How to represent the value of player production

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TooLiveBrew	How to represent the value of player production		Lead	[-]
Posts: 11307 October 18, 2009 4:50 PM BF.net Jedi	Tags : None I apologize for the relatively vague thread title. I think my question is fairly simple, but I don't trust my own mathematical 'abilities'. Is the best way to think of the value of player production an exponential curve, or is it more linear? I ask, because obviously an OPS of, say, .750, is far more common than an OPS of 1.000. I hope this makes enough sense for others to understand what I'm asking. I swear it's a valid question inside my head. That takes sum' GUTS. Jon Gruden's telling you.
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Baldkin		#1	[url]	[-]
Posts: 1262 October 19, 2009 5:21 PM	It depends what exactly you're trying to represent... Showing all the data for the entire league, you'd end up with some sort of a bell curve... the terrible and the great being few, and the masses being between .700 and .850 OPS. As for player value, using something like WAR, it would actually be linear. Every WAR is worth approximately the same so a 6 WAR player is worth 6x as much as a 1 WAR player. "And here comes Johnny Walker... I mean Johnny Estrada to the plate." -Bob Uecker 7/23/07
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sbrylski06		#2	[url]	[-]
Posts: 6550 October 19, 2009 6:52 PM	Here's one study that kind of gets at the question: http://baseballanalysts.com/archives/2009/05/findings_from_t.php I only read the first half, and not the part about pitchers velocity, but it seems to conclude that in terms of how much they are paid, player value is linear. Of course, that might just be because it is an inefficient market, and there's an advantage to be gained here through proper analysis. (And here's a quote from Bill James used in the linked article that might state what you did in the first post a little better: "Talent in baseball is not normally distributed. It is a pyramid. For every player who is 10 percent above the average player, there are probably twenty players who are 10 percent below average.") "This song is Copyrighted in U.S., under Seal of Copyright # 154085, for a period of 28 years, and anybody caught singin it without our permission, will be mighty good friends of ourn, cause we don't give a dern. Publish it. Write it. Sing it. Swing to it. Yodel it. We wrote it, that's all we wanted to do."
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rluzinski		#3	[url]	[-]
Posts: 16809 October 21, 2009 9:33 PM	According to Tom Tango (tangotiger.net), teams pay linearly for wins above replacement. A guy who's 4 wins over a AAAA player is twice as valuable as a 2 win player. While the 4 win player is much more rare, it doesn't appear to translate into exponentially more value. I think there's just enough slots to fill that a 0 - 2 WAR upgrade is always available. If a team had only 3 slots to fill, I think the 4 win player would be worth non-linearly more. Another Baseball Blog
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sbrylski06		#4	[url]	[-]
Posts: 6556 October 22, 2009 1:57 AM	I think there's just enough slots to fill that a 0 - 2 WAR upgrade is always available. If a team had only 3 slots to fill, I think the 4 win player would be worth non-linearly more. Can you clarify or reword this? I have read that value is paid linearly. I don't know the why, because intuitively I'm with TLB. You appear to be stating the why here, but I don't follow. (Maybe because its 3 AM.) "This song is Copyrighted in U.S., under Seal of Copyright # 154085, for a period of 28 years, and anybody caught singin it without our permission, will be mighty good friends of ourn, cause we don't give a dern. Publish it. Write it. Sing it. Swing to it. Yodel it. We wrote it, that's all we wanted to do."
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rluzinski		#5	[url]	[-]
Posts: 16810 October 22, 2009 11:31 AM	A 4 WAR player is more rare but you can just use two 2 WAR players to get the same value. It's rare to find a team that already has all 2 WAR players. If a starting lineup was just 2 batters and 1 pitcher, I'm speculating that a 4 WAR player would be exponentially more valuable than a 2 WAR player. Now, it still gives you a little more flexability to have one 4 WAR player over two, 2 WAR players, so it's reasonable to conclude the 4 WAR player is worth more than twice a 2 WAR. Tango has concluded that teams don't pay more than twice. Perhaps injury related risks of having so much value tied to one player compensates for the small flexibility advantage? Not sure if I explained that any better the second time. Another Baseball Blog
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sbrylski06		#6	[url]	[-]
Posts: 6557 October 22, 2009 1:05 PM	No, that makes more sense. Thanks. "This song is Copyrighted in U.S., under Seal of Copyright # 154085, for a period of 28 years, and anybody caught singin it without our permission, will be mighty good friends of ourn, cause we don't give a dern. Publish it. Write it. Sing it. Swing to it. Yodel it. We wrote it, that's all we wanted to do."
