THE BOOK--Playing The Percentages In Baseball

Excellent. I had the same basic idea (click my name), but I’m glad someone with much better technical ability thought of it.

Three thoughts that I also posted at BallHype:

1. Dave may already be planning this, but it should be combined with WPA, so that both in-game and season leverage/context are factored in.

2. This may make things a lot more complicated, but it would be nice to factor in whether the team’s opponent is also in the pennant race. A Phillies game against the Mets is more important than one against the Padres.

3. I’ll be curious to see the pure results, but he may also want to create a version that sets both a max and min LI for individual games. The pure method will probably crown John Danks AL MVP because he pitched a shutout in game 163 against the Twins and that game will probably count 100 times more than an average game. And I’m not sure if it’s fair to say that a player’s performance once his team his eliminated from the race can never be worth more than 0.

hmmm, that link didn’t work:

http://www.insidethebook.com/ee/index.php/site/comments/best_performances_of_2008_as_of_today/#12

Right, the “Pennant WPA” never makes sense to me.

At the start of the season, teams would start off at 8/30 (.25 in the NL, .29 in the AL) chance of making the playoffs (presuming they are all equals of course).

So, over the course of 162 games, some teams will go from .27ish to 1.00 (meaning gaining an average of .0045 per game), while others will go down to zero (meaning losing .0016 per game).

However, if you are down to game 163, each team sits at .50, meaning that one will gain .5000 in one game, while the other loses as much.  That makes this game some 200 times more important than an average game in the season.  That means that getting 4 PA in this game, has the same impact as 800 PA.  This game is worth as much as the rest of the season combined!

Indeed, if you look at the 9th inning of a close game #163, all of a sudden, that last PA will be worth 2000 times as much as an average PA in the season.

***

It’s stuff like this that should make you turn your back on WPA itself… and embrace WPA/paLI * boLI.

I don’t think everyone has to agree that Pennant WPA (PPA?) is the new standard for choosing the MVP, but for the group of people who want to give significantly more weight to September and/or teams who win their divisions, PPA will be a more accurate way of doing so.

I don’t think there’s one correct way to define “value,” it’s a philosophical debate. But, once a person defines value for himself, he should have the best tools available to measure value based on his definition. For people who choose to define the MVP as the player who did the most to get their team into the postseason, PPA will be a very useful tool.

There’s a reason why a run in the 9th inning is not worth the same as a run in the 1st inning: there are strategical implications, especially if you are considering the value of Mariano Rivera. 

There is NO reason why a win in April is not worth as much as a win in September. 

Delgado tanking Apr-Jun and being Pujols-like Jul-Sept, or vice-versa, has no difference whatsoever.

There’s a reason why a run in the 9th inning is not worth the same as a run in the 1st inning: there are strategical implications, especially if you are considering the value of Mariano Rivera.

But this isn’t about strategy.  It’s about the story.  As I’ve said before, I like WPA because it captures the emotion of the game, the story of the game.  It’s a quantification of what happened.  Fans and sportswriters pay lots more attention to what happened in September than in April, and so does this stat.

It sounds like you’ve backed away from WPA as a useful stat, and are just concentrating on LI and WPA/LI.  That’s cool, but don’t forget that WPA has its uses, and applying the general methodology to seasonal games seems pretty interesting to me.  It’s what sportswriters claim drives their MVP voting.

And I’m not suggesting we turn it into a full-time stat or something like that.

Right, WPA is a story stat, and you put it well once.  It captures our emotion and quantifies it.

And certainly, what you are doing in terms of expanding on WPA to make it pennant-driven is a great thing, as it provides more quantification for a story stat.  Indeed, by doing what you are doing, you will as a byproduct expose the ridiculousness of the Ryan Howard scenario.  BBWAA has no idea how much more the story is worth in September than April, and you are providing that quantification.  Obviously, April is not a “zero” story, and September is not a “1000” story.

