A statistical analysis of our playoff hopes

Diclaimer: This post is not only long, it is intentionally optimistic. I'm doing everything i can to the numbers to see how its possible for the Cubs to make the playoffs. That said, you should still feel free to fire away your critiques!

I decided to go into a statistical analysis of what the Cubs need to do in the 2nd half of the season to make the playoffs (or, more accurately, the remaining 75/162nds of the season). I made all these calculations based on data from ESPN's RPI rankings page, The Cubs' remaining schedule, and 2004 and 2005 win shares from The Harball Times.

Lets start by assuming the Cubs play just as they did in the first half of the year. On first approximation, that would mean a repeat of the first half record-wise. They have gone 43-44, a win rate of .494. If they continued to win games at this rate, they would win 37 more games for a final record of 80-82, a touch under .500 and well out of playoff contention.

However, win-loss records are a worse predictor of what a team will do the remainder of the season than their runs scored and runs against are. Based on the number of runs the Cubs have scored and have given up, they should win half of their remaining games (37.5 wins). Given that they've been a half game "unlucky" thus far, lets assume regression to the mean gives them the extra half win, giving them 38 "second-half" wins for a final record of 81-81, right at .500.

I wanted to go into a little more detail, since even the runs scored and runs against do not take into account that the Cubs have played through the toughest half of their schedule. Their strength of schedule (SOS, the cumulative win rate of all the teams played thus far, weighted by games played) is .504. The strength of the remainder of the schedule (the cumulative win rate of all teams left to play, weighted by games) is .493. We are left to figure out how many wins can the Cubs expect out of the easier schedule. Lets do this based on RPI. The Cubs current Relative Power Index (RPI) is .502. RPI is a weighted average of a team's win rate (25%), its opponents' win rate, i.e. a team's SOS (50%), and its opponents' opponents' win rate, i.e. a team's opponents' SOS (25%). If we assume that the Cubs' RPI will remain constant (the starting assumption), as will their opponents' SOS's (the lazy, i don't want to do any more work assumption), then we can calculate what the team's win rate the remainder of the season will be, based on the strength of their remaining schedule. You can even do this team-by-team, if you wish. The results are a prediction that the Cubs will go 4-10 against the Cardinals (blech!), and 36-24 against everyone else, piling up 40 more wins for a final record of 83-79, just above .500 and almost certainly out of the playoffs. If you repeat all of this using expected W-L records based on runs scored and allowed to calculate SOS, the results are similar: 39 more wins the rest of the season for a final record of 82-80.

Now, all this is based on what the Cubs did in the first half. I'm not going to make predictions of any changes in performance from individuals in the second half, but in the interests of looking for a best-case scenario, i will now see how much change we can expect from recent or near future additions to the roster. In other words, i will see what impacts a healthy roster and some major Jim Hendry acquisitions could have on the second "half" of the season...

First, lets assume we get a healthy second half from Kerry Wood, Mark Prior, Scott Williamson and Nomar Garciaparra, as well as a full second half from Jerome Williams. Next, lets assume that the players they are replacing are average bench players (on average, they basically are). Then, lets use win shares above bench (WSAB) to calculate the wins they will add to the club remainder of the season (an explanation of win shares is here). We'll do this based on this year's WSAB or on last year's WSAB, based on which is more appropriate (this is admittedly arbitrary, and i mostly use last year's for the sake of sample size and to avoid bad 1st half numbers that are the result of injury/soreness. If someone has career WSAB numbers, i'd be happy to recalculate things based on those). In order to account for having only 75 games left on the schedule, we'll prorate WSAB by number of starts/appearances. Then, we subtract the WSAB earned in the first half from what we can expect in the second half, and we'll get the expected improvement in the Cubs' record from adding these guys to the roster, in units of win shares. Got all that? If not, follow along with the following example for adding Kerry Wood to the roster:

In the first half, Kerry earned 0 WSAB, so any win shares he earns in the second half are gravy. Based on last year's win shares, Kerry Wood earned 2 WSAB. He did that in 22 starts, a rate of 0.09 WSABs/start. If he gets 15 starts the rest of the year (75 games/5 games per start=15 starts), then we can expect about (2/22)*(15)=1.36 WSAB from Kerry the rest of the way. Subtract the 0 WSAB Kerry earned in the 1st half, and our record should improve by 1.36 win shares in the second half. In order to convert win shares to wins, you divide by 3, so the Cubs can expect about .45 more wins the rest of the year due to having a healthy Wood.

The remainder of the additional win shares resulting from additions that have already happened or we can count on happening in the near future are as follows...

Prior: 1 extra win share (Note: Prior had enough starts for me to feel comfortable using this year's WSAB data, as he had 12 starts, just short of the 17 we'd expect).
Garciaparra: 3.36 extra win shares (this large number is partly due to Nomar's WSAB rate last year, and partly due to the -2 WSAB he "earned" in his early season slump. Also note i used 58 games for Nomar, assuming an August 1 return date).
J. Williams: 1.5 win shares (Note: I again used this year's win shares for Williams, as he seems to have fixed the weight issues he has had in the past so i felt this year's numbers would be best).
S. Williamson: 1.36 extra win shares (Note: i used 19 appearances the rest of the year, assuming an August 1 return date and an appearance every 3rd day).

The total for all these changes is an additional 8.58 win shares. Before you get too excited, remember you have to divide by 3 to convert win shares to wins. This means we can expect about another 2.86 (call it 3) wins for the Cubs in the second half. If you add this to the most optimistic projections above, that leaves us with a final record of 86-76. That's a solid season, but i'm not sure if it gets us a playoff spot.

I'm thinking we would need over 90 wins to get to the postseason. That means we would need to add another 5 wins, or 15 WSABs to our roster. Lets look at WSABs for players in the first half, and consider adding two OF bats and a reliever. Lets go all out and assume what is in my opinion the best case scenario - that we add a power OF bat, a leadoff OF bat, and a setup man. Specifically, if we add Adam Dunn, Matt Lawton, and Mike Gonzalez (i told you this was best-case), that would give us an additional 15 win shares, or 5 more wins. That would bring the season record to 91-71, probably good enough for a playoff spot.

It looks like we can make the plaoffs. However, in order to get there, the Cubs will have to stay healthy, and Hendry will have to make a couple major moves.

Of course, if we just do better than 4-10 against the Cardinals, then we woudn't need all the fancy win share math to show how we can make the playoffs. Reversing that and going 10-4 against them would leave us with 89 wins instead of 83, and at that point we'd be close to a playoff spot without any major moves.