thought it was intentional, i would continue to bet for similar results. if i felt it was random, i would expect results to slowly work their way back to the norm.

and i've never seen a study that attempted to assign value to the impact ref have on the outcome of a game. that is why i asked the second question in this thread. i wonder if oddsmakers factor in the ref at all when considering the spread or total.

sorry for that meandering, barely coherent reply. but if you could make any sense of it, would you suggest an alternative to binomial?

[Wrecktangle]

unfortunately, it could be like the NFL points dist. Nothing may fit.

But if you can dig it out, and post it here at SBR you could make a name for yourself. Get the Nobel-nerd peace prize for sports statistics or a Golden Geek award.

[statnerds]

But if you can dig it out, and post it here at SBR you could make a name for yourself. Get the Nobel-nerd peace prize for sports statistics or a Golden Geek award.

that is my top ambition in life, glory and recognition at SBR. joke.

the data is already a couple of years old and i am not going to do the last two years, way too much work. i was only looking to use it as possibly one part of handicapping a game. wouldn't blindly bet on a Total based solely on a ref's numbers, but if i liked the Over i would want and need to know if that ref showed a bias toward Over or Under while determining possible +EV on a game.

also, i couldn't find the ref crew listed for a game before it started. nearly impossible. i just found it strange that with so much attention paid to Umpires and NBA refs, why we act like NFL ref's have zero affect on the games they officiate.

thanks for your insight.

[donjuan]

i was using it because the time period i researched had the home teams covering 49.8% or some number damn close to 50%. therefore i knew the system that the refs operate in, comprised of the compiled records of each ref. so i should assume that, given enough games, the number of home covers for each ref would trend toward being 50%. same thing with totals. games went Over the total slightly more than 50% of the time.

so then i needed to assign values to each ref to determine what constituted a potential or definite bias. i didn't even explore possible reasons for the bias, merely if one could possibly exist. again, given a large enough sample size for each ref i would expect the numbers to be near 50%. i used binomial dist so that i could use the total number of independent events (all records), the sample size (each ref), the number of successes (ATS win or Over). i wanted to assign a probability to each record for each ref.

so i ran all the numbers and most refs did not display abnormal results. Hoculi was actually the best as his numbers most closely mirrored the expected results.

You're missing that the bias of each ref could already be factored in by the market. It's entirely possible that Hochuli is the most biased of all but that the market simply recognized this and adjusted.

[Wrecktangle]

I don't know where you'd find ref assignments prior to and NFL game, NBA is pretty easy to find; covers has a nice tab for it, for example.

[statnerds]

sometimes local newspapers would mention it when breaking down the match-up. but they way the NFL downplays the importance of referees is strange. statfox has a frikkin umpire report listing all of their stats. there are only 16 regular crews in the NFL with 1 or 2 other crews for sub spots or something. the crews tend to stay together from season to the next unless someone gets their own crew or retires. it would be easy to track, but no one, and i mean no one does it.

it is like everyone involved acts as if the refs have no effect on the game, when we know they do, but we don't have a proper value or even a system to gauge it. but to deny any factor is foolish. we've seen the extremes like the Hoculi non-fumble game in Denver a few years back and then the Brady tuck rule when the refs literally invented a new rule in the middle of a playoff game.

i think tracking totals could be profitable. i'm sure the players know which refs call games closer than others, as far as defensive backs getting away with more holding or grabbing. but it is all moot as the NFL pretends refs don't exist.

thanks for helping me talk through that one. there is something there, but it is near impossible to employ...

[username474]

I don't know where you'd find ref assignments prior to and NFL game, NBA is pretty easy to find; covers has a nice tab for it, for example.

I will send 1000$ to anyone that can find a source for the ref assignments prior to game time. Nba is the only league that posts before game time. MLB at least has a rotation after the first game of a series. Ref/umpire data vs. team/ hitter/pitcher has always played a big role in are models. Alot of Nba totals seem to move a few minutes after ref assignments a released.

[statnerds]

I will send 1000$ to anyone that can find a source for the ref assignments prior to game time.

i find it strange that no one really cares about which crew is working an NFL game or why the NFL downplays it to the extent they do. it is almost as if the NFL is saying the referee doesn't matter, which would be hugely inaccurate. then any ref could work the playoffs and superbowl, but we know that is not the case.

they are humans. they will make mistakes. some will show a bias, intentional or otherwise, toward overs or unders or heavy favorites not covering. it makes no sense to operate with the assumption that the ref will have zero impact on a contest.

i had a live one to track too in Bill Vinovich, but the bastard retired. i know the sample size was small, but they only work about 14 games or so a season. but that fukking guy was 15-28-3 O/U and then quit working.