Do Non Baysians Disagree With This?

David Sklansky · #1 07-13-2007, 03:27 AM

There are 100 examples of a particular type of professional baseball matchup. Interleague night games with two righthanded pitchers. Whatever. Your only information is the results of those games and a mild familiarity with the rules of the game.

The National League Team won 53 of those games. But mostly by one run. The total score of the 100 games had the American League team ahead by 63 runs. Would non Baysians disagree with me that when the next game occurred the American League team should be the choice to bet on at even money?

Siegmund · #2 07-13-2007, 04:23 AM

I am not so sure that the Bayesians would agree with you either. The structure of the game is such that a disproportionate number of games end with a margin of one run. It's not at all obvious (to a non-baseball-playing statistician) what relative importance to assign to the two quoted numbers.

A more positive way of putting it is that Bayesians and non-Bayesians alike would likely regard this as not significantly different from an even-money bet.

Alex-db · #3 07-13-2007, 06:19 AM

Being British, I only have a "mild familiarity with the rules" and this certainly wouldn't be clear to me.

But in games in general, if a player or team can play with an erratic style, such that they consistenly lose slightly more often, but win by a bigger margin when they do win, they would not be a good even money bet.

T50_Omaha8 · #4 07-13-2007, 08:03 AM

Expected wins and losses, which is a function of runs scored and runs allowed in previous games, is usually a better indicator of a team's future performance than their winning percentage.

I believe this correlation is strong enough that any educated person would back the AL.

djames · #5 07-13-2007, 10:01 AM

What if in the first game the AL wins 70-0? Then the other 99 the NL wins 53 of them by exactly 1 run and loses 46 of them by exactly 1 run. Even a Bayesian would have trouble selecting adequate distributions without excluding the single outlier. In practice, they would likely exclude it and conclude NL is the better choice in an even money bet if they were forced into a selection. If they weren't forced to bet, they may use the knowledge of the possibility of an outlier to state there isn't enough confidence to take an even money bet in this league.

luckyme · #6 07-13-2007, 10:41 AM

I'd have to know more about baseball to weigh it but the winning by 63 vs a team that actually beats you the majority of the time indicates those huge wins are the result of the losing team doing something weird. If there is no glory in 2nd ( no cost to losing by 63 rather than 1) then in other fields it could be that the National team when in a losing situation experiments with some plays equivalent to pulling the goalie in hockey or taking a big non-percentage play in tournament bridge looking for a swing.

If the American league won their games by a more realistic amount, say 6 pts, that would have more validity because it would be a better indicater they won those by that amount 'on their own'. Iow, the 63 pt is fishy.

Not sure if it applies to baseball, but a majority of small, tight wins and a minority of huge loses would often be the result of either going down fighting or experimenting when in a sure loss situation, or extracting information from the other team and/or playing conditions or some external factors ( the equivalent of improving your handicap position, say).

The order of the wins and losses would matter. Perhaps the National team was giving up too easily earlier in the season and could have salvaged some of their loses if they didn't pull their goalie etc so readily and if the late season ratio is better they may have learned something in that area.

Summation, I dunno. with the facts I have I could swing either way with just a tad more info/understanding.

luckyme

felson · #7 07-13-2007, 12:51 PM

It depends on whether the Poisson distribution is a good model for runs scored.

knowledgeORbust · #8 07-13-2007, 01:38 PM

I'm with Siegmund. No one can know enough simply by looking at the statistics. Maybe the American League players are better technically. Maybe the National Team is good in the clutch. A larger sample size would be better, but for now it is "not significantly different from an even-money bet."

David Sklansky · #9 07-13-2007, 01:43 PM

Firstly the 63 runs were for the totality of the games. .63 runs a game. Secondly your only information is that which was given. So if there is a 70-0 game, you don't know about it. Thirdly, this is baseball, which means there is very little propensity for teams that are ahead to find it easier to run up the score.

In point of fact the statistics I described makes the AL an incredibly clear favorite. In other words if you knew the AL outscored the NL by 63 runs over 100 games that piece of evidence is much stronger than the evidence of 53 vs 47 wins. I'm not here to argue that slam dunk fact. I just wanted to know whether non Baysians are required to dispute that if they want to remain true to their philosophy.

djames · #10 07-13-2007, 02:09 PM

[ QUOTE ]
In point of fact the statistics I described makes the AL an incredibly clear favorite. In other words if you knew the AL outscored the NL by 63 runs over 100 games that piece of evidence is much stronger than the evidence of 53 vs 47 wins. I'm not here to argue that slam dunk fact. I just wanted to know whether non Baysians are required to dispute that if they want to remain true to their philosophy.

[/ QUOTE ]

Oh, ok. No, they are not required to do so. A frequentist with slightly more baseball knowledge than "mild familiarity" with baseball can come to the same slam-dunk (I agree) conclusion that the better bet is the AL. They can do so by empirically using the average number of runs scored per game for NL & AL. While these two values are not known based on the given information, their difference is known (and is quite large at 0.63). So frequentists armed with enough knowledge to model baseball don't need to pick NL just because of the 53/47 result.

But, this is so obvious that it can't be what you're after. So, what are you after from frequentists (or other non-Bayesians)?

PS. It's tough to know how much knowledge you will allow a non Bayesian with "mild familiarity." I assume you are talking about someone knowledgeable enough to actually know they are a non Bayesian, but that may have never seen a box-score. Such a person will surely reach the conclusion that AL is best if you allow them time to learn baseball, but if they have literally no knowledge of baseball they may not infer the clear strength of the AL from the data you've given. Unfortunately "mild familiarity" may be crucial here.