My feelings on what WPA is and is not was elaborated here, and I haven’t changed my position:
http://www.insidethebook.com/ee/index.php/site/comments/wpa_is_wpa_is_not/

I posted about this here: http://www.insidethebook.com/ee/index.php/site/comments/mlb_playoff_race/#6

The average change (post 7 of the same thread) in 2007 was 4.46, so the Padres/Rockies playoff game would have a “pennant race” LI of 19.3. The highest LI in that game was 4.61 (Khalil Greene hitting into a DP in the top of the 11th with runners on 1st and 2nd and 1 out). So, Greene’s GIDP was 19.3 x 4.61 = 89x more meaningful than the average at-bat. I think that’s reasonable.

That post might not have been clear. If the winner of a game sees its playoff odds increase by 10% (from 40% to 50%) and the loser’s falls by 8% (from 60% to 52%), then the total change for the game was 10 + 8 = 18% (adding together the absolute value of the change in playoff odds for each team), and the “pennant race” LI would be 18/4.46 = 4.03.

Another neato way to play with the data is to plot the average change by calendar day (2007 season at: http://www.editgrid.com/user/dackle/dailyLI). Studes is modelling a steady increase in leverage toward September, but ... for a handful of teams September is very important, but for most teams it’s meaningless. The graph linked above shows a steady decline in intensity until late July, and then an increase into late August, and then into September it weakens (for the average team) as teams are eliminated from the race. Not clear though whether that pattern holds for all seasons, or if it was just a quirk of the schedule in 2007.

Dackle: that’s sweet.  Can you also plot the standard deviation, per day?

Studes is modelling a steady increase in leverage toward September, but ... for a handful of teams September is very important, but for most teams it’s meaningless.

Dackle, to clarify: this was the first of several articles on the subject.  I put the idea out there of using binomial distribution to calculate leverage instead of playoff probabilities.  As a next step, I’ll apply that method to individual teams.

Tango, I’d like to do an update for 2008, hopefully this weekend or within the next week. Will be interesting actually to compare the shape of the graph to what was observed for 2007. I’ll grab the standard deviation at that point.

Studes, sorry, I just referred to your model from a comparative perspective (not passing judgment on whether it is right or wrong). Looking forward to the upcoming articles (BTW, when’s the next edition of 10 Things I Learned...? Been a while—great column!)

No problems, dack.  I was just clarifying that I wasn’t modeling a general steady increase through September.  It will differ by team, of course.

I don’t think I have the energy anymore for Ten Things.  Those articles are a lot of work.  I intended to post them regularly this past season and couldn’t keep it up.

Dackle, that is a great idea.

I think the true “importance” of a game depends not only on how the playoff odds changed afterwards, but also on how the odds would have changed if the other team had won. In the COL/SD playoff game, the odds changed by 43% for both teams (because, I suppose, BP had the Rockies at 57% to win). If the Padres had won, the odds would have changed by 57% for both teams. The calculation should take both figures into account, so either

.5*(43+43) + .5*(57+57)

or

.57*(43+43) + .43*(57+57)

Of course this would be a lot harder to calculate in general, and what you did is almost always going to be close enough.

I don’t think playoff probability is the best metric to use (at least for my purposes).  Changes in playoff probability are “after the fact”, and may not reflect the underlying importance of the game itself.  For instance, if two teams that are tied for the lead late in the season both win, their playoff probability will change very little, although the games will have been very important.

That’s why I’m taking my approach.  It’s sort of like the difference between WPA and LI.  WPA is the outcome, but a big change in WPA may no be reflective of the underlying LI.

It would be better to know the potential swing in playoff odds before the game. Just to be devil’s advocate—if the Phillies and the Mets head into the last game of the season tied for first, and they’re both playing teams that are out of the race, then the playoff odds for both teams are 50%. If they both win the last game of the season, then their odds stay at 50% (because they head into a one-game playoff). But, if the Mets lose and the Phillies win then pennant on a Ryan Howard grand slam in the bottom of the 11th, then the Phils playoff odds go from 50% to 100%. But ... if you were just calculating the potential change in odds before the game, then Howard’s HR would be no more important than a HR in a game when both teams won. I think most people would want to credit Howard for the pennant winning HR.

Also, I think the calculation is more complicated than just hitting a particular wins target. For example, if two teams are tied for the wild card lead, their odds (excluding all other teams) are 50%, but if three teams are tied then their odds are 33%, even though the wins target is the same in both cases. Then it gets doubly complicated for the divisions where the first-place team has fewer wins (or the second-place team has more wins) than the wild card leader.

