S.O., plz don't FAIL me now...

[Okla-homey]

I need a smart at math or baseball stats people.

Here's the deal.

I need the mathematical proof that the difference between a given player's batting around .250 versus better than .300 over a 25 week MLB season is one extra hit per week by that player.

I'm pretty sure this is true, but I cannot begin to lay out the mathematical proof to survive challenge.

I would really appreciate it if one of you math/baseball smart people would be kind enough to express this for me in such a way I can make an exhibit and make a finder of fact understand.

TIA

[StoopTroup]

x=?

[Vaevictis]

No such proof exists. Averages have too many paths to arrive at a certain number; results will vary immensely with number of at bats.

Counter-examples:

Jose Reyes, 681 AB in 2007. Assume he's hitting .250; that's 170 hits. Add 1 hit per week (26), and you've got 196/681=.287.

Take a hypothetical individual who's at bat 4 times in week one; he gets one hit. For the rest of the season, he's at bat exactly once and gets a hit every time. Now his average is close to 1.

You see what I mean.

[yermom]

so you are basically alleging everyone has ~500 at bats? and ~20 per week?

.300-.250 = .05 = 1/20

+25 hits /500 at bats = an extra .05

that sounds a bit off to me, but i'm not sure

[Vaevictis]

You could perhaps show that if the average .250 player were to get an additional 26 hits in a season, he'd be on average around .300.

That's a much weaker level of evidence though, especially because you'd be throwing confidence intervals into the mix. It's certainly not a proof.

[tommieharris91]

Bleh, BA is such a bad statistic to measure offensive effectiveness now. There's now OBP, SLG, OPS, IsoP, IsoD, VORP, OPS+, I could go on and on...

[StoopTroup]

Then there's the choke factor.

Depending on which team you play for...your either going to choke in the clutch or your not.

[jthomasou78]

The average MLB player plays 6 games a week and 4 at bats per game.

So thats 24 AB's a week.

24 X .300 = 7.2 hits a week

24 x .250 = 6.0 hits a week

[Getem]

At 500 AB it's exactly true - any more than that and the avg is less.

500 AB at .250 = 125 hits = 5.0 per week
500 AB at .300 = 150 hits = 6.0 per week

at 520 AB you get .298; at 480 you get .302

[stoopified]

500 at bats over a 25 week season,in order to hit .250 you need 125 hits.In order to bat .300 you need 150 hits.150-125=25 hits spread out over 25 weeks or 1 hit per week.Did NOBODY pay attention during BULL DURHAM?Crash(Kevin Costner) explained this very thing.

[Getem]

The math formula is AVG = .250 + (25 / AB)

I still got it

[Okla-homey]

At 500 AB it's exactly true - any more than that and the avg is less.

500 AB at .250 = 125 hits = 5.0 per week
500 AB at .300 = 150 hits = 6.0 per week

at 520 AB you get .298; at 480 you get .302

That'll work. Thanks to you all. You guys are the shizzle forizzle.

In case you're wondering, I'm taking this Arbitration class.

My final project this week involves a mock MLB salary arbitration. The course is taught by a federal judge.

I represent the player, a catcher who has more than 3 but less than 6 years in the majors and thus is not yet a free agent. His only option for a better salary is through arbitration pursuant to the MLBPA contract.

Here's where this all comes in. When healthy, he hit .303 with 30 HR while throwing out 37% of basestealers. Thus, a very good catcher. In fact, only one other catcher evar hit over .300 and hit 30 homers in a season.

In one of the last games of his second season in the majors, he hurt his neck (herniated disc at C5/C6) when he hit the backstop hard while reeling in a foul tip and making the play. The following season he batted .247 and hit no dingers.

He had surgery at the end of that year and now is 100%. It's now February and salary arbitration season. The team has offered even less than they paid him last year based (I'll argue unfairly) on the fact he sucked last year.

I'm gonna argue those first two seasons were not a fluke and the crappy third season was the result of the painful and debilitating neck injury. I intend to posit that the average of one extra hit per week he needed to bat .300 was denied him because his danged neck was killing him. Ditto the homers because, surprise!, your neck is used in hitting a baseball. The fact he's off the D/L and rarin' to go makes him worth the money I'm asking for on his behalf.

[royalfan5]

A good representative would have got his arbitration years bought out after the 30 dinger year, and not have to go through this.

[reevie]

Did the injury occur at his home field, or on the road? If it was an injury at home, I'd consider arguing that the team did not provide sufficient padding/protection on the backstop. Had the organization provided a safer "worksite" his production would not have suffered. Also make sure you have the team's training staff on record that he is back to 100%.

[tommieharris91]

That'll work. Thanks to you all. You guys are the shizzle forizzle.

In case you're wondering, I'm taking this Arbitration class.

My final project this week involves a mock MLB salary arbitration. The course is taught by a federal judge.

I represent the player, a catcher who has more than 3 but less than 6 years in the majors and thus is not yet a free agent. His only option for a better salary is through arbitration pursuant to the MLBPA contract.

Here's where this all comes in. When healthy, he hit .303 with 30 HR while throwing out 37% of basestealers. Thus, a very good catcher. In fact, only one other catcher evar hit over .300 and hit 30 homers in a season.

In one of the last games of his second season in the majors, he hurt his neck (herniated disc at C5/C6) when he hit the backstop hard while reeling in a foul tip and making the play. The following season he batted .247 and hit no dingers.

He had surgery at the end of that year and now is 100%. It's now February and salary arbitration season. The team has offered even less than they paid him last year based (I'll argue unfairly) on the fact he sucked last year.

I'm gonna argue those first two seasons were not a fluke and the crappy third season was the result of the painful and debilitating neck injury. I intend to posit that the average of one extra hit per week he needed to bat .300 was denied him because his danged neck was killing him. Ditto the homers because, surprise!, your neck is used in hitting a baseball. The fact he's off the D/L and rarin' to go makes him worth the money I'm asking for on his behalf.

I'll put it this way as a fan: if this is how Geovany Soto's career ends up and he wins more than $10.0M in arbitration for that one season, I'd be pretty unhappy. But, I'm also not a neck specialist, and I have no idea how long the effects of a herniated disk linger. I'm also getting an unrepresentative view of how good this player is without a few other numbers, specifically OPS and SLG (I would expect an OPS between .850-.950). I also don't know how old he is.

Also, what RF5 said. His agent shoulda got him an extension.

[Frozen Sooner]

Pft. Counselor, I submit that both your client's slow recovery AND dropoff in production are due to his discontinuation of steroid use.

[Gandalf_The_Grey]

How DARE YOU!!!!


it was HGH!!

[Scott D]

That'll work. Thanks to you all. You guys are the shizzle forizzle.

In case you're wondering, I'm taking this Arbitration class.

My final project this week involves a mock MLB salary arbitration. The course is taught by a federal judge.

I represent the player, a catcher who has more than 3 but less than 6 years in the majors and thus is not yet a free agent. His only option for a better salary is through arbitration pursuant to the MLBPA contract.

Here's where this all comes in. When healthy, he hit .303 with 30 HR while throwing out 37% of basestealers. Thus, a very good catcher. In fact, only one other catcher evar hit over .300 and hit 30 homers in a season.

In one of the last games of his second season in the majors, he hurt his neck (herniated disc at C5/C6) when he hit the backstop hard while reeling in a foul tip and making the play. The following season he batted .247 and hit no dingers.

He had surgery at the end of that year and now is 100%. It's now February and salary arbitration season. The team has offered even less than they paid him last year based (I'll argue unfairly) on the fact he sucked last year.

I'm gonna argue those first two seasons were not a fluke and the crappy third season was the result of the painful and debilitating neck injury. I intend to posit that the average of one extra hit per week he needed to bat .300 was denied him because his danged neck was killing him. Ditto the homers because, surprise!, your neck is used in hitting a baseball. The fact he's off the D/L and rarin' to go makes him worth the money I'm asking for on his behalf.

I think the team has a stronger argument that the first two seasons may have in fact been a fluke, and that on average the career expectancy of a catcher is lower than that of any position outside of hard throwing pitchers (tend to show signs of elbow/shoulder problems within 5 years, unless they are nolan ryan).

Also, the timing of the injury will work against you, because provided this team was one of a majority of teams that didn't make the playoffs he had plenty of time to get surgery or rehab before the following season.

I say 80% you lose your case using 'potential' statistics. :)

[Okla-homey]

I'll put it this way as a fan: if this is how Geovany Soto's career ends up and he wins more than $10.0M in arbitration for that one season, I'd be pretty unhappy. But, I'm also not a neck specialist, and I have no idea how long the effects of a herniated disk linger. I'm also getting an unrepresentative view of how good this player is without a few other numbers, specifically OPS and SLG (I would expect an OPS between .850-.950). I also don't know how old he is.

Also, what RF5 said. His agent shoulda got him an extension.

He's 26. Black. Very popular with fans. Herniated discs do not heal on their own. They must be surgically corrected. (although a chiropractor might say otherwise, I really don't know). Surgery performed by a neurosurgeon who swears this guy is a-ok.

And the reason he doesn't have a contract for all his pre-free agency years is he was traded at the end of his second season. That team traded him following the on-field injury (although they didn't know at the time he was hurt as bad as he was) for some a-hole they thought was going to be a pitching stud.

[Gandalf_The_Grey]

I am assuming this isn't a real life scenario becauses catchers are so typically hard to have that most teams will gladly pay a little extra to have just a backup plan

[Okla-homey]

I am assuming this isn't a real life scenario becauses catchers are so typically hard to have that most teams will gladly pay a little extra to have just a backup plan

You are correct. Its a hypothetical scenario. However, our given facts involve the fact his team already has two other catchers on its roster.

I'm also charged with getting a him a "no-cut" and "no release" contract if possible.

They funny part is the three person arbitral panel I have to pitch this to this week is made up of 1) a British law student who doesn't know jack about baseball, 2) an African law student who doesn't know jack about baseball, and 3) an American guy who is not a baseball fan.:O

I'm putting on two witnesses. My player and his surgeon.

The team is putting on the owner and the manager.

[Gandalf_The_Grey]

I would also attempt to locate salary information on other 26 year old catchers' salaries and cost and compare the stats. Establish a small market value

[Gandalf_The_Grey]

http://mlbcontracts.blogspot.com/2000/05/most-lucrative-contracts.html

An interesting side note is that a Benji Molina is getting paid around 6 million this year. If your player has anything close to those stats, you could argue he is way underpaid

Year Ag Tm Lg G AB R H 2B 3B HR RBI SB CS BB SO BA OBP SLG *OPS+ TB SH SF IBB HBP GDP
+--------------+---+----+----+----+---+--+---+----+---+--+---+---+-----+-----+-----+----+----+---+---+---+---+---+
1998 23 ANA (http://www.baseball-reference.com/teams/ANA/1998.shtml) AL (http://www.baseball-reference.com/leagues/AL_1998.shtml) 2 1 0 0 0 0 0 0 0 0 0 0 .000 .000 .000 -100 0 0 0 0 0 0
1999 24 ANA (http://www.baseball-reference.com/teams/ANA/1999.shtml) AL (http://www.baseball-reference.com/leagues/AL_1999.shtml) 31 101 8 26 5 0 1 10 0 1 6 6 .257 .312 .337 67 34 0 0 0 2 5
2000 25 ANA (http://www.baseball-reference.com/teams/ANA/2000.shtml) AL (http://www.baseball-reference.com/leagues/AL_2000.shtml) 130 473 59 133 20 2 14 71 1 0 23 33 .281 .318 .421 84 199 4 7 0 6 17 RoY-4 (http://www.baseball-reference.com/awards/awards_2000.shtml#ALroy)
2001 26 ANA (http://www.baseball-reference.com/teams/ANA/2001.shtml) AL (http://www.baseball-reference.com/leagues/AL_2001.shtml) 96 325 31 85 11 0 6 40 0 1 16 51 .262 .309 .351 73 114 2 4 3 8 8
2002 27 ANA (http://www.baseball-reference.com/teams/ANA/2002.shtml) AL (http://www.baseball-reference.com/leagues/AL_2002.shtml) 122 428 34 105 18 0 5 47 0 0 15 34 .245 .274 .322 58 138 6 6 3 4 15
2003 28 ANA (http://www.baseball-reference.com/teams/ANA/2003.shtml) AL (http://www.baseball-reference.com/leagues/AL_2003.shtml) 119 409 37 115 24 0 14 71 1 1 13 31 .281 .304 .443 96 181 2 4 2 2 17
2004 29 ANA (http://www.baseball-reference.com/teams/ANA/2004.shtml) AL (http://www.baseball-reference.com/leagues/AL_2004.shtml) 97 337 36 93 13 0 10 54 0 1 18 35 .276 .313 .404 88 136 2 4 1 2 18
2005 30 LAA (http://www.baseball-reference.com/teams/LAA/2005.shtml) AL (http://www.baseball-reference.com/leagues/AL_2005.shtml) 119 410 45 121 17 0 15 69 0 2 27 41 .295 .336 .446 108 183 5 6 2 1 14
2006 31 TOR (http://www.baseball-reference.com/teams/TOR/2006.shtml) AL (http://www.baseball-reference.com/leagues/AL_2006.shtml) 117 433 44 123 20 1 19 57 1 1 19 47 .284 .319 .467 100 202 0 2 1 4 15
2007 32 SFG (http://www.baseball-reference.com/teams/SFG/2007.shtml) NL (http://www.baseball-reference.com/leagues/NL_2007.shtml) 134 497 38 137 19 1 19 81 0 0 15 53 .276 .298 .433 86 215 1 2 2 2 13
2008 33 SFG (http://www.baseball-reference.com/teams/SFG/2008.shtml) NL (http://www.baseball-reference.com/leagues/NL_2008.shtml) 16 65 7 19 3 0 3 13 0 0 1 4 .292 .299 .477 102 31 0 1 0 0 0

[Ike]

So you have N years of 'good' stats vs. 1 year of 'bad' stats. The 1 year of bad stats, it was known that the player had an aggravating condition that required surgery in the off season. The player should be evaluated on the N years of good performance, and his salary should be based upon the standard aging curves for catchers with such stats. (Every MLB team has some sort of 'aging' curve for each position...IOW, how to project the effects of a player getting older).

On the other hand, there is no evidence that he is actually at 100%. IOW, no dingers have actually been hit by the guy since the injury.

[royalfan5]

It should be pointed out that MLB rules incorporate a maximum paycut in an arb year of 20%. So the player should make out okay if he has already went through arbitration once to establish a base. If that is the case, he's probably pretty lucky he didn't get non-tendered give his Jason Kendallization.

[tommieharris91]

So, if we say his PECOTA projections for the season after his arbitration case is heard comes out to be something like .275/.380/.430 and a 10% CS rate (overall a slightly below average catcher), and this guy wins the case to the tune of a $9M payout over that next season, knowledgable fans wouldn't be very happy. At $9M, a no-release clause, and those numbers, I think he would be somewhat overvalued and should deserve something more like $6.5M without the benefits.

There is a few other things that could affect the case positively i.e., good rep handling pitchers, lower number of passed ball/wild pitches after the injury, etc. Benji Molina is known for being above-average defensively with a pretty good arm from C, so he has that goin' for him.