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TooLiveBrew		#7	[url]	[-]
Posts: 11345 October 22, 2009 4:18 PM BF.net Jedi	Thanks baldkin, sbrylski, & rluz. I knew this was the right place to ask this question. I guess what I really was trying to ask was answered by baldkin (the bell curve), but he also raised an interesting angle that I hadn't really considered (player compensation). A short thread, but a great one. Thanks again. That takes sum' GUTS. Jon Gruden's telling you.
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rluzinski		#8	[url]	[-]
Posts: 16811 October 23, 2009 9:30 AM	This might be obvious but I'll point it out, regardless. The MLB distribution of something like OBP, might look roughly like a bell curve but it's more complicated than that. In terms of skill, the pool of players MLB draws from is from one extreme tail of the bell curve. Even bad major leaguers are 3+ standard deviations away from the average skill level of the population of adults playing organized baseball. So it's really more like a pyramid. It's just that the AAAA type major leaguers don't get as many PA's, which somehwat cuts down the fat end of the pyramid. I'm not sure what the resulting distribution looks like exactly. Can we use BR.com to estimate the # of PA in 2009 that was between a certain OBP? Another Baseball Blog
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rluzinski		#9	[url]	[-]
Posts: 16811 October 23, 2009 9:30 AM	This might be obvious but I'll point it out, regardless. The MLB distribution of something like OBP, might look roughly like a bell curve but it's more complicated than that. In terms of skill, the pool of players MLB draws from is from one extreme tail of the bell curve. Even bad major leaguers are 3+ standard deviations away from the average skill level of the population of adults playing organized baseball. So it's really more like a pyramid. It's just that the AAAA type major leaguers don't get as many PA's, which somehwat cuts down the fat end of the pyramid. I'm not sure what the resulting distribution looks like exactly. Can we use BR.com to estimate the # of PA in 2009 that was between a certain OBP? Another Baseball Blog
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rluzinski		#10	[url]	[-]
Posts: 16813 October 23, 2009 11:25 AM	Just did the 2009 AL, non-pitchers. Used 1.8OBP+SLG. Looks like a bell curve but it's not! I'd like to see what the distribution looks like for actual skill (not just sample stats). Another Baseball Blog
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endaround		#11	[url]	[-]
Posts: 14353 October 25, 2009 5:45 PM	Why wouldn't it be? Just because you draw from a given population doesn't mean the conditional distribution wouldn't be approximately normal. And that's what you are looking at.
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Baldkin		#12	[url]	[-]
Posts: 1273 October 26, 2009 8:05 AM	We're drawing from the set of MLB players for the data represented....not the set of every person on the planet. Those two data sets should look different. "And here comes Johnny Walker... I mean Johnny Estrada to the plate." -Bob Uecker 7/23/07
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rluzinski		#13	[url]	[-]
Posts: 16822 October 28, 2009 10:14 PM	We start with a tail of a normal distribution (the most skilled players in the world). The players that are better get more PA, but injuries are proportional to playing time. The end result is something that approximates a normal distribution. Just thought that was odd/interesting. Another Baseball Blog
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endaround		#14	[url]	[-]
Posts: 14369 October 29, 2009 6:49 AM	But you have enough observations that you're in CLT territory.
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rluzinski		#15	[url]	[-]
Posts: 16825 October 29, 2009 10:10 PM	Please elaborate. Another Baseball Blog
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endaround		#16	[url]	[-]
Posts: 14375 October 30, 2009 9:28 AM	Central limit theorem. Since you're basically dealing with a type of binomial distribution (or a series or bernoulli experiments) it will end up asymptotically normal.
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rluzinski		#17	[url]	[-]
Posts: 16831 November 4, 2009 12:23 PM	I guess that I will need a more in-depth explanation to wrap my brain around this one. I don't understand how this ends up as a kind of bernouli experiement. I see it as more of an illustration of selective sampling. That said, all I know about probability theory is what I learned from basic stat courses in college and Google. An endaround 1 sentance explanation isn't going to be enough, sadly Another Baseball Blog
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