Ken Roberts has a nice approach to the problem (http://www.sportsclubstats.com/NHL.html). Here are his odds (scroll to the bottom of the link) for tonight’s Red Wings/Avs tilt:

    Red Wings    vs    Avalanche        7:00 PM
           Chance in playoffs if:    
        Red Wings win  Avalanche wins    
Avalanche    29.7          39.9    
Red Wings    96.7          94.0    
Oilers       47.1          46.3    
Canucks      67.6          66.9    
Wild         47.0          46.4    
Coyotes      39.3          38.7    
Flames       62.5          61.9    
Predators    50.8          50.0    
Ducks        67.4          66.8    
Kings        39.2          38.5    
Blue Jackets 28.5          28.0    
Blues        24.5          24.0    
Stars        19.7          19.2    
Blackhawks   80.4          80.0

The importance of the game is the sum of the potential swing on all other teams in the league (eg 39.9 - 29.7 = 10.2 for the Avs, plus 96.7 - 94.0 = 2.7 for the Wings, etc for all other teams).

As a follow-up to post #8, here are the 10 biggest regular-season games of 2008 as ranked by combined absolute change in BP’s playoff odds.

 Date  Vis Hom Score Av LI Vis chg Hom chg Total
Sep 30 MIN CHA  0-1   1.13   43.3    43.3   86.5
Sep 28 CHN MIL  1-3   1.35    0.0    54.7   54.7
Sep 28 FLO NYN  4-2   1.14    0.0    54.7   54.7
Sep 25 CHA MIN  6-7   1.31   24.5    24.5   49.0
Sep 14 MIL PHI  3-7   1.11   18.9    28.0   47.0
Sep 14 MIL PHI  1-6   0.40   18.9    28.0   47.0
Sep 26 FLO NYN  6-1   0.81    0.0    37.5   37.5
Sep 26 CHN MIL  1-5   1.02    0.0    33.5   33.5
Sep 27 CHN MIL  7-3   0.92    0.0    31.1   31.1
Sep 27 FLO NYN  0-2   0.94    0.0    30.4   30.4

Here’s a spreadsheet of all the games, along with a graph of the average change and standard deviation of changes per day. Comments in row 1 will explain the headings.

http://www.editgrid.com/user/dackle/2008biggames

Interestingly, there wasn’t an increase in tension in late August as there was in 2007.

It would be better to know the potential swing in playoff odds before the game.

Right, exactly.  That’s what my method does.  It looks at the potential impact of a win or a loss on the playoff probability, and the bigger the difference, the more important the game.

But, if the Mets lose and the Phillies win then pennant on a Ryan Howard grand slam in the bottom of the 11th, then the Phils playoff odds go from 50% to 100%. But ... if you were just calculating the potential change in odds before the game, then Howard’s HR would be no more important than a HR in a game when both teams won. I think most people would want to credit Howard for the pennant winning HR.

That’s true, and he will.  That game will have the highest Leverage index possible, the same as if it were a one-game playoff.  I take the conservative approach in late-season games like that and assume the other team wins its one game.  When you think about it, it makes a lot of sense from an impact perspective.  You can’t depend on the other team losing that one game.

Actually, in thinking this through (almost all I’ve been doing for a couple of weeks), I think I should change that.  I think the one-game playoff must have greater impact than the home run on the last game of the season.  True, Howard’s pennant-winning HR would be huge, but it would be the stuff of legend if it came in a one-game playoff.

The trick is to make my binomial distribution tables work for half games.  Time to rewrite my spreadsheet.  Oy.

I think the next step would be to work in the actual standings somehow. If the Mets and Phils are both 90-71 heading into the last day of season, and Ryan Howard hits a dramatic walk-off home run, then it’s a pennant-winning HR if the Mets and Phils are playing eachother. But if they’re playing separate games, then there’s a ~50% chance that the Mets also win and they face off in a one-game playoff. Or, let’s say it’s the day earlier and both teams are 90-70 and so is the wild card leader, who happens to be playing the Phils, and the second-place wild card team is 89-70 and has to potentially make up a rainout.

The tradeoff though is that you’d probably need to set up a sim, which is messier than your